01716nas a2200169 4500008004100000245005800041210005800099260001300157520120700170100002501377700002001402700001801422700002801440700001901468700002201487856003701509 2024 eng d00aIntegrability of Goldilocks quantum cellular automata0 aIntegrability of Goldilocks quantum cellular automata c4/3/20243 a

Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in opposite basis states. Here, we prove that a subclass of Goldilocks QCA -- including the one implemented experimentally -- map onto free fermions and therefore can be classically simulated efficiently. We support this claim with two independent proofs, one involving a Jordan--Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers against known solutions. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, the latter QCA conserve one quantity useful for error mitigation. Our work provides a parametric quantum circuit with tunable integrability properties with which to test quantum hardware.

1 aHillberry, Logan, E.1 aPiroli, Lorenzo1 aVernier, Eric1 aHalpern, Nicole, Yunger1 aProsen, Tomaž1 aCarr, Lincoln, D. uhttps://arxiv.org/abs/2404.0299401404nas 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/2310.0705801778nas a2200157 4500008004100000245006400041210006300105260001400168520129800182100001301480700002201493700001901515700002401534700002501558856003701583 2023 eng d00aImproved Digital Quantum Simulation by Non-Unitary Channels0 aImproved Digital Quantum Simulation by NonUnitary Channels c7/24/20233 a

Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the randomization of Suzuki-Trotter product formulas have been shown to be a powerful approach to reducing the errors of quantum simulation and lowering the gate count. In this paper, we study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations. We focus our analysis on two approaches for constructing circuit ensembles for averaging: (i) permuting the order of the terms in the Hamiltonian and (ii) applying a set of global symmetry transformations. We compare our analytical error bounds to empirical performance and show that empirical error reduction surpasses our analytical estimates in most cases. Finally, we test our method on an IonQ trapped-ion quantum computer accessed via the Amazon Braket cloud platform, and benchmark the performance of the averaging approach.

1 aGong, W.1 aKharkov, Yaroslav1 aTran, Minh, C.1 aBienias, Przemyslaw1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2307.1302801951nas a2200217 4500008004100000245008300041210006900124260001500193490000600208520129200214100002001506700002301526700001701549700002201566700002401588700002301612700001301635700002301648700002501671856003701696 2022 eng d00aImplementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions0 aImplementing a Fast Unbounded Quantum Fanout Gate Using PowerLaw c10/27/20220 v43 a

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α≤D. As a corollary, we show that power-law systems with α≤D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques. 

1 aGuo, Andrew, Y.1 aDeshpande, Abhinav1 aChu, Su-Kuan1 aEldredge, Zachary1 aBienias, Przemyslaw1 aDevulapalli, Dhruv1 aSu, Yuan1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2007.0066202357nas a2200145 4500008004100000245007100041210006900112260001400181490000600195520190500201100002302106700002502129700002002154856003702174 2022 eng d00aImportance of the Spectral gap in Estimating Ground-State Energies0 aImportance of the Spectral gap in Estimating GroundState Energie c12/9/20220 v33 a

The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields. The main object of study is the LocalHamiltonian problem, which is concerned with estimating the ground-state energy of a local Hamiltonian and is complete for the class QMA, a quantum generalization of the class NP. A major challenge in the field is to understand the complexity of the LocalHamiltonian problem in more physically natural parameter regimes. One crucial parameter in understanding the ground space of any Hamiltonian in many-body physics is the spectral gap, which is the difference between the smallest two eigenvalues. Despite its importance in quantum many-body physics, the role played by the spectral gap in the complexity of the LocalHamiltonian is less well-understood. In this work, we make progress on this question by considering the precise regime, in which one estimates the ground-state energy to within inverse exponential precision. Computing ground-state energies precisely is a task that is important for quantum chemistry and quantum many-body physics.
In the setting of inverse-exponential precision, there is a surprising result that the complexity of LocalHamiltonian is magnified from QMA to PSPACE, the class of problems solvable in polynomial space. We clarify the reason behind this boost in complexity. Specifically, we show that the full complexity of the high precision case only comes about when the spectral gap is exponentially small. As a consequence of the proof techniques developed to show our results, we uncover important implications for the representability and circuit complexity of ground states of local Hamiltonians, the theory of uniqueness of quantum witnesses, and techniques for the amplification of quantum witnesses in the presence of postselection.

