@article {3493, title = {Topology and entanglement of molecular phase space}, year = {2024}, month = {3/7/2024}, abstract = {

We formulate a quantum phase space for molecular rotational and nuclear-spin states. Taking in molecular geometry and nuclear-spin data, our framework yields admissible position and momentum states, inter-convertible via a generalized Fourier transform. We classify molecules into three types -- asymmetric, rotationally symmetric, and perrotationally symmetric -- with the last type having no macroscopic analogue due to nuclear-spin statistics constraints. We identify two features in perrotationally symmetric state spaces that are Hamiltonian-independent and induced solely by symmetry and spin statistics. First, many molecular species are intrinsically rotation-spin entangled in a way that cannot be broken without transitioning to another species or breaking symmetry. Second, each molecular position state houses an internal pseudo-spin or \"fiber\" degree of freedom, and the fiber\&$\#$39;s Berry phase or matrix after adiabatic changes in position yields naturally robust operations, akin to braiding anyonic quasiparticles or realizing fault-tolerant quantum gates. We outline scenarios where these features can be experimentally probed.

}, url = {https://arxiv.org/abs/2403.04572}, author = {Victor V. Albert and Eric Kubischta and Mikhail Lemeshko and Lee R. Liu} } @article {3509, title = {Trainability Barriers in Low-Depth QAOA Landscapes}, year = {2024}, month = {2/15/2024}, abstract = {

The Quantum Alternating Operator Ansatz (QAOA) is a prominent variational quantum algorithm for solving combinatorial optimization problems. Its effectiveness depends on identifying input parameters that yield high-quality solutions. However, understanding the complexity of training QAOA remains an under-explored area. Previous results have given analytical performance guarantees for a small, fixed number of parameters. At the opposite end of the spectrum, barren plateaus are likely to emerge at Ω(n) parameters for n qubits. In this work, we study the difficulty of training in the intermediate regime, which is the focus of most current numerical studies and near-term hardware implementations. Through extensive numerical analysis of the quality and quantity of local minima, we argue that QAOA landscapes can exhibit a superpolynomial growth in the number of low-quality local minima even when the number of parameters scales logarithmically with n. This means that the common technique of gradient descent from randomly initialized parameters is doomed to fail beyond small n, and emphasizes the need for good initial guesses of the optimal parameters.

}, url = {https://arxiv.org/abs/2402.10188}, author = {Joel Rajakumar and John Golden and Andreas B{\"a}rtschi and Stephan Eidenbenz} } @article {3270, title = {A theory of quantum differential equation solvers: limitations and fast-forwarding}, year = {2023}, month = {3/2/2023}, abstract = {

We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous. On the one hand, for generic homogeneous linear ODEs, by proving worst-case lower bounds, we show that quantum algorithms suffer from computational overheads due to two types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39;: real part gap and non-normality of the coefficient matrix. We then show that homogeneous ODEs in the absence of both types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39; are equivalent to quantum dynamics, and reach the conclusion that quantum algorithms for quantum dynamics work best. We generalize our results to the inhomogeneous case and find that existing generic quantum ODE solvers cannot be substantially improved. To obtain these lower bounds, we propose a general framework for proving lower bounds on quantum algorithms that are amplifiers, meaning that they amplify the difference between a pair of input quantum states. On the other hand, we show how to fast-forward quantum algorithms for solving special classes of ODEs which leads to improved efficiency. More specifically, we obtain quadratic improvements in the evolution time T for inhomogeneous ODEs with a negative semi-definite coefficient matrix, and exponential improvements in both T and the spectral norm of the coefficient matrix for inhomogeneous ODEs with efficiently implementable eigensystems, including various spatially discretized linear evolutionary partial differential equations. We give fast-forwarding algorithms that are conceptually different from existing ones in the sense that they neither require time discretization nor solving high-dimensional linear systems.

