01404nas a2200205 4500008004100000022001400041245010400055210006900159260001400228490000700242520076300249100002401012700002401036700001601060700001701076700002101093700002301114700002401137856003701161 2024 eng d a1089-762300aIon trap with in-vacuum high numerical aperture imaging for a dual-species modular quantum computer0 aIon trap with invacuum high numerical aperture imaging for a dua c3/26/20240 v953 a

Photonic interconnects between quantum systems will play a central role in both scalable quantum computing and quantum networking. Entanglement of remote qubits via photons has been demonstrated in many platforms; however, improving the rate of entanglement generation will be instrumental for integrating photonic links into modular quantum computers. We present an ion trap system that has the highest reported free-space photon collection efficiency for quantum networking. We use a pair of in-vacuum aspheric lenses, each with a numerical aperture of 0.8, to couple 10% of the 493 nm photons emitted from a 138Ba+ ion into single-mode fibers. We also demonstrate that proximal effects of the lenses on the ion position and motion can be mitigated.

1 aCarter, Allison, L.1 aO’Reilly, Jameson1 aToh, George1 aSaha, Sagnik1 aShalaev, Mikhail1 aGoetting, Isabella1 aMonroe, Christopher uhttps://arxiv.org/abs/2310.0705801965nas a2200205 4500008004100000245009400041210006900135260001400204520132100218100002001539700002101559700001701580700002301597700001701620700001801637700001801655700002501673700002401698856003701722 2024 eng d00aLong-Distance Nuclear Matrix Elements for Neutrinoless Double-Beta Decay from Lattice QCD0 aLongDistance Nuclear Matrix Elements for Neutrinoless DoubleBeta c2/14/20243 a

Neutrinoless double-beta (0νββ) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on 0νββ-decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum-chromodynamics (LQCD) calculation of the matrix element for 0νββ decay in a multi-nucleon system, specifically the nn→ppee transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of mπ=806 MeV at a single lattice spacing and volume. The statistically cleaner Σ−→Σ+ee transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for 0νββ decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of 0νββ decay.

1 aDavoudi, Zohreh1 aDetmold, William1 aFu, Zhenghao1 aGrebe, Anthony, V.1 aJay, William1 aMurphy, David1 aOare, Patrick1 aShanahan, Phiala, E.1 aWagman, Michael, L. uhttps://arxiv.org/abs/2402.0936202067nas a2200169 4500008004100000245008100041210006900122260001300191520151900204100002001723700002701743700002001770700002301790700001901813700002801832856003701860 2024 eng d00aQuantum thermodynamics of nonequilibrium processes in lattice gauge theories0 aQuantum thermodynamics of nonequilibrium processes in lattice ga c4/3/20243 a

A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early universe and in particle colliders, starting from the Standard Model. Classical-computing methods, via the framework of lattice gauge theory, have experienced limited success in this mission. Quantum simulation of lattice gauge theories holds promise for overcoming computational limitations. Because of local constraints (Gauss's laws), lattice gauge theories have an intricate Hilbert-space structure. This structure complicates the definition of thermodynamic properties of systems coupled to reservoirs during equilibrium and nonequilibrium processes. We show how to define thermodynamic quantities such as work and heat using strong-coupling thermodynamics, a framework that has recently burgeoned within the field of quantum thermodynamics. Our definitions suit instantaneous quenches, simple nonequilibrium processes undertaken in quantum simulators. To illustrate our framework, we compute the work and heat exchanged during a quench in a Z2 lattice gauge theory coupled to matter in 1+1 dimensions. The thermodynamic quantities, as functions of the quench parameter, evidence an expected phase transition. For general thermal states, we derive a simple relation between a quantum many-body system's entanglement Hamiltonian, measurable with quantum-information-processing tools, and the Hamiltonian of mean force, used to define strong-coupling thermodynamic quantities.

1 aDavoudi, Zohreh1 aJarzynski, Christopher1 aMueller, Niklas1 aOruganti, Greeshma1 aPowers, Connor1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2404.0296502358nas a2200145 4500008004100000245007400041210006900115260001400184520188700198100002002085700002002105700002802125700002202153856003702175 2023 eng d00aEfficient learning of ground & thermal states within phases of matter0 aEfficient learning of ground thermal states within phases of mat c1/30/20233 a

We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum phase of matter. In both cases, we wish to minimise the number of samples we use to learn these properties to a given precision.
For the first task, we develop new techniques to learn parameterisations of classes of systems, including quantum Gibbs states of non-commuting Hamiltonians with exponential decay of correlations and the approximate Markov property. We show it is possible to infer the expectation values of all extensive properties of the state from a number of copies that not only scales polylogarithmically with the system size, but polynomially in the observable's locality -- an exponential improvement. This set of properties includes expected values of quasi-local observables and entropies.  For the second task, we develop efficient algorithms for learning observables in a phase of matter of a quantum system. By exploiting the locality of the Hamiltonian, we show that M local observables can be learned with probability 1−δ to precision ϵ with using only N=O(log(Mδ)epolylog(ϵ−1)) samples -- an exponential improvement on the precision over previous bounds. Our results apply to both families of ground states of Hamiltonians displaying local topological quantum order, and thermal phases of matter with exponential decay of correlations. In addition, our sample complexity applies to the worse case setting whereas previous results only applied on average.
Furthermore, we develop tools of independent interest, such as robust shadow tomography algorithms, Gibbs approximations to ground states, and generalisations of transportation cost inequalities for Gibbs states.

1 aOnorati, Emilio1 aRouzé, Cambyse1 aFrança, Daniel, Stilck1 aWatson, James, D. uhttps://arxiv.org/abs/2301.1294602618nas a2200229 4500008004100000245007500041210006900116260001500185520193200200100001902132700002002151700002602171700001702197700001802214700001802232700002302250700002202273700001502295700001802310700002302328856003702351 2023 eng d00aMicrowave signal processing using an analog quantum reservoir computer0 aMicrowave signal processing using an analog quantum reservoir co c12/26/20233 a

Quantum reservoir computing (QRC) has been proposed as a paradigm for performing machine learning with quantum processors where the training is efficient in the number of required runs of the quantum processor and takes place in the classical domain, avoiding the issue of barren plateaus in parameterized-circuit quantum neural networks. It is natural to consider using a quantum processor based on superconducting circuits to classify microwave signals that are analog -- continuous in time. However, while theoretical proposals of analog QRC exist, to date QRC has been implemented using circuit-model quantum systems -- imposing a discretization of the incoming signal in time, with each time point input by executing a gate operation. In this paper we show how a quantum superconducting circuit comprising an oscillator coupled to a qubit can be used as an analog quantum reservoir for a variety of classification tasks, achieving high accuracy on all of them. Our quantum system was operated without artificially discretizing the input data, directly taking in microwave signals. Our work does not attempt to address the question of whether QRCs could provide a quantum computational advantage in classifying pre-recorded classical signals. However, beyond illustrating that sophisticated tasks can be performed with a modest-size quantum system and inexpensive training, our work opens up the possibility of achieving a different kind of advantage than a purely computational advantage: superconducting circuits can act as extremely sensitive detectors of microwave photons; our work demonstrates processing of ultra-low-power microwave signals in our superconducting circuit, and by combining sensitive detection with QRC processing within the same system, one could achieve a quantum sensing-computational advantage, i.e., an advantage in the overall analysis of microwave signals comprising just a few photons.