1 aDeshpande, Abhinav1 aGorshkov, Alexey, V.1 aFefferman, Bill uhttps://arxiv.org/abs/2007.1158201641nas a2200181 4500008004100000245008700041210006900128260001400197520106300211100001801274700002301292700002101315700002001336700002701356700002001383700001901403856003701422 2022 eng d00aInfinite-randomness criticality in monitored quantum dynamics with static disorder0 aInfiniterandomness criticality in monitored quantum dynamics wit c5/27/20223 a

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size ℓ scales as S∼ℓ√; moreover, the dynamical critical exponent z=∞. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion. 

1 aZabalo, Aidan1 aWilson, Justin, H.1 aGullans, Michael1 aVasseur, Romain1 aGopalakrishnan, Sarang1 aHuse, David, A.1 aPixley, J., H. uhttps://arxiv.org/abs/2205.1400201220nas a2200157 4500008004100000245008300041210006900124260001400193300001100207490000800218520072400226100001800950700002200968700001500990856005701005 2022 eng d00aIsolation and manipulation of a single-donor detector in a silicon quantum dot0 aIsolation and manipulation of a singledonor detector in a silico c9/27/2022 a1254230 v1063 a

We demonstrate the isolation and electrostatic control of a single phosphorus donor in a silicon quantum dot by making use of source-drain bias during cooldown and biases applied to capacitively coupled gates. Characterization of the device at low temperatures and in magnetic fields shows single donors can be electrostatically isolated near one of the quantum dot's tunnel barriers with either single or double occupancy. This model is well supported by capacitance-based simulations. The ability to use the D 0 state of such isolated donors as a charge detector is demonstrated by observing the charge stability diagram of a nearby and capacitively coupled semiconnected double quantum dot.

1 aLasek, A., A.1 aBarnes, C., H. W.1 aFerrus, T. uhttps://link.aps.org/doi/10.1103/PhysRevB.106.12542301365nas a2200145 4500008004100000245008500041210006900126260001400195520089800209100001801107700001901125700001601144700002201160856003701182 2021 eng d00aOn the Impossibility of Post-Quantum Black-Box Zero-Knowledge in Constant Rounds0 aImpossibility of PostQuantum BlackBox ZeroKnowledge in Constant  c3/20/20213 a

We investigate the existence of constant-round post-quantum black-box zero-knowledge protocols for NP. As a main result, we show that there is no constant-round post-quantum black-box zero-knowledge argument for NP unless NP⊆BQP. As constant-round black-box zero-knowledge arguments for NP exist in the classical setting, our main result points out a fundamental difference between post-quantum and classical zero-knowledge protocols. Combining previous results, we conclude that unless NP⊆BQP, constant-round post-quantum zero-knowledge protocols for NP exist if and only if we use non-black-box techniques or relax certain security requirements such as relaxing standard zero-knowledge to ϵ-zero-knowledge. Additionally, we also prove that three-round and public-coin constant-round post-quantum black-box ϵ-zero-knowledge arguments for NP do not exist unless NP⊆BQP.

1 aChia, Nai-Hui1 aChung, Kai-Min1 aLiu, Qipeng1 aYamakawa, Takashi uhttps://arxiv.org/abs/2103.1124402349nas a2200313 4500008004100000245007100041210006900112260001400181520145100195100001601646700003401662700001701696700001801713700001301731700001801744700001901762700002101781700001401802700002201816700001601838700002501854700001801879700001901897700002001916700002001936700001801956700002401974856003701998 2021 eng d00aInteractive Protocols for Classically-Verifiable Quantum Advantage0 aInteractive Protocols for ClassicallyVerifiable Quantum Advantag c12/9/20213 a

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor's algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use "interactions" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover's responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.