}, url = {https://arxiv.org/abs/2211.05246}, author = {Dong An and Jin-Peng Liu and Daochen Wang and Qi Zhao} } @article {3288, title = {Thermally driven quantum refrigerator autonomously resets superconducting qubit}, year = {2023}, month = {5/26/2023}, abstract = {

The first thermal machines steered the industrial revolution, but their quantum analogs have yet to prove useful. Here, we demonstrate a useful quantum absorption refrigerator formed from superconducting circuits. We use it to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments. The environments consist of microwave waveguides populated with synthesized thermal photons. The target qubit, if initially fully excited, reaches a steady-state excited-level population of 5\×10\−4\±5\×10\−4 (an effective temperature of 23.5~mK) in about 1.6~μs. Our results epitomize how quantum thermal machines can be leveraged for quantum information-processing tasks. They also initiate a path toward experimental studies of quantum thermodynamics with superconducting circuits coupled to propagating thermal microwave fields.

}, url = {https://arxiv.org/abs/2305.16710}, author = {Mohammed Ali Aamir and Paul Jamet Suria and Jos{\'e} Antonio Mar{\'\i}n Guzm{\'a}n and Claudia Castillo-Moreno and Jeffrey M. Epstein and Nicole Yunger Halpern and Simone Gasparinetti} } @article {3418, title = {Thresholds in the Robustness of Error Mitigation in Noisy Quantum Dynamics}, year = {2023}, month = {10/30/2023}, abstract = {

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of such strategies when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of a threshold in the robustness of error mitigation for random spatially local circuits in spatial dimensions D\≥2: noise characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an O(1) time for any imperfection in the characterization of disorder. As a result, error mitigation is only a practical method for sufficiently well-characterized noise. We discuss further implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

}, url = {https://arxiv.org/abs/2302.04278}, author = {Pradeep Niroula and Sarang Gopalakrishnan and Michael Gullans} } @article {3206, title = {Time-energy uncertainty relation for noisy quantum metrology}, journal = {PRX Quantum}, volume = {4(4)}, year = {2023}, month = {12/5/2023}, abstract = {

Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. We consider a quantum system initialized in a pure state and whose evolution is goverened by a Hamiltonian H; a measurement can later estimate the time t for which the system has evolved. In this work, we introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which Alice prepares an initial pure state of the clock, allows the clock to evolve for a time t that is not precisely known, and then transmits the clock through a noisy channel to Bob. The environment (Eve) receives any information that is lost. We prove that Bob\&$\#$39;s loss of quantum Fisher information (QFI) about t is equal to Eve\&$\#$39;s gain of QFI about a complementary energy parameter. We also prove a more general trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two non-commuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise. These are a subset of the Knill-Laflamme error-correction conditions; states satisfying these conditions are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of our results to sensing using a many-body state subject to erasure or amplitude-damping noise.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.4.040336}, url = {https://arxiv.org/abs/2207.13707}, author = {Faist, Philippe and Woods, Mischa P. and Victor V. Albert and Renes, Joseph M. and Eisert, Jens and Preskill, John} } @article {3399, title = {Transition of Anticoncentration in Gaussian Boson Sampling}, year = {2023}, month = {12/13/2023}, abstract = {

Gaussian Boson Sampling is a promising method for experimental demonstrations of quantum advantage because it is easier to implement than other comparable schemes. While most of the properties of Gaussian Boson Sampling are understood to the same degree as for these other schemes, we understand relatively little about the statistical properties of its output distribution. The most relevant statistical property, from the perspective of demonstrating quantum advantage, is the anticoncentration of the output distribution as measured by its second moment. The degree of anticoncentration features in arguments for the complexity-theoretic hardness of Gaussian Boson Sampling, and it is also important to know when using cross-entropy benchmarking to verify experimental performance. In this work, we develop a graph-theoretic framework for analyzing the moments of the Gaussian Boson Sampling distribution. Using this framework, we show that Gaussian Boson Sampling undergoes a transition in anticoncentration as a function of the number of modes that are initially squeezed compared to the number of photons measured at the end of the circuit. When the number of initially squeezed modes scales sufficiently slowly with the number of photons, there is a lack of anticoncentration. However, if the number of initially squeezed modes scales quickly enough, the output probabilities anticoncentrate weakly.