1 aSenanian, Alen1 aPrabhu, Sridhar1 aKremenetski, Vladimir1 aRoy, Saswata1 aCao, Yingkang1 aKline, Jeremy1 aOnodera, Tatsuhiro1 aWright, Logan, G.1 aWu, Xiaodi1 aFatemi, Valla1 aMcMahon, Peter, L. uhttps://arxiv.org/abs/2312.1616602360nas a2200145 4500008004100000245007900041210006900120260001500189520188900204100002002093700002002113700002802133700002202161856003102183 2023 eng d00aProvably Efficient Learning of Phases of Matter via Dissipative Evolutions0 aProvably Efficient Learning of Phases of Matter via Dissipative  c11/13/20233 a

The combination of quantum many-body and machine learning techniques has recently proved to be a fertile ground for new developments in quantum computing. Several works have shown that it is possible to classically efficiently predict the expectation values of local observables on all states within a phase of matter using a machine learning algorithm after learning from data obtained from other states in the same phase. However, existing results are restricted to phases of matter such as ground states of gapped Hamiltonians and Gibbs states that exhibit exponential decay of correlations. In this work, we drop this requirement and show how it is possible to learn local expectation values for all states in a phase, where we adopt the Lindbladian phase definition by Coser \& Pérez-García [Coser \& Pérez-García, Quantum 3, 174 (2019)], which defines states to be in the same phase if we can drive one to other rapidly with a local Lindbladian. This definition encompasses the better-known Hamiltonian definition of phase of matter for gapped ground state phases, and further applies to any family of states connected by short unitary circuits, as well as non-equilibrium phases of matter, and those stable under external dissipative interactions. Under this definition, we show that N=O(log(n/δ)2polylog(1/ϵ)) samples suffice to learn local expectation values within a phase for a system with n qubits, to error ϵ with failure probability δ. This sample complexity is comparable to previous results on learning gapped and thermal phases, and it encompasses previous results of this nature in a unified way. Furthermore, we also show that we can learn families of states which go beyond the Lindbladian definition of phase, and we derive bounds on the sample complexity which are dependent on the mixing time between states under a Lindbladian evolution.

1 aOnorati, Emilio1 aRouzé, Cambyse1 aFrança, Daniel, Stilck1 aWatson, James, D. uarXiv:2311.07506 Search...05435nas a2201621 4500008004100000245010800041210006900149260001500218520094500233100001801178700002301196700001601219700002801235700002001263700002001283700001601303700002001319700002101339700002401360700001901384700001901403700002601422700001801448700002301466700002101489700001601510700001701526700002101543700002301564700002101587700001601608700001701624700003101641700003401672700001801706700001801724700002101742700001801763700002401781700001801805700002001823700003501843700002201878700001601900700002001916700001901936700001701955700001901972700002301991700001802014700002402032700002302056700002302079700001802102700001702120700001902137700002602156700002002182700001902202700001902221700002302240700001802263700002202281700001802303700001902321700002802340700002402368700001902392700002002411700002002431700002702451700001202478700001702490700001502507700002102522700001802543700001902561700003202580700002402612700002202636700003102658700001702689700002302706700002402729700002002753700001902773700001902792700001602811700001702827700001802844700001802862700002002880700001902900700002302919700001902942700001702961700002602978700001603004700002003020700001603040700001803056700002803074700002103102700001803123700002403141700001403165700002303179700002003202700002103222700002003243700001803263700001803281700002103299700002103320700002303341700001803364700001803382700001403400700001903414700001603433700001503449700002003464700002103484700002103505700001703526700002803543700002203571700002303593700002603616700001503642700001703657700002303674700002403697700001803721700001703739700002003756856003703776 2023 eng d00aQuantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions0 aQuantumcentric Supercomputing for Materials Science A Perspectiv c12/14/20233 a

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

1 aAlexeev, Yuri1 aAmsler, Maximilian1 aBaity, Paul1 aBarroca, Marco, Antonio1 aBassini, Sanzio1 aBattelle, Torey1 aCamps, Daan1 aCasanova, David1 aChoi, Young, jai1 aChong, Frederic, T.1 aChung, Charles1 aCodella, Chris1 aCorcoles, Antonio, D.1 aCruise, James1 aDi Meglio, Alberto1 aDubois, Jonathan1 aDuran, Ivan1 aEckl, Thomas1 aEconomou, Sophia1 aEidenbenz, Stephan1 aElmegreen, Bruce1 aFare, Clyde1 aFaro, Ismael1 aFernández, Cristina, Sanz1 aFerreira, Rodrigo, Neumann Ba1 aFuji, Keisuke1 aFuller, Bryce1 aGagliardi, Laura1 aGalli, Giulia1 aGlick, Jennifer, R.1 aGobbi, Isacco1 aGokhale, Pranav1 aGonzalez, Salvador, de la Puen1 aGreiner, Johannes1 aGropp, Bill1 aGrossi, Michele1 aGull, Emmanuel1 aHealy, Burns1 aHuang, Benchen1 aHumble, Travis, S.1 aIto, Nobuyasu1 aIzmaylov, Artur, F.1 aJavadi-Abhari, Ali1 aJennewein, Douglas1 aJha, Shantenu1 aJiang, Liang1 aJones, Barbara1 ade Jong, Wibe, Albert1 aJurcevic, Petar1 aKirby, William1 aKister, Stefan1 aKitagawa, Masahiro1 aKlassen, Joel1 aKlymko, Katherine1 aKoh, Kwangwon1 aKondo, Masaaki1 aKurkcuoglu, Doga, Murat1 aKurowski, Krzysztof1 aLaino, Teodoro1 aLandfield, Ryan1 aLeininger, Matt1 aLeyton-Ortega, Vicente1 aLi, Ang1 aLin, Meifeng1 aLiu, Junyu1 aLorente, Nicolas1 aLuckow, Andre1 aMartiel, Simon1 aMartin-Fernandez, Francisco1 aMartonosi, Margaret1 aMarvinney, Claire1 aMedina, Arcesio, Castaneda1 aMerten, Dirk1 aMezzacapo, Antonio1 aMichielsen, Kristel1 aMitra, Abhishek1 aMittal, Tushar1 aMoon, Kyungsun1 aMoore, Joel1 aMotta, Mario1 aNa, Young-Hye1 aNam, Yunseong1 aNarang, Prineha1 aOhnishi, Yu-ya1 aOttaviani, Daniele1 aOtten, Matthew1 aPakin, Scott1 aPascuzzi, Vincent, R.1 aPenault, Ed1 aPiontek, Tomasz1 aPitera, Jed1 aRall, Patrick1 aRavi, Gokul, Subramania1 aRobertson, Niall1 aRossi, Matteo1 aRydlichowski, Piotr1 aRyu, Hoon1 aSamsonidze, Georgy1 aSato, Mitsuhisa1 aSaurabh, Nishant1 aSharma, Vidushi1 aSharma, Kunal1 aShin, Soyoung1 aSlessman, George1 aSteiner, Mathias1 aSitdikov, Iskandar1 aSuh, In-Saeng1 aSwitzer, Eric1 aTang, Wei1 aThompson, Joel1 aTodo, Synge1 aTran, Minh1 aTrenev, Dimitar1 aTrott, Christian1 aTseng, Huan-Hsin1 aTureci, Esin1 aValinas, David, García1 aVallecorsa, Sofia1 aWever, Christopher1 aWojciechowski, Konrad1 aWu, Xiaodi1 aYoo, Shinjae1 aYoshioka, Nobuyuki1 aYu, Victor, Wen-zhe1 aYunoki, Seiji1 aZhuk, Sergiy1 aZubarev, Dmitry uhttps://arxiv.org/abs/2312.0973301289nas a2200169 4500008004100000245004100041210004100082260001400123520084200137100002300979700001601002700001801018700001201036700001701048700001701065856003701082 2023 eng d00aStreaming quantum state purification0 aStreaming quantum state purification c9/28/20233 a

Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum computation with imperfect devices, but has only been studied previously for the case of qubits. We derive an efficient purification procedure based on the swap test for qudits of any dimension, starting with any initial error parameter. Treating the initial error parameter and the dimension as constants, we show that our procedure has sample complexity asymptotically optimal in the final error parameter. Our protocol has a simple recursive structure that can be applied when the states are provided one at a time in a streaming fashion, requiring only a small quantum memory to implement.