1 aZhu, Daiwei1 aKahanamoku-Meyer, Gregory, D.1 aLewis, Laura1 aNoel, Crystal1 aKatz, Or1 aHarraz, Bahaa1 aWang, Qingfeng1 aRisinger, Andrew1 aFeng, Lei1 aBiswas, Debopriyo1 aEgan, Laird1 aGheorghiu, Alexandru1 aNam, Yunseong1 aVidick, Thomas1 aVazirani, Umesh1 aYao, Norman, Y.1 aCetina, Marko1 aMonroe, Christopher uhttps://arxiv.org/abs/2112.0515601231nas a2200121 4500008004100000245006200041210005800103260001100161300001200172520081200184100001700996856009601013 2020 eng d00aThe impossibility of efficient quantum weak coin flipping0 aimpossibility of efficient quantum weak coin flipping c6/2020 a916-9293 a

How can two parties with competing interests carry out a fair coin flip across a quantum communication channel? This problem (quantum weak coin-flipping) was formalized more than 15 years ago, and, despite some phenomenal theoretical progress, practical quantum coin-flipping protocols with vanishing bias have proved hard to find. In the current work we show that there is a reason that practical weak quantum coin-flipping is difficult: any quantum weak coin-flipping protocol with bias є must use at least exp( Ω (1/√є )) rounds of communication. This is a large improvement over the previous best known lower bound of Ω ( log log(1/є )) due to Ambainis from 2004. Our proof is based on a theoretical construction (the two-variable profile function) which may find further applications.

1 aMiller, Carl uhttps://www.quics.umd.edu/publications/impossibility-efficient-quantum-weak-coin-flipping-001375nas a2200145 4500008004100000245008100041210006900122260001400191520090600205100001901111700002101130700001601151700002501167856003701192 2020 eng d00aImpossibility of Quantum Virtual Black-Box Obfuscation of Classical Circuits0 aImpossibility of Quantum Virtual BlackBox Obfuscation of Classic c5/13/20203 a

Virtual black-box obfuscation is a strong cryptographic primitive: it encrypts a circuit while maintaining its full input/output functionality. A remarkable result by Barak et al. (Crypto 2001) shows that a general obfuscator that obfuscates classical circuits into classical circuits cannot exist. A promising direction that circumvents this impossibility result is to obfuscate classical circuits into quantum states, which would potentially be better capable of hiding information about the obfuscated circuit. We show that, under the assumption that learning-with-errors (LWE) is hard for quantum computers, this quantum variant of virtual black-box obfuscation of classical circuits is generally impossible. On the way, we show that under the presence of dependent classical auxiliary input, even the small class of classical point functions cannot be quantum virtual black-box obfuscated.

1 aAlagic, Gorjan1 aBrakerski, Zvika1 aDulek, Yfke1 aSchaffner, Christian uhttps://arxiv.org/abs/2005.0643201721nas a2200121 4500008004100000245007400041210006900115260001400184520132600198100001901524700001901543856003701562 2020 eng d00aInformation scrambling at finite temperature in local quantum systems0 aInformation scrambling at finite temperature in local quantum sy c5/21/20203 a

This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, m, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature T. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O(N) non-linear sigma model, which is analytically tractable at large N. Using the ladder diagram technique, we find that operators spread at a speed T/m−−−−√ at low temperatures, T≪m. In contrast to the numerical findings of spin chain, the large N computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.