}, url = {https://arxiv.org/abs/2312.08433}, author = {Adam Ehrenberg and Joseph T. Iosue and Abhinav Deshpande and Dominik Hangleiter and Alexey V. Gorshkov} } @article {3308, title = {On the Two-sided Permutation Inversion Problem}, year = {2023}, month = {6/23/2023}, abstract = {

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This is a fundamental problem in query complexity, and appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation -- except that the challenge value cannot be submitted to the latter. Within that setting, we consider two options for the inversion algorithm: whether it can get quantum advice about the permutation, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the inversion problem, and establish a number of lower bounds. Our results indicate that, perhaps surprisingly, the inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse, provided it cannot query the challenge itself.

}, url = {https://arxiv.org/abs/2306.13729}, author = {Gorjan Alagic and Chen Bai and Alexander Poremba and Kaiyan Shi} } @article {3199, title = {Tailoring three-dimensional topological codes for biased noise}, year = {2022}, month = {11/3/2022}, abstract = {

Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for several advantages including a transversal implementation of non-Clifford logical gates, single-shot decoding strategies, parallelized decoding in the case of fracton codes as well as construction of fractal lattice codes. Motivated by this, we tailor 3D topological codes for enhanced storage performance under biased Pauli noise. We present Clifford deformations of various 3D topological codes, such that they exhibit a threshold error rate of 50\% under infinitely biased Pauli noise. Our examples include the 3D surface code on the cubic lattice, the 3D surface code on a checkerboard lattice that lends itself to a subsystem code with a single-shot decoder, the 3D color code, as well as fracton models such as the X-cube model, the Sierpinski model and the Haah code. We use the belief propagation with ordered statistics decoder (BP-OSD) to study threshold error rates at finite bias. We also present a rotated layout for the 3D surface code, which uses roughly half the number of physical qubits for the same code distance under appropriate boundary conditions. Imposing coprime periodic dimensions on this rotated layout leads to logical operators of weight O(n) at infinite bias and a corresponding exp[\−O(n)] subthreshold scaling of the logical failure rate, where n is the number of physical qubits in the code. Even though this scaling is unstable due to the existence of logical representations with O(1) low-rate Pauli errors, the number of such representations scales only polynomially for the Clifford-deformed code, leading to an enhanced effective distance.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.02116}, url = {https://arxiv.org/abs/2211.02116}, author = {Huang, Eric and Pesah, Arthur and Chubb, Christopher T. and Vasmer, Michael and Dua, Arpit} } @article {2765, title = {Theoretical bounds on data requirements for the ray-based classification}, journal = {SN Comput. Sci.}, volume = {3}, year = {2022}, month = {02/26/2022}, abstract = {

The problem of classifying high-dimensional shapes in real-world data grows in complexity as the dimension of the space increases. For the case of identifying convex shapes of different geometries, a new classification framework has recently been proposed in which the intersections of a set of one-dimensional representations, called rays, with the boundaries of the shape are used to identify the specific geometry. This ray-based classification (RBC) has been empirically verified using a synthetic dataset of two- and three-dimensional shapes [1] and, more recently, has also been validated experimentally [2]. Here, we establish a bound on the number of rays necessary for shape classification, defined by key angular metrics, for arbitrary convex shapes. For two dimensions, we derive a lower bound on the number of rays in terms of the shape\&$\#$39;s length, diameter, and exterior angles. For convex polytopes in R^N, we generalize this result to a similar bound given as a function of the dihedral angle and the geometrical parameters of polygonal faces. This result enables a different approach for estimating high-dimensional shapes using substantially fewer data elements than volumetric or surface-based approaches.