1 aChilds, Andrew, M.1 aFu, Honghao1 aLeung, Debbie1 aLi, Zhi1 aOzols, Maris1 aVyas, Vedang uhttps://arxiv.org/abs/2309.1638702149nas a2200457 4500008004100000245005300041210005200094260001400146520077300160653005700933653002700990653004601017653004901063100003401112700002201146700002101168700001901189700001901208700002201227700001901249700002201268700002501290700001901315700001701334700001901351700002101370700002101391700001801412700001401430700002701444700002201471700002201493700001601515700002001531700001701551700002501568700002201593700001401615700002501629856003701654 2022 eng d00aSnowmass 2021 White Paper: The Windchime Project0 aSnowmass 2021 White Paper The Windchime Project c3/14/20223 a

The absence of clear signals from particle dark matter in direct detection experiments motivates new approaches in disparate regions of viable parameter space. In this Snowmass white paper, we outline the Windchime project, a program to build a large array of quantum-enhanced mechanical sensors. The ultimate aim is to build a detector capable of searching for Planck mass-scale dark matter purely through its gravitational coupling to ordinary matter. In the shorter term, we aim to search for a number of other physics targets, especially some ultralight dark matter candidates. Here, we discuss the basic design, open R&D challenges and opportunities, current experimental efforts, and both short- and long-term physics targets of the Windchime project.

10aCosmology and Nongalactic Astrophysics (astro-ph.CO)10aFOS: Physical sciences10aHigh Energy Physics - Experiment (hep-ex)10aHigh Energy Physics - Phenomenology (hep-ph)1 aCollaboration, The, Windchime1 aAttanasio, Alaina1 aBhave, Sunil, A.1 aBlanco, Carlos1 aCarney, Daniel1 aDemarteau, Marcel1 aElshimy, Bahaa1 aFebbraro, Michael1 aFeldman, Matthew, A.1 aGhosh, Sohitri1 aHickin, Abby1 aHong, Seongjin1 aLang, Rafael, F.1 aLawrie, Benjamin1 aLi, Shengchao1 aLiu, Zhen1 aMaldonado, Juan, P. A.1 aMarvinney, Claire1 aOo, Hein, Zay Yar1 aPai, Yun-Yi1 aPooser, Raphael1 aQin, Juehang1 aSparmann, Tobias, J.1 aTaylor, Jacob, M.1 aTian, Hao1 aTunnell, Christopher uhttps://arxiv.org/abs/2203.0724202078nas a2200277 4500008004100000245006700041210006600108260001500174520125200189100002201441700001801463700002501481700002101506700002401527700002501551700002101576700002001597700002501617700002601642700001601668700001901684700002301703700001801726700001901744856003701763 2021 eng d00aDevice-independent Randomness Expansion with Entangled Photons0 aDeviceindependent Randomness Expansion with Entangled Photons c01/28/20213 a

With the growing availability of experimental loophole-free Bell tests, it has become possible to implement a new class of device-independent random number generators whose output can be certified to be uniformly random without requiring a detailed model of the quantum devices used. However, all of these experiments require many input bits in order to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is used. Here, we devise a device-independent spot-checking protocol which uses only uniform bits as input. Implemented with a photonic loophole-free Bell test, we can produce 24% more certified output bits (1,181,264,237) than consumed input bits (953,301,640), which is 5 orders of magnitude more efficient than our previous work [arXiv:1812.07786]. The experiment ran for 91.0 hours, creating randomness at an average rate of 3606 bits/s with a soundness error bounded by 5.7×10−7 in the presence of classical side information. Our system will allow for greater trust in public sources of randomness, such as randomness beacons, and the protocols may one day enable high-quality sources of private randomness as the device footprint shrinks.

1 aShalm, Lynden, K.1 aZhang, Yanbao1 aBienfang, Joshua, C.1 aSchlager, Collin1 aStevens, Martin, J.1 aMazurek, Michael, D.1 aAbellán, Carlos1 aAmaya, Waldimar1 aMitchell, Morgan, W.1 aAlhejji, Mohammad, A.1 aFu, Honghao1 aOrnstein, Joel1 aMirin, Richard, P.1 aNam, Sae, Woo1 aKnill, Emanuel uhttps://arxiv.org/abs/1912.1115801422nas a2200145 4500008004100000245007300041210006900114260001400183490000600197520097400203100002301177700001801200700002101218856003701239 2021 eng d00aHigh-precision quantum algorithms for partial differential equations0 aHighprecision quantum algorithms for partial differential equati c11/4/20210 v53 a

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ε), where ε is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be poly(d,log(1/ε)), where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations. 

1 aChilds, Andrew, M.1 aLiu, Jin-Peng1 aOstrander, Aaron uhttps://arxiv.org/abs/2002.0786802237nas a2200121 4500008004100000245011500041210006900156260001300225520179100238100002502029700002402054856003702078 2020 eng d00aAuditing and Debugging Deep Learning Models via Decision Boundaries: Individual-level and Group-level Analysis0 aAuditing and Debugging Deep Learning Models via Decision Boundar c1/2/20203 a

Deep learning models have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Nevertheless, they are consistently utilized in many applications, consequential to humans' lives, mostly because of their better performance. Therefore, there is a great need for computational methods that can explain, audit, and debug such models. Here, we use flip points to accomplish these goals for deep learning models with continuous output scores (e.g., computed by softmax), used in social applications. A flip point is any point that lies on the boundary between two output classes: e.g. for a model with a binary yes/no output, a flip point is any input that generates equal scores for "yes" and "no". The flip point closest to a given input is of particular importance because it reveals the least changes in the input that would change a model's classification, and we show that it is the solution to a well-posed optimization problem. Flip points also enable us to systematically study the decision boundaries of a deep learning classifier. The resulting insight into the decision boundaries of a deep model can clearly explain the model's output on the individual-level, via an explanation report that is understandable by non-experts. We also develop a procedure to understand and audit model behavior towards groups of people. Flip points can also be used to alter the decision boundaries in order to improve undesirable behaviors. We demonstrate our methods by investigating several models trained on standard datasets used in social applications of machine learning. We also identify the features that are most responsible for particular classifications and misclassifications.