1 aSahu, Subhayan1 aSwingle, Brian uhttps://arxiv.org/abs/2005.1081401721nas a2200121 4500008004100000245007400041210006900115260001400184520132600198100001901524700001901543856003701562 2020 eng d00aInformation scrambling at finite temperature in local quantum systems0 aInformation scrambling at finite temperature in local quantum sy c5/21/20203 a

This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, m, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature T. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O(N) non-linear sigma model, which is analytically tractable at large N. Using the ladder diagram technique, we find that operators spread at a speed T/m−−−−√ at low temperatures, T≪m. In contrast to the numerical findings of spin chain, the large N computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.

1 aSahu, Subhayan1 aSwingle, Brian uhttps://arxiv.org/abs/2005.1081401878nas a2200169 4500008004100000245007200041210006900113260001500182490000800197520135800205100002801563700001801591700001601609700002501625700002201650856003601672 2019 eng d00aInteracting Qubit-Photon Bound States with Superconducting Circuits0 aInteracting QubitPhoton Bound States with Superconducting Circui c2018/01/300 vX 93 a

Qubits strongly coupled to a photonic crystal give rise to many exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Here, we present experimental results from a device with two qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and inter-bound state interactions. We observe a fourth-order two photon virtual process between bound states indicating strong coupling between the photonic crystal and qubits. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits' spatial organization, a key criterion for realization of certain quantum many-body models. The widely tunable, strong and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems of bound states.

1 aSundaresan, Neereja, M.1 aLundgren, Rex1 aZhu, Guanyu1 aGorshkov, Alexey, V.1 aHouck, Andrew, A. uhttp://arxiv.org/abs/1801.1016701253nas a2200145 4500008004100000245008900041210006900130260001500199490000800214520078100222100002101003700002501024700002101049856003701070 2019 eng d00aInteraction-induced transition in the quantum chaotic dynamics of a disordered metal0 aInteractioninduced transition in the quantum chaotic dynamics of c03/25/20190 v4053 a

We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.

1 aSyzranov, S., V.1 aGorshkov, Alexey, V.1 aGalitski, V., M. uhttps://arxiv.org/abs/1709.0929601480nas 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/1908.0280201552nas a2200109 4500008004100000245008900041210006900130520116300199100002701362700001601389856003701405 2018 eng d00aImplicit regularization and solution uniqueness in over-parameterized matrix sensing0 aImplicit regularization and solution uniqueness in overparameter3 a

We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-r positive semi-definite (PSD) matrices in Rn×n, with a sensing mechanism that satisfies the restricted isometry property (RIP). The algorithm we study is that of \emph{factored gradient descent}, where we model the low-rankness and PSD constraints with the factorization UU⊤, where U∈Rn×r. Surprisingly, recent work argues that the choice of r≤n is not pivotal: even setting U∈Rn×n is sufficient for factored gradient descent to find the rank-r solution, which suggests that operating over the factors leads to an implicit regularization. In this note, we provide a different perspective. We show that, in the noiseless case, under certain conditions, the PSD constraint by itself is sufficient to lead to a unique rank-r matrix recovery, without implicit or explicit low-rank regularization. \emph{I.e.}, under assumptions, the set of PSD matrices, that are consistent with the observed data, is a singleton, irrespective of the algorithm used.

1 aKyrillidis, Anastasios1 aKalev, Amir uhttps://arxiv.org/abs/1806.0204601190nas a2200109 4500008004100000245007100041210006800112300000700180520083900187100001701026856003701043 2018 eng d00aIn Defense of a "Single-World" Interpretation of Quantum Mechanics0 aIn Defense of a SingleWorld Interpretation of Quantum Mechanics a153 a

In a recent result, Frauchiger and Renner argue that if quantum theory accurately describes complex systems like observers who perform measurements, then "we are forced to give up the view that there is one single reality." Following a review of the Frauchiger-Renner argument, I argue that quantum mechanics should be understood probabilistically, as a new sort of non-Boolean probability theory, rather than representationally, as a theory about the elementary constituents of the physical world and how these elements evolve dynamically over time. I show that this way of understanding quantum mechanics is not in conflict with a consistent "single-world" interpretation of the theory.