}, doi = {https://doi.org/10.1007/s42979-021-00921-0}, url = {https://arxiv.org/abs/2103.09577}, author = {Brian J. Weber and Sandesh S. Kalantre and Thomas McJunkin and J. M. Taylor and Justyna P. Zwolak} } @article {3192, title = {A theory of quantum differential equation solvers: limitations and fast-forwarding}, year = {2022}, month = {11/9/2022}, abstract = {

We study the limitations and fast-forwarding of quantum algorithms for solving linear ordinary differential equation (ODE) systems with particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous. On the one hand, for generic homogeneous linear ODEs, by proving worst-case lower bounds, we show that quantum algorithms suffer from computational overheads due to two types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39;: real part gap and non-normality of the coefficient matrix. We then show that ODEs in the absence of both types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39; are equivalent to quantum dynamics, and reach the conclusion that quantum algorithms for quantum dynamics work best. We generalize our results to the inhomogeneous case and find that existing generic quantum ODE solvers cannot be substantially improved. To obtain these lower bounds, we propose a general framework for proving lower bounds on quantum algorithms that are amplifiers, meaning that they amplify the difference between a pair of input quantum states. On the other hand, we show how to fast-forward quantum algorithms for solving special classes of ODEs which leads to improved efficiency. More specifically, we obtain quadratic to exponential improvements in terms of the evolution time T and the spectral norm of the coefficient matrix for the following classes of ODEs: inhomogeneous ODEs with a negative definite coefficient matrix, inhomogeneous ODEs with a coefficient matrix having an eigenbasis that can be efficiently prepared on a quantum computer and eigenvalues that can be efficiently computed classically, and the spatially discretized inhomogeneous heat equation and advection-diffusion equation. We give fast-forwarding algorithms that are conceptually different from existing ones in the sense that they neither require time discretization nor solving high-dimensional linear systems.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, Numerical Analysis (math.NA), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.05246}, url = {https://arxiv.org/abs/2211.05246}, author = {Dong An and Liu, Jin-Peng and Wang, Daochen and Zhao, Qi} } @article {3012, title = {Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond}, year = {2022}, month = {2/10/2022}, abstract = {

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by U(1)2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2n-dimensional qudits that feature surface anyons described by U(1)2n Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

}, keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2202.05442}, url = {https://arxiv.org/abs/2202.05442}, author = {Shirley, Wilbur and Chen, Yu-An and Dua, Arpit and Ellison, Tyler D. and Tantivasadakarn, Nathanan and Williamson, Dominic J.} } @article {3197, title = {Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr{\"o}dinger Equation}, journal = {Quantum}, volume = {6}, year = {2022}, month = {apr}, pages = {690}, abstract = {

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schr{\"o}dinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.

}, doi = {10.22331/q-2022-04-15-690}, url = {https://arxiv.org/abs/2111.03103v2}, author = {Dong An and Di Fang and Lin Lin} } @article {3069, title = {Topological Edge Mode Tapering}, year = {2022}, month = {6/14/2022}, abstract = {

Mode tapering, or the gradual manipulation of the size of some mode, is a requirement for any system that aims to efficiently interface two or more subsystems of different mode sizes. While high efficiency tapers have been demonstrated, they often come at the cost of a large device footprint or challenging fabrication. Topological photonics, offering robustness to certain types of disorder as well as chirality, has proved to be a well-suited design principle for numerous applications in recent years. Here we present a new kind of mode taper realized through topological bandgap engineering. We numerically demonstrate a sixfold change in mode width over an extremely compact 8μm distance with near unity efficiency in the optical domain. With suppressed backscattering and no excitation of higher-order modes, such a taper could enable new progress in the development of scalable, multi-component systems in classical and quantum optics.