1 aYousefzadeh, Roozbeh1 aO'Leary, Dianne, P. uhttps://arxiv.org/abs/2001.0068201709nas a2200205 4500008004100000245006400041210006200105260001400167490000800181520108400189100002401273700002101297700002301318700002801341700003001369700002401399700001801423700002501441856003701466 2020 eng d00aExotic photonic molecules via Lennard-Jones-like potentials0 aExotic photonic molecules via LennardJoneslike potentials c9/19/20200 v1253 a

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a F{ö}rster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters ("molecules") of photons. We demonstrate that for a few-body problem, the multi-body interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in 2D preferentially arrange themselves in a line-configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

1 aBienias, Przemyslaw1 aGullans, Michael1 aKalinowski, Marcin1 aCraddock, Alexander, N.1 aOrnelas-Huerta, Dalia, P.1 aRolston, Steven, L.1 aPorto, J., V.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2003.0786401697nas a2200205 4500008004100000245010900041210006900150260001300219520100800232100003001240700002801270700003101298700002401329700001601353700001601369700002501385700002301410700002101433856003701454 2020 eng d00aOn-demand indistinguishable single photons from an efficient and pure source based on a Rydberg ensemble0 aOndemand indistinguishable single photons from an efficient and  c3/4/20203 a

Single photons coupled to atomic systems have shown to be a promising platform for developing quantum technologies. Yet a bright on-demand, highly pure and highly indistinguishable single-photon source compatible with atomic platforms is lacking. In this work, we demonstrate such a source based on a strongly interacting Rydberg system. The large optical nonlinearities in a blockaded Rydberg ensemble convert coherent light into a single-collective excitation that can be coherently retrieved as a quantum field. We observe a single-transverse-mode efficiency up to 0.18(2), g(2)=2.0(1.5)×10−4, and indistinguishability of 0.982(7), making this system promising for scalable quantum information applications. Accounting for losses, we infer a generation probability up to 0.40(4). Furthermore, we investigate the effects of contaminant Rydberg excitations on the source efficiency. Finally, we introduce metrics to benchmark the performance of on-demand single-photon sources. 

1 aOrnelas-Huerta, Dalia, P.1 aCraddock, Alexander, N.1 aGoldschmidt, Elizabeth, A.1 aHachtel, Andrew, J.1 aWang, Yidan1 aBienias, P.1 aGorshkov, Alexey, V.1 aRolston, Steve, L.1 aPorto, James, V. uhttps://arxiv.org/abs/2003.0220202525nas a2200169 4500008004100000245006600041210006200107260001400169300000700183490000600190520198300196100001902179700002002198700001702218700002302235856009702258 2020 eng d00aOn Quantum Chosen-Ciphertext Attacks and Learning with Errors0 aQuantum ChosenCiphertext Attacks and Learning with Errors c3/21/2020 a100 v43 a

Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong “quantum access” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND−CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally “just as secure” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.

1 aAlagic, Gorjan1 aJeffery, Stacey1 aOzols, Maris1 aPoremba, Alexander uhttps://www.quics.umd.edu/publications/quantum-chosen-ciphertext-attacks-and-learning-errors01529nas a2200145 4500008004100000245007400041210006900115260001500184490000800199520104100207100002601248700001701274700002201291856007001313 2020 eng d00aQuantum Lifshitz criticality in a frustrated two-dimensional XY model0 aQuantum Lifshitz criticality in a frustrated twodimensional XY m c01/09/20200 v1013 a

Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states,
driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point.
Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. Specifically, we show that, unlike the SU (2) symmetric Lifshitz case, in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the Néel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.

1 aKharkov, Yaroslav, A.1 aOitmaa, Jaan1 aSushkov, Oleg, P. uhttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.101.03511401558nas a2200217 4500008004100000245008100041210006900122260001500191520086200206100002301068700001601091700002401107700002101131700003001152700002801182700002401210700001801234700002601252700002501278856003701303 2020 eng d00aResonant enhancement of three-body loss between strongly interacting photons0 aResonant enhancement of threebody loss between strongly interact c10/19/20203 a

Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly-interacting, and topological phases of matter. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the three-body Schrödinger equation, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiment

1 aKalinowski, Marcin1 aWang, Yidan1 aBienias, Przemyslaw1 aGullans, Michael1 aOrnelas-Huerta, Dalia, P.1 aCraddock, Alexander, N.1 aRolston, Steven, L.1 aPorto, J., V.1 aBüchler, Hans, Peter1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2010.0977201588nas a2200157 4500008004100000245006600041210006600107260001400173490000800187520113200195100001701327700001701344700001701361700001501378856003701393 2020 eng d00aSimulating large quantum circuits on a small quantum computer0 aSimulating large quantum circuits on a small quantum computer c12/8/20200 v1253 a

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters K and d of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most d with at most K qubits of inter-cluster quantum communication. Our main result is a simulation scheme of any (K,d)-clustered quantum circuit on a d-qubit machine in time roughly 2O(K). An important application of our result is the simulation of clustered quantum systems---such as large molecules---that can be partitioned into multiple significantly smaller clusters with weak interactions among them. Another potential application is quantum optimization: we demonstrate numerically that variational quantum eigensolvers can still perform well when restricted to clustered circuits, thus making it feasible to study large quantum systems on small quantum devices.

1 aPeng, Tianyi1 aHarrow, Aram1 aOzols, Maris1 aWu, Xiaodi uhttps://arxiv.org/abs/1904.0010202955nas a2200397 4500008004100000245008600041210006900127260001500196520181200211100002102023700002302044700002002067700001702087700002202104700001702126700002502143700001802168700001902186700001702205700001702222700002702239700001502266700001702281700001802298700001702316700001602333700002002349700001902369700002302388700002502411700002402436700001802460700002002478700002202498856003702520 2019 eng d00aDevelopment of Quantum InterConnects for Next-Generation Information Technologies0 aDevelopment of Quantum InterConnects for NextGeneration Informat c12/13/20193 a

Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years. 

1 aAwschalom, David1 aBerggren, Karl, K.1 aBernien, Hannes1 aBhave, Sunil1 aCarr, Lincoln, D.1 aDavids, Paul1 aEconomou, Sophia, E.1 aEnglund, Dirk1 aFaraon, Andrei1 aFejer, Marty1 aGuha, Saikat1 aGustafsson, Martin, V.1 aHu, Evelyn1 aJiang, Liang1 aKim, Jungsang1 aKorzh, Boris1 aKumar, Prem1 aKwiat, Paul, G.1 aLončar, Marko1 aLukin, Mikhail, D.1 aMiller, David, A. B.1 aMonroe, Christopher1 aNam, Sae, Woo1 aNarang, Prineha1 aOrcutt, Jason, S. uhttps://arxiv.org/abs/1912.0664201284nas a2200145 4500008004100000245004700041210004700088260001500135490000600150520088800156100002301044700002101067700001301088856003701101 2019 eng d00aFaster quantum simulation by randomization0 aFaster quantum simulation by randomization c08/28/20190 v33 a

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that our randomized algorithm may be advantageous even for near-term quantum simulation.