1 aBub, Jeffrey uhttps://arxiv.org/abs/1804.0326701169nas a2200133 4500008004100000245009300041210006900134260001500203520072300218100001900941700001900960700001900979856003700998 2018 eng d00aInformation-Theoretic Privacy For Distributed Average Consensus: Bounded Integral Inputs0 aInformationTheoretic Privacy For Distributed Average Consensus B c03/28/20193 a

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding passive adversarial agents, as long as the set of colluding passive adversarial agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents' inputs against any t colluding agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. The agent' inputs are bounded integers, where the bounds are apriori known to all the agents.

1 aGupta, Nirupam1 aKatz, Jonathan1 aChopra, Nikhil uhttps://arxiv.org/abs/1809.0179406429nas a2200121 4500008004100000245006700041210006600108520603900174100001906213700001906232700001906251856003706270 2018 eng d00aInformation-Theoretic Privacy in Distributed Average Consensus0 aInformationTheoretic Privacy in Distributed Average Consensus3 a

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding semi-honest (passively adversarial) agents, as long as the set of colluding semi-honest agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents' inputs against any t colluding semi-honest agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. 

1 aGupta, Nirupam1 aKatz, Jonathan1 aChopra, Nikhil uhttps://arxiv.org/abs/1809.0179401674nas a2200181 4500008004100000245007500041210006900116260001500185300001100200490000700211520113600218100001501354700001101369700001901380700001801399700001901417856005601436 2017 eng d00aInput-output theory for spin-photon coupling in Si double quantum dots0 aInputoutput theory for spinphoton coupling in Si double quantum  c2017/12/22 a2354340 v963 a

The interaction of qubits via microwave frequency photons enables long-distance qubit-qubit coupling and facilitates the realization of a large-scale quantum processor. However, qubits based on electron spins in semiconductor quantum dots have proven challenging to couple to microwave photons. In this theoretical work we show that a sizable coupling for a single electron spin is possible via spin-charge hybridization using a magnetic field gradient in a silicon double quantum dot. Based on parameters already shown in recent experiments, we predict optimal working points to achieve a coherent spin-photon coupling, an essential ingredient for the generation of long-range entanglement. Furthermore, we employ input-output theory to identify observable signatures of spin-photon coupling in the cavity output field, which may provide guidance to the experimental search for strong coupling in such spin-photon systems and opens the way to cavity-based readout of the spin qubit.

1 aBenito, M.1 aMi, X.1 aTaylor, J., M.1 aPetta, J., R.1 aBurkard, Guido uhttps://link.aps.org/doi/10.1103/PhysRevB.96.23543401550nas a2200145 4500008004100000245009200041210006900133260001500202300001100217490000800228520107800236100002001314700001901334856005101353 2016 eng d00aInteracting atomic interferometry for rotation sensing approaching the Heisenberg Limit0 aInteracting atomic interferometry for rotation sensing approachi c2016/11/11 a2030020 v1173 a

Atom interferometers provide exquisite measurements of the properties of non-inertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly-interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent non-interacting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.