}, url = {https://arxiv.org/abs/2206.07056}, author = {Christopher J. Flower and Sabyasachi Barik and Sunil Mittal and Mohammad Hafezi} } @article {3005, title = {Toward Robust Autotuning of Noisy Quantum dot Devices}, journal = {Physical Review Applied}, volume = {17}, year = {2022}, month = {02/26/2022}, abstract = {

The current autotuning approaches for quantum dot (QD) devices, while showing some success, lack an assessment of data reliability. This leads to unexpected failures when noisy or otherwise low-quality data is processed by an autonomous system. In this work, we propose a framework for robust autotuning of QD devices that combines a machine learning (ML) state classifier with a data quality control module. The data quality control module acts as a \"gatekeeper\" system, ensuring that only reliable data are processed by the state classifier. Lower data quality results in either device recalibration or termination. To train both ML systems, we enhance the QD simulation by incorporating synthetic noise typical of QD experiments. We confirm that the inclusion of synthetic noise in the training of the state classifier significantly improves the performance, resulting in an accuracy of 95.0(9) \% when tested on experimental data. We then validate the functionality of the data quality control module by showing that the state classifier performance deteriorates with decreasing data quality, as expected. Our results establish a robust and flexible ML framework for autonomous tuning of noisy QD devices.

}, doi = {https://doi.org/10.1103/PhysRevApplied.17.024069}, url = {https://arxiv.org/abs/2108.00043}, author = {Joshua Ziegler and Thomas McJunkin and E.S. Joseph and Sandesh S. Kalantre and Benjamin Harpt and D.E. Savage and M.G. Lagally and M.A. Eriksson and Jacob M. Taylor and Justyna P. Zwolak} } @article {3004, title = {Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice}, journal = {Science}, volume = {377}, year = {2022}, month = {8/18/2022}, pages = {885-889}, abstract = {

Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. Here, we do this by combining the fast, programmable control provided by optical tweezer arrays with the scalable, homogeneous environment of an optical lattice. Using this new combination of tools we study continuous-time quantum walks of single atoms on a 2D square lattice, and perform proof-of-principle demonstrations of spatial search using these walks. When scaled to more particles, the capabilities demonstrated here can be extended to study a variety of problems in quantum information science and quantum simulation, including the deterministic assembly of ground and excited states in Hubbard models with tunable interactions, and performing versions of spatial search in a larger graph with increased connectivity, where search by quantum walk can be more effective.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1126/science.abo0608}, url = {https://arxiv.org/abs/2202.01204}, author = {Young, Aaron W. and Eckner, William J. and Schine, Nathan and Andrew M. Childs and Kaufman, Adam M.} } @article {2774, title = {Testing quantum gravity with interactive information sensing}, year = {2021}, month = {1/27/2021}, abstract = {

We suggest a test of a central prediction of perturbatively quantized general relativity: the coherent communication of quantum information between massive objects through gravity. To do this, we introduce the concept of interactive quantum information sensing, a protocol tailored to the verification of dynamical entanglement generation between a pair of systems. Concretely, we propose to monitor the periodic wavefunction collapse and revival in an atomic interferometer which is gravitationally coupled to a mechanical oscillator. We prove a theorem which shows that, under the assumption of time-translation invariance, this collapse and revival is possible if and only if the gravitational interaction forms an entangling channel. Remarkably, as this approach improves at moderate temperatures and relies primarily upon atomic coherence, our numerical estimates indicate feasibility with current devices.

}, url = {https://arxiv.org/abs/2101.11629}, author = {Daniel Carney and Holger M{\"u}ller and Jacob M. Taylor} } @article {2506, title = {Theory of Trotter Error with Commutator Scaling}, journal = {Phys. Rev. X}, volume = {11}, year = {2021}, month = {2/1/2021}, pages = {49}, chapter = {011020}, abstract = {

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, k-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of 5, and is close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011020}, url = {https://arxiv.org/abs/1912.08854}, author = {Andrew M. Childs and Yuan Su and Minh C. Tran and Nathan Wiebe and Shuchen Zhu} } @article {2731, title = {A Threshold for Quantum Advantage in Derivative Pricing}, journal = {Quantum}, volume = {5}, year = {2021}, pages = {463}, abstract = {

We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing - the re-parameterization method - that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 7.5k logical qubits and a T-depth of 46 million and thus estimate that quantum advantage would require a logical clock speed of 10Mhz. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.\ 