1 aChilds, Andrew, M.1 aOstrander, Aaron1 aSu, Yuan uhttps://arxiv.org/abs/1805.0838501480nas a2200193 4500008004100000245009000041210006900131260001400200490000800214520086300222100002601085700003101111700002301142700002501165700002001190700002101210700001801231856003701249 2019 eng d00aInterference of Temporally Distinguishable Photons Using Frequency-Resolved Detection0 aInterference of Temporally Distinguishable Photons Using Frequen c9/24/20190 v1233 a

We demonstrate quantum interference of three photons that are distinguishable in time, by resolving them in the conjugate parameter, frequency. We show that the multiphoton interference pattern in our setup can be manipulated by tuning the relative delays between the photons, without the need for reconfiguring the optical network. Furthermore, we observe that the symmetries of our optical network and the spectral amplitude of the input photons are manifested in the interference pattern. Moreover, we demonstrate time-reversed HOM-like interference in the spectral correlations using time-bin entangled photon pairs. By adding a time-varying dispersion using a phase modulator, our setup can be used to realize dynamically reconfigurable and scalable boson sampling in the time domain as well as frequency-resolved multiboson correlation sampling.

1 aOrre, Venkata, Vikram1 aGoldschmidt, Elizabeth, A.1 aDeshpande, Abhinav1 aGorshkov, Alexey, V.1 aTamma, Vincenzo1 aHafezi, Mohammad1 aMittal, Sunil uhttps://arxiv.org/abs/1904.0322202184nas a2200121 4500008004100000245005100041210005100092260001500143520181800158100002501976700002402001856003702025 2019 eng d00aInterpreting Neural Networks Using Flip Points0 aInterpreting Neural Networks Using Flip Points c03/20/20193 a

Neural networks have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Here, we introduce a novel technique, interpreting a trained neural network by investigating its flip points. A flip point is any point that lies on the boundary between two output classes: e.g. for a neural network with a binary yes/no output, a flip point is any input that generates equal scores for "yes" and "no". The flip point closest to a given input is of particular importance, and this point is the solution to a well-posed optimization problem. This paper gives an overview of the uses of flip points and how they are computed. Through results on standard datasets, we demonstrate how flip points can be used to provide detailed interpretation of the output produced by a neural network. Moreover, for a given input, flip points enable us to measure confidence in the correctness of outputs much more effectively than softmax score. They also identify influential features of the inputs, identify bias, and find changes in the input that change the output of the model. We show that distance between an input and the closest flip point identifies the most influential points in the training data. Using principal component analysis (PCA) and rank-revealing QR factorization (RR-QR), the set of directions from each training input to its closest flip point provides explanations of how a trained neural network processes an entire dataset: what features are most important for classification into a given class, which features are most responsible for particular misclassifications, how an adversary might fool the network, etc. Although we investigate flip points for neural networks, their usefulness is actually model-agnostic.

1 aYousefzadeh, Roozbeh1 aO'Leary, Dianne, P. uhttps://arxiv.org/abs/1903.0878901719nas a2200121 4500008004100000245006500041210006500106260001300171520132800184100002501512700002301537856003701560 2019 eng d00aInvestigating Decision Boundaries of Trained Neural Networks0 aInvestigating Decision Boundaries of Trained Neural Networks c8/7/20193 a

Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision boundaries, and therefore, many of the studies about deep learning models speculate about the decision boundaries, and sometimes make simplifying assumptions about them. So far, finding exact points on the decision boundaries of trained deep models has been considered an intractable problem. Here, we compute exact points on the decision boundaries of these models and provide mathematical tools to investigate the surfaces that define the decision boundaries. Through numerical results, we confirm that some of the speculations about the decision boundaries are accurate, some of the computational methods can be improved, and some of the simplifying assumptions may be unreliable, for models with nonlinear activation functions. We advocate for verification of simplifying assumptions and approximation methods, wherever they are used. Finally, we demonstrate that the computational practices used for finding adversarial examples can be improved and computing the closest point on the decision boundary reveals the weakest vulnerability of a model against adversarial attack.

1 aYousefzadeh, Roozbeh1 aO'Leary, Dianne, P uhttps://arxiv.org/abs/1908.0280202399nas a2200145 4500008004100000245007900041210006900120300001400189520193400203100001902137700002002156700001702176700002302193856003702216 2019 eng d00aOn non-adaptive quantum chosen-ciphertext attacks and Learning with Errors0 anonadaptive quantum chosenciphertext attacks and Learning with E a1:1-1:23 3 a

Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF- and PRP-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key uses a linear number of decryption queries, and this is optimal. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should *not* be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones. 

1 aAlagic, Gorjan1 aJeffery, Stacey1 aOzols, Maris1 aPoremba, Alexander uhttps://arxiv.org/abs/1808.0965502010nas a2200409 4500008004100000245006800041210006600109260001500175520084400190100001901034700002601053700002001079700002001099700002001119700001701139700002501156700002201181700001901203700001701222700002201239700002101261700002501282700001901307700002301326700001801349700001901367700002101386700002101407700001501428700002001443700002401463700001801487700002301505700001901528700001601547856003701563 2019 eng d00aOpportunities for Nuclear Physics & Quantum Information Science0 aOpportunities for Nuclear Physics Quantum Information Science c03/13/20193 a

his whitepaper is an outcome of the workshop Intersections between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28-30 March 2018 [www.phy.anl.gov/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

1 aCloët, I., C.1 aDietrich, Matthew, R.1 aArrington, John1 aBazavov, Alexei1 aBishof, Michael1 aFreese, Adam1 aGorshkov, Alexey, V.1 aGrassellino, Anna1 aHafidi, Kawtar1 aJacob, Zubin1 aMcGuigan, Michael1 aMeurice, Yannick1 aMeziani, Zein-Eddine1 aMueller, Peter1 aMuschik, Christine1 aOsborn, James1 aOtten, Matthew1 aPetreczky, Peter1 aPolakovic, Tomas1 aPoon, Alan1 aPooser, Raphael1 aRoggero, Alessandro1 aSaffman, Mark1 aVanDevender, Brent1 aZhang, Jiehang1 aZohar, Erez uhttps://arxiv.org/abs/1903.0545301348nas a2200121 4500008004100000245010600041210006900147260001400216520091000230100002501140700002401165856003701189 2019 eng d00aA Probabilistic Framework and a Homotopy Method for Real-time Hierarchical Freight Dispatch Decisions0 aProbabilistic Framework and a Homotopy Method for Realtime Hiera c2019/12/83 a

We propose a real-time decision framework for multimodal freight dispatch through a system of hierarchical hubs, using a probabilistic model for transit times. Instead of assigning a fixed time to each transit, we advocate using historical records to identify characteristics of the probability density function for each transit time. We formulate a nonlinear optimization problem that defines dispatch decisions that minimize expected cost, using this probabilistic information. Finally, we propose an effective homotopy algorithm that (empirically) outperforms standard optimization algorithms on this problem by taking advantage of its structure, and we demonstrate its effectiveness on numerical examples. 

1 aYousefzadeh, Roozbeh1 aO'Leary, Dianne, P. uhttps://arxiv.org/abs/1912.0373301091nas a2200145 4500008004100000245005500041210005500096260001500151490000800166520066600174100002300840700002400863700002100887856003700908 2019 eng d00aQuantum Algorithm for Simulating the Wave Equation0 aQuantum Algorithm for Simulating the Wave Equation c03/24/20190 v99 3 a

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.