1 aRagole, Stephen1 aTaylor, J., M. uhttps://doi.org/10.1103/PhysRevLett.117.20300201515nas a2200181 4500008004100000245007100041210006900112260001500181300001100196490000700207520099200214100001701206700001601223700002101239700001901260700001801279856003601297 2015 eng d00aInjection Locking of a Semiconductor Double Quantum Dot Micromaser0 aInjection Locking of a Semiconductor Double Quantum Dot Micromas c2015/11/02 a0538020 v923 a Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models. 1 aLiu, Y., -Y.1 aStehlik, J.1 aGullans, Michael1 aTaylor, J., M.1 aPetta, J., R. uhttp://arxiv.org/abs/1508.0414701205nas a2200145 4500008004100000245007600041210006900117260001500186490000700201520076300208100001500971700001900986700001701005856003701022 2013 eng d00aIndividual Addressing in Quantum Computation through Spatial Refocusing0 aIndividual Addressing in Quantum Computation through Spatial Ref c2013/11/210 v883 a Separate addressing of individual qubits is a challenging requirement for scalable quantum computation, and crosstalk between operations on neighboring qubits remains as a significant source of noise for current experimental implementation of multi-qubit platforms. We propose a scheme based on spatial refocusing from interference of several coherent laser beams to significantly reduce the crosstalk noise for any type of quantum gates. A general framework is developed for the spatial refocusing technique, in particular with practical Gaussian beams, and we show under typical experimental conditions, the crosstalk-induced infidelity of quantum gates can be reduced by several orders of magnitude with a moderate cost of a few correction laser beams. 1 aShen, Chao1 aGong, Zhe-Xuan1 aDuan, Luming uhttp://arxiv.org/abs/1305.2798v300982nas 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/1306.5992v101002nas a2200193 4500008004100000020002200041245005400063210005100117260001500168300001200183490000900195520045300204100002500657700002900682700001900711700002000730700002100750856003700771 2013 eng d a978-3-642-38986-300aAn Introduction to Quantum Programming in Quipper0 aIntroduction to Quantum Programming in Quipper c2013/07/05 a110-1240 v79483 a Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quipper's language features by developing a few well known examples of Quantum computation, including quantum teleportation, the quantum Fourier transform, and a quantum circuit for addition. 1 aGreen, Alexander, S.1 aLumsdaine, Peter, LeFanu1 aRoss, Neil, J.1 aSelinger, Peter1 aValiron, Benoît uhttp://arxiv.org/abs/1304.5485v101106nas a2200145 4500008004100000245006700041210006700108260001300175490000700188520065800195100002700853700002100880700002200901856003700923 2011 eng d00aImplications of the Babinet Principle for Casimir Interactions0 aImplications of the Babinet Principle for Casimir Interactions c2011/9/10 v843 a We formulate the Babinet Principle (BP) as a relation between the scattering amplitudes for electromagnetic waves, and combine it with multiple scattering techniques to derive new properties of Casimir forces. We show that the Casimir force exerted by a planar conductor or dielectric on a self- complementary perforated planar mirror is approximately half that on a uniform mirror independent of the distance between them. The BP suggests that Casimir edge effects are anomalously small, supporting results obtained earlier in special cases. Finally, we illustrate how the BP can be used to estimate Casimir forces between perforated planar mirrors. 1 aMaghrebi, Mohammad, F.1 aAbravanel, Ronen1 aJaffe, Robert, L. uhttp://arxiv.org/abs/1103.5395v100913nas a2200145 4500008004100000245004700041210004700088260001300135490000700148520050500155100002600660700001900686700002500705856003700730 2011 eng d00aInterferometry with Synthetic Gauge Fields0 aInterferometry with Synthetic Gauge Fields c2011/3/30 v833 aWe propose a compact atom interferometry scheme for measuring weak, time-dependent accelerations. Our proposal uses an ensemble of dilute trapped bosons with two internal states that couple to a synthetic gauge field with opposite charges. The trapped gauge field couples spin to momentum to allow time dependent accelerations to be continuously imparted on the internal states. We generalize this system to reduce noise and estimate the sensitivity of such a system to be S~10^-7 m / s^2 / Hz^1/2. 1 aAnderson, Brandon, M.1 aTaylor, J., M.1 aGalitski, Victor, M. uhttp://arxiv.org/abs/1008.3910v201273nas a2200145 4500008004100000245009500041210006900136260001400205490000700219520078700226100002301013700002401036700002301060856004401083 2007 eng d00aImproved quantum algorithms for the ordered search problem via semidefinite programming 0 aImproved quantum algorithms for the ordered search problem via s c2007/3/260 v753 a One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm. 1 aChilds, Andrew, M.1 aLandahl, Andrew, J.1 aParrilo, Pablo, A. uhttp://arxiv.org/abs/quant-ph/0608161v1