}, doi = {https://doi.org/10.22331/q-2021-06-01-463}, url = {https://arxiv.org/abs/2012.03819}, author = {Shouvanik Chakrabarti and Rajiv Krishnakumar and Guglielmo Mazzola and Nikitas Stamatopoulos and Stefan Woerner and William J. Zeng} } @article {2909, title = {Tight bounds on the convergence of noisy random circuits to uniform}, year = {2021}, month = {12/1/2021}, abstract = {

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work.\ 

}, url = {https://arxiv.org/abs/2112.00716}, author = {Abhinav Deshpande and Bill Fefferman and Alexey V. Gorshkov and Michael Gullans and Pradeep Niroula and Oles Shtanko} } @article {2414, title = {Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point}, journal = {Phys. Rev. B}, volume = {103}, year = {2021}, month = {3/15/2021}, pages = {125128}, abstract = {

We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with nD=4 component Dirac spinors in D=(2+1) dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or π-flux square lattice. The torus energy spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here, we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical torus energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus energy spectrum analytically using the perturbative expansion in ε=4\−D, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar order-parameter field strongly influences the critical torus energy spectrum and we observe prominent multiplicity features related to an emergent symmetry predicted from the quantum field theory. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum.

}, doi = {https://doi.org/10.1103/PhysRevB.103.125128}, url = {https://arxiv.org/abs/1907.05373}, author = {Michael Schuler and Stephan Hesselmann and Seth Whitsitt and Thomas C. Lang and Stefan Wessel and Andreas M. L{\"a}uchli} } @article {2775, title = {Trading Locality for Time: Certifiable Randomness from Low-Depth Circuits}, journal = {Communications in Mathematical Physics}, volume = {382}, year = {2021}, month = {2/9/2021}, pages = {49 - 86}, abstract = {

The generation of certifiable randomness is the most fundamental informationtheoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion using a\ single quantum device. The protocol calls for the device to implement a simple quantum circuit of constant depth on a 2D lattice of qubits. The output of the circuit can be\ verified classically in linear time, and is guaranteed to contain a polynomial number of\ certified random bits assuming that the device used to generate the output operated using\ a (classical or quantum) circuit of sub-logarithmic depth. This assumption contrasts with\ the locality assumption used for randomness certification based on Bell inequality violation and more recent proposals for randomness certification based on computational\ assumptions. Furthermore, to demonstrate randomness generation it is sufficient for a\ device to sample from the ideal output distribution within constant statistical distance.\ \ Our procedure is inspired by recent work of Bravyi et al. (Science 362(6412):308\–311,\ 2018), who introduced a relational problem that can be solved by a constant-depth quantum circuit, but provably cannot be solved by any classical circuit of sub-logarithmic\ depth. We develop the discovery of Bravyi et al. into a framework for robust randomness\ expansion. Our results lead to a new proposal for a demonstrated quantum advantage\ that has some advantages compared to existing proposals. First, our proposal does not\ rest on any complexity-theoretic conjectures, but relies on the physical assumption that\ the adversarial device being tested implements a circuit of sub-logarithmic depth. Second, success on our task can be easily verified in classical linear time. Finally, our task\ is more noise-tolerant than most other existing proposals that can only tolerate multiplicative error, or require additional conjectures from complexity theory; in contrast, we\ are able to allow a small constant additive error in total variation distance between the\ sampled and ideal distributions.

}, issn = {0010-3616}, doi = {10.1007/s00220-021-03963-w}, url = {https://link.springer.com/content/pdf/10.1007/s00220-021-03963-w.pdf}, author = {Matthew Coudron and Stark, Jalex and Vidick, Thomas} } @article {2764, title = {Trapped electrons and ions as particle detectors}, journal = {Phys. Rev. Lett.}, volume = {127}, year = {2021}, month = {8/5/2021}, abstract = {

Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As an illustration, we show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges <}, doi = {https://doi.org/10.1103/PhysRevLett.127.061804}, url = {https://arxiv.org/abs/2104.05737}, author = {Daniel Carney and Hartmut H{\"a}ffner and David C. Moore and J. M. Taylor} } @article {2682, title = {Tunable three-body loss in a nonlinear Rydberg medium}, journal = {Phys. Rev. Lett., in press }, year = {2021}, month = {9/28/2020}, abstract = {