1 aCosta, Pedro, C.S.1 aJordan, Stephen, P.1 aOstrander, Aaron uhttps://arxiv.org/abs/1711.0539401498nas a2200121 4500008004100000245007200041210006900113260001300182520109600195100002501291700002301316856003701339 2019 eng d00aRefining the Structure of Neural Networks Using Matrix Conditioning0 aRefining the Structure of Neural Networks Using Matrix Condition c8/6/20193 a

Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error. While a small network with few neurons might not be able to capture the intricacies of a given task, having too many neurons can lead to overfitting and poor generalization. Here, we propose a practical method that employs matrix conditioning to automatically design the structure of layers of a feed-forward network, by first adjusting the proportion of neurons among the layers of a network and then scaling the size of network up or down. Results on sample image and non-image datasets demonstrate that our method results in small networks with high accuracies. Finally, guided by matrix conditioning, we provide a method to effectively squeeze models that are already trained. Our techniques reduce the human cost of designing deep learning models and can also reduce training time and the expense of using neural networks for applications.

1 aYousefzadeh, Roozbeh1 aO'Leary, Dianne, P uhttps://arxiv.org/abs/1908.0240001943nas a2200169 4500008004100000245007600041210006900117520143500186100001601621700001801637700001801655700002101673700001201694700001501706700001501721856003701736 2018 eng d00aParallel Entangling Operations on a Universal Ion Trap Quantum Computer0 aParallel Entangling Operations on a Universal Ion Trap Quantum C3 a

The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

1 aFiggatt, C.1 aOstrander, A.1 aLinke, N., M.1 aLandsman, K., A.1 aZhu, D.1 aMaslov, D.1 aMonroe, C. uhttps://arxiv.org/abs/1810.1194801846nas a2200169 4500008004100000245006600041210006500107520131000172100001701482700001801499700002801517700002501545700002201570700002301592700002401615856003701639 2018 eng d00aStudying community development: a network analytical approach0 aStudying community development a network analytical approach3 a

Research shows that community plays a central role in learning, and strong community engages students and aids in student persistence. Thus, understanding the function and structure of communities in learning environments is essential to education. We use social network analysis to explore the community dynamics of students in a pre-matriculation, two-week summer program. Unlike previous network analysis studies in PER, we build our networks from classroom video that has been coded for student interactions using labeled, directed ties. We define 3 types of interaction: on task interactions (regarding the assigned task), on topic interactions (having to do with science, technology, engineering, and mathematics (STEM)), and off topic interactions (unrelated to the assignment or STEM). To study the development of community in this program, we analyze the shift in conversation topicality over the course of the program. Conversations are more on-task toward the end of the program and we propose that this conversational shift represents a change in student membership within their forming community. 

1 aHass, C., A.1 aGenz, Florian1 aKustusch, Mary, Bridget1 aOuime, Pierre-P., A.1 aPomian, Katarzyna1 aSayre, Eleanor, C.1 aZwolak, Justyna, P. uhttps://arxiv.org/abs/1808.0819301082nas a2200181 4500008004100000022001400041245007000055210006900125260001500194300001400209490000700223520042300230100001800653700002100671700002100692700001600713856017100729 2017 eng d a1944-417600aDomination with decay in triangular matchstick arrangement graphs0 aDomination with decay in triangular matchstick arrangement graph c2017/05/14 a749 - 7660 v103 a

We provide results for the exponential dominating numbers and total exponential dominating numbers of a family of triangular grid graphs. We then prove inequalities for these numbers and compare them with inequalities that hold more generally for exponential dominating numbers of graphs.

1 aCochran, Jill1 aHenderson, Terry1 aOstrander, Aaron1 aTaylor, Ron uhttp://msp.org/involve/http://msp.org/involve/2017/10-5/index.xhtmlhttp://msp.org/involve/2017/10-5/p03.xhtmlhttp://msp.org/involve/2017/10-5/involve-v10-n5-p03-s.pdf01826nas a2200169 4500008004100000245005800041210005800099260001500157490000700172520131900179100001901498700002401517700002001541700001701561700002401578856005401602 2017 eng d00aHamiltonian Simulation with Optimal Sample Complexity0 aHamiltonian Simulation with Optimal Sample Complexity c2017/03/310 v133 a
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631--633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.
 
 
1 aKimmel, Shelby1 aLin, Cedric, Yen-Yu1 aLow, Guang, Hao1 aOzols, Maris1 aYoder, Theodore, J. uhttps://www.nature.com/articles/s41534-017-0013-701208nas a2200169 4500008004100000245005700041210005600098260001500154300001100169490000700180520068400187100002600871700002700897700002500924700002000949856006900969 2017 eng d00aMulticritical behavior in dissipative {I}sing models0 aMulticritical behavior in dissipative I sing models c2017/04/26 a0421330 v953 a

We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

1 aOverbeck, Vincent, R.1 aMaghrebi, Mohammad, F.1 aGorshkov, Alexey, V.1 aWeimer, Hendrik uhttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.04213301429nas a2200169 4500008004100000245010800041210006900149260001500218300001400233490000800247520088200255100002301137700002301160700002101183700001801204856003701222 2017 eng d00aQuantum algorithm for linear differential equations with exponentially improved dependence on precision0 aQuantum algorithm for linear differential equations with exponen c2017/12/01 a1057-10810 v3563 a

We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.

1 aBerry, Dominic, W.1 aChilds, Andrew, M.1 aOstrander, Aaron1 aWang, Guoming uhttps://arxiv.org/abs/1701.0368402646nas a2200241 4500008004100000245008200041210006900123260001500192520190700207100002902114700002302143700001802166700002302184700001502207700002002222700002702242700002402269700001902293700002002312700001702332700001802349856003702367 2017 eng d00aOn the readiness of quantum optimization machines for industrial applications0 areadiness of quantum optimization machines for industrial applic c2017/08/313 a

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for near-term quantum annealers.