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential to generate novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study a three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wavefunction and analytical estimates based on Fermi\&$\#$39;s Golden Rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

}, url = {https://arxiv.org/abs/2009.13599}, author = {Dalia P. Ornelas Huerta and Przemyslaw Bienias and Alexander N. Craddock and Michael Gullans and Andrew J. Hachtel and Marcin Kalinowski and Mary E. Lyon and Alexey V. Gorshkov and Steven L. Rolston and J. V. Porto} } @article {2519, title = {Time evolution of correlation functions in quantum many-body systems}, journal = {Phys. Rev. Lett}, volume = {124}, year = {2020}, month = {3/19/2020}, abstract = {

We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green\&$\#$39;s functions-- in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times \⟨A(t)B\⟩β\→\⟨A\⟩β\⟨B\⟩β, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values, and does not increase with system size. We give numerical examples that show that this bound is a good estimate in non-integrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.

}, doi = {https://doi.org/10.1103/PhysRevLett.124.110605}, url = {https://arxiv.org/abs/1906.11280}, author = {{\'A}lvaro M. Alhambra and Jonathon Riddell and Luis Pedro Garc{\'\i}a-Pintos} } @article {2402, title = {Time-dependent Hamiltonian simulation with L1-norm scaling}, journal = {Quantum}, volume = {4}, year = {2020}, month = {4/20/2020}, abstract = {

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For the case of sparse Hamiltonian simulation, the gate complexity scales with the L1 norm \∫t0dτ||H(τ)||max, whereas the best previous results scale with tmaxτ\∈[0,t]||H(τ)||max. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schr{\"o}dinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. By leveraging the L1-norm information, we obtain polynomial speedups for semi-classical simulations of scattering processes in quantum chemistry.

}, doi = {https://doi.org/10.22331/q-2020-04-20-254}, url = {https://arxiv.org/abs/1906.07115}, author = {Dominic W. Berry and Andrew M. Childs and Yuan Su and Xin Wang and Nathan Wiebe} } @article {2518, title = {Time-information uncertainty relations in thermodynamics}, journal = {Nat. Phys.}, year = {2020}, month = {09/21/2020}, abstract = {

Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit -- a time-information uncertainty relation -- imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its initial standard deviation. From this general bound, we establish a family of speed limits for heat, work, entropy production, and entropy flow depending on the experimental constraints on the system. In all of these inequalities, the time scale of transient dynamical fluctuations is universally bounded by the Fisher information. Moreover, they all have a mathematical form that mirrors the Mandelstam-Tamm version of the time-energy uncertainty relation in quantum mechanics. These bounds on the speed of arbitrary observables apply to transient systems away from thermodynamic equilibrium, independent of the physical assumptions about the stochastic dynamics or their function.\ 

}, doi = {https://doi.org/10.1038/s41567-020-0981-y}, url = {https://arxiv.org/abs/2001.05418}, author = {Schuyler B. Nicholson and Luis Pedro Garc{\'\i}a-Pintos and Adolfo del Campo and Jason R. Green} } @article {2453, title = {Towards analog quantum simulations of lattice gauge theories with trapped ions}, journal = {Physical Review Research }, volume = {2}, year = {2020}, month = {4/8/2020}, abstract = {

Gauge field theories play a central role in modern physics and are at the heart of the Standard Model of elementary particles and interactions. Despite significant progress in applying classical computational techniques to simulate gauge theories, it has remained a challenging task to compute the real-time dynamics of systems described by gauge theories. An exciting possibility that has been explored in recent years is the use of highly-controlled quantum systems to simulate, in an analog fashion, properties of a target system whose dynamics are difficult to compute. Engineered atom-laser interactions in a linear crystal of trapped ions offer a wide range of possibilities for quantum simulations of complex physical systems. Here, we devise practical proposals for analog simulation of simple lattice gauge theories whose dynamics can be mapped onto spin-spin interactions in