1 aPerdomo-Ortiz, Alejandro1 aFeldman, Alexander1 aOzaeta, Asier1 aIsakov, Sergei, V.1 aZhu, Zheng1 aO'Gorman, Bryan1 aKatzgraber, Helmut, G.1 aDiedrich, Alexander1 aNeven, Hartmut1 ade Kleer, Johan1 aLackey, Brad1 aBiswas, Rupak uhttps://arxiv.org/abs/1708.0978001589nas a2200193 4500008004100000245008100041210006900122260001500191300001100206490000700217520100800224100002301232700002501255700001901280700001901299700002001318700002101338856003601359 2015 eng d00aDemonstration of Robust Quantum Gate Tomography via Randomized Benchmarking0 aDemonstration of Robust Quantum Gate Tomography via Randomized B c2015/11/05 a1130190 v173 a Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing each of the elements of the Clifford group in single `atomic' pulses and custom control hardware to enable large overhead protocols. We show a robust reconstruction of several single-qubit quantum gates, including a unitary outside the Clifford group. We demonstrate that RBT yields physical gate reconstructions that are consistent with fidelities obtained by randomized benchmarking. 1 aJohnson, Blake, R.1 ada Silva, Marcus, P.1 aRyan, Colm, A.1 aKimmel, Shelby1 aChow, Jerry, M.1 aOhki, Thomas, A. uhttp://arxiv.org/abs/1505.0668600689nas a2200157 4500008004100000022001400041245006100055210006100116260001500177300001400192490000800206520020400214653002100418100002100439856007100460 2015 eng d a0024-379500aLaplacian matrices and Alexandrov topologies of digraphs0 aLaplacian matrices and Alexandrov topologies of digraphs c2015/09/15 a174 - 1850 v4813 aWe explore the spectral properties of digraph Laplacians and how they relate to topological properties of digraphs (such as openness, closure, and strong connectedness) under the Alexandrov topology.10aLaplacian matrix1 aOstrander, Aaron uhttp://www.sciencedirect.com/science/article/pii/S002437951500284002343nas a2200169 4500008004100000245009200041210006900133260001500202300001400217490000800231520180600239100002602045700002002071700002402091700002102115856003702136 2014 eng d00aAdaptive change of basis in entropy-based moment closures for linear kinetic equations0 aAdaptive change of basis in entropybased moment closures for lin c2014/02/01 a489 - 5080 v2583 a Entropy-based (M_N) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and efficiently. We present a complete and practical numerical algorithm for solving the dual problem in one-dimensional, slab geometries. The closure is only well-defined on the set of moments that are realizable from a positive underlying distribution, and as the boundary of the realizable set is approached, the dual problem becomes increasingly difficult to solve due to ill-conditioning of the Hessian matrix. To improve the condition number of the Hessian, we advocate the use of a change of polynomial basis, defined using a Cholesky factorization of the Hessian, that permits solution of problems nearer to the boundary of the realizable set. We also advocate a fixed quadrature scheme, rather than adaptive quadrature, since the latter introduces unnecessary expense and changes the computationally realizable set as the quadrature changes. For very ill-conditioned problems, we use regularization to make the optimization algorithm robust. We design a manufactured solution and demonstrate that the adaptive-basis optimization algorithm reduces the need for regularization. This is important since we also show that regularization slows, and even stalls, convergence of the numerical simulation when refining the space-time mesh. We also simulate two well-known benchmark problems. There we find that our adaptive-basis, fixed-quadrature algorithm uses less regularization than alternatives, although differences in the resulting numerical simulations are more sensitive to the regularization strategy than to the choice of basis. 1 aAlldredge, Graham, W.1 aHauck, Cory, D.1 aO'Leary, Dianne, P.1 aTits, André, L. uhttp://arxiv.org/abs/1306.2881v101231nas a2200145 4500008004100000245014400041210006900185260001500254300001100269490000700280520070100287100002100988700002101009856005501030 2014 eng d00aExtended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model in an oscillating field0 aExtended order parameter and conjugate field for the dynamic pha c2014/02/12 a0221140 v893 aWe present numerical evidence for an extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model driven by an oscillating field. The order parameter, previously taken to be the time-averaged magnetization, comprises the deviations of the Fourier components of the magnetization from their values at the critical period. The conjugate field, previously taken to be the time-averaged magnetic field, comprises the even Fourier components of the field. The scaling exponents β and δ associated with the extended order parameter and conjugate field are shown numerically to be consistent with their values in the equilibrium mean-field model.1 aRobb, Daniel, T.1 aOstrander, Aaron uhttp://link.aps.org/doi/10.1103/PhysRevE.89.02211401337nas a2200169 4500008004100000245007700041210006900118260001400187490000600201520082000207100001901027700002501046700001901071700002301090700001701113856003701130 2014 eng d00aRobust Extraction of Tomographic Information via Randomized Benchmarking0 aRobust Extraction of Tomographic Information via Randomized Benc c2014/3/250 v43 a We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution, or more generally, any unital trace-preserving evolution. This approach inherits randomized benchmarking's robustness to preparation and measurement imperfections, therefore avoiding systematic errors caused by these imperfections. We also extend these techniques to efficiently estimate the average fidelity of a quantum map to unitary maps outside of the Clifford group. The unitaries we consider include operations commonly used to achieve universal quantum computation in a fault-tolerant setting. In addition, we rigorously bound the time and sampling complexities of randomized benchmarking procedures. 1 aKimmel, Shelby1 ada Silva, Marcus, P.1 aRyan, Colm, A.1 aJohnson, Blake, R.1 aOhki, Thomas uhttp://arxiv.org/abs/1306.2348v101395nas a2200169 4500008004100000245006500041210006500106260001500171300001000186490000700196520090400203100002301107700001901130700001701149700002201166856003701188 2013 eng d00aEasy and hard functions for the Boolean hidden shift problem0 aEasy and hard functions for the Boolean hidden shift problem c2013/04/16 a50-790 v223 a We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state; its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem. 1 aChilds, Andrew, M.1 aKothari, Robin1 aOzols, Maris1 aRoetteler, Martin uhttp://arxiv.org/abs/1304.4642v101336nas a2200169 4500008004100000245006500041210006300106260001300169300001600182490000800198520084400206100002301050700001801073700002101091700001701112856003701129 2013 eng d00aA framework for bounding nonlocality of state discrimination0 aframework for bounding nonlocality of state discrimination c2013/9/4 a1121 - 11530 v3233 a We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99]. 1 aChilds, Andrew, M.1 aLeung, Debbie1 aMancinska, Laura1 aOzols, Maris uhttp://arxiv.org/abs/1206.5822v100982nas a2200169 4500008004100000245008200041210006900123260001500192300001100207490000700218520047100225100002300696700001800719700002100737700001700758856003700775 2013 eng d00aInterpolatability distinguishes LOCC from separable von Neumann measurements0 aInterpolatability distinguishes LOCC from separable von Neumann  c2013/06/25 a1122040 v543 a Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations. 1 aChilds, Andrew, M.1 aLeung, Debbie1 aMancinska, Laura1 aOzols, Maris uhttp://arxiv.org/abs/1306.5992v101523nas a2200181 4500008004100000245009800041210006900139260001500208300001000223520092900233100002101162700002201183700001701205700001601222700002401238700002801262856005101290 2013 eng d00aMultilingual Summarization: Dimensionality Reduction and a Step Towards Optimal Term Coverage0 aMultilingual Summarization Dimensionality Reduction and a Step T c2013/08/09 a55-633 aIn this paper we present three term weighting approaches for multi-lingual document summarization and give results on the DUC 2002 data as well as on the 2013 Multilingual Wikipedia feature articles data set. We introduce a new intervalbounded nonnegative matrix factorization. We use this new method, latent semantic analysis (LSA), and latent Dirichlet allocation (LDA) to give three term-weighting methods for multi-document multi-lingual summarization. Results on DUC and TAC data, as well as on the MultiLing 2013 data, demonstrate that these methods are very promising, since they achieve oracle coverage scores in the range of humans for 6 of the 10 test languages. Finally, we present three term weighting approaches for the MultiLing13 single document summarization task on the Wikipedia featured articles. Our submissions signifi- cantly outperformed the baseline in 19 out of 41 languages. 1 aConroy, John, M.1 aDavis, Sashka, T.1 aKubina, Jeff1 aLiu, Yi-Kai1 aO'Leary, Dianne, P.1 aSchlesinger, Judith, D. uhttp://aclweb.org/anthology/W/W13/W13-3108.pdf00860nas a2200169 4500008004100000245005600041210005600097260001500153300001100168490000700179520036800186100002100554700001900575700002400594700001700618856005500635 2012 eng d00aGluon chain formation in presence of static charges0 aGluon chain formation in presence of static charges c2012/12/10 a1140150 v863 aWe consider the origins of the gluon chain model. The model serves as a realization of the dynamics of the chromoelectric flux between static quark-antiquark sources. The derivation is based on the large-NC limit of the Coulomb gauge Hamiltonian in the presence of a background field introduced to model magnetic charge condensation inducing electric confinement.1 aOstrander, Aaron1 aSantopinto, E.1 aSzczepaniak, A., P.1 aVassallo, A. uhttp://link.aps.org/doi/10.1103/PhysRevD.86.11401500871nas a2200157 4500008004100000245006300041210006200104260001500166490000700181520037400188100001900562700002200581700002100603700001900624856007000643 2012 eng d00aNon-Recursively Constructible Recursive Families of Graphs0 aNonRecursively Constructible Recursive Families of Graphs c2012/04/160 v193 aIn a publication by Noy and Ribó, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples to this conjecture, which we then extend to an infinite family of counterexamples.1 aBouey, Colleen1 aGraves, Christina1 aOstrander, Aaron1 aPalma, Gregory uhttp://www.combinatorics.org/ojs/index.php/eljc/article/view/221101526nas a2200157 4500008004100000245005100041210005000092260001500142520108300157100002201240700001901262700001701281700001601298700001701314856003701331 2011 eng d00aContinuous-variable quantum compressed sensing0 aContinuousvariable quantum compressed sensing c2011/11/033 a We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise. 1 aOhliger, Matthias1 aNesme, Vincent1 aGross, David1 aLiu, Yi-Kai1 aEisert, Jens uhttp://arxiv.org/abs/1111.0853v301088nas a2200169 4500008004100000245005200041210005100093260001400144490000800158520060000166100002500766700002400791700002600815700001700841700002300858856003700881 2011 eng d00aPhoton-Photon Interactions via Rydberg Blockade0 aPhotonPhoton Interactions via Rydberg Blockade c2011/9/220 v1073 a We develop the theory of light propagation under the conditions of electromagnetically induced transparency (EIT) in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving few-photon pulses. We demonstrate that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon quantum gates, as well as for studying many-body phenomena with strongly correlated photons. 1 aGorshkov, Alexey, V.1 aOtterbach, Johannes1 aFleischhauer, Michael1 aPohl, Thomas1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/1103.3700v101458nas a2200145 4500008004100000245005700041210005600098260001500154520102700169100002301196700001801219700002101237700001701258856003701275 2010 eng d00aCharacterization of universal two-qubit Hamiltonians0 aCharacterization of universal twoqubit Hamiltonians c2010/04/093 a Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of qubits. We say H is n-universal if it can be used to approximate any unitary operation on n qubits. While it is well known that almost any 2-qubit Hamiltonian is 2-universal (Deutsch, Barenco, Ekert 1995; Lloyd 1995), an explicit characterization of the set of non-universal 2-qubit Hamiltonians has been elusive. Our main result is a complete characterization of 2-non-universal 2-qubit Hamiltonians. In particular, there are three ways that a 2-qubit Hamiltonian H can fail to be universal: (1) H shares an eigenvector with the gate that swaps two qubits, (2) H acts on the two qubits independently (in any of a certain family of bases), or (3) H has zero trace. A 2-non-universal 2-qubit Hamiltonian can still be n-universal for some n >= 3. We give some partial results on 3-universality. Finally, we also show how our characterization of 2-universal Hamiltonians implies the well-known result that almost any 2-qubit unitary is universal. 1 aChilds, Andrew, M.1 aLeung, Debbie1 aMancinska, Laura1 aOzols, Maris uhttp://arxiv.org/abs/1004.1645v201038nas a2200169 4500008004100000245008300041210006900124260001300193490000800206520050000214100002500714700002400739700001900763700002600782700002300808856003700831 2010 eng d00aPhotonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain 0 aPhotonic Phase Gate via an Exchange of Fermionic Spin Waves in a c2010/8/50 v1053 a We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the pi phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed. 1 aGorshkov, Alexey, V.1 aOtterbach, Johannes1 aDemler, Eugene1 aFleischhauer, Michael1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/1001.0968v302052nas a2200193 4500008004100000245002200041210002200063260001300085300001200098490000800110520156800118100002301686700001901709700002201728700002301750700002401773700002401797856003701821 2010 eng d00aQuantum Computing0 aQuantum Computing c2010/3/4 a45 - 530 v4643 a Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future. 1 aLadd, Thaddeus, D.1 aJelezko, Fedor1 aLaflamme, Raymond1 aNakamura, Yasunobu1 aMonroe, Christopher1 aO'Brien, Jeremy, L. uhttp://arxiv.org/abs/1009.2267v101174nas a2200133 4500008004100000245005700041210005700098260001500155490000600170520076400176100002500940700002400965856005100989 2009 eng d00aLocality Bounds on Hamiltonians for Stabilizer Codes0 aLocality Bounds on Hamiltonians for Stabilizer Codes c2009/09/220 v93 aIn this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of k-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations. 1 aBullock, Stephen, S.1 aO'Leary, Dianne, P. uhttp://www.cs.umd.edu/~oleary/reprints/j91.pdf01260nas a2200133 4500008004100000245010100041210006900142260001400211490000700225520080900232100002401041700002401065856003701089 2009 eng d00aQuadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing 0 aQuadratic fermionic interactions yield effective Hamiltonians fo c2009/3/240 v793 a Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. A direct consequence is that the one-dimensional cluster state can be found in polynomial time using adiabatic quantum computing. 1 aO'Hara, Michael, J.1 aO'Leary, Dianne, P. uhttp://arxiv.org/abs/0808.1768v101156nas a2200133 4500008004100000245005100041210004700092260001400139490000700153520077700160100002400937700002400961856003700985 2008 eng d00aThe adiabatic theorem in the presence of noise0 aadiabatic theorem in the presence of noise c2008/4/220 v773 a We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee the adiabatic approximation performs within a prescribed tolerance. Our new results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field, and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results. 1 aO'Hara, Michael, J.1 aO'Leary, Dianne, P. uhttp://arxiv.org/abs/0801.3872v101525nas a2200145 4500008004100000245005200041210005200093260001400145490000700159520109700166100002401263700002301287700002501310856004401335 2006 eng d00aParallelism for Quantum Computation with Qudits0 aParallelism for Quantum Computation with Qudits c2006/9/280 v743 a Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a protocol for implementing parallelized non-local two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates. 1 aO'Leary, Dianne, P.1 aBrennen, Gavin, K.1 aBullock, Stephen, S. uhttp://arxiv.org/abs/quant-ph/0603081v101765nas a2200145 4500008004100000245006400041210006300105260001400168490000700182520131400189100002501503700002401528700002301552856004401575 2005 eng d00aAsymptotically Optimal Quantum Circuits for d-level Systems0 aAsymptotically Optimal Quantum Circuits for dlevel Systems c2005/6/140 v943 a As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an n-qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa (VMS) use the QR matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a generic (symmetry-less) n-qudit evolution. However, the VMS result applied to virtual-qubits only recovers optimal order in the case that d is a power of two. We further construct a QR decomposition for d-multi-level quantum logics, proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing the complexity question for all d-level systems (d finite.) Gray codes are not required, and the optimal Theta(d^{2n}) asymptotic also applies to gate libraries where two-qudit interactions are restricted by a choice of certain architectures. 1 aBullock, Stephen, S.1 aO'Leary, Dianne, P.1 aBrennen, Gavin, K. uhttp://arxiv.org/abs/quant-ph/0410116v201715nas a2200145 4500008004100000245004200041210004200083260001400125490000700139520130700146100002301453700002401476700002501500856004401525 2005 eng d00aCriteria for Exact Qudit Universality0 aCriteria for Exact Qudit Universality c2005/5/160 v713 a We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states |0>, |1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. Their technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H_{jk}^x=\hbar\Omega (|k>k iff H_{jk}^{x,y} are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=-\hbar\Omega |d-1,d-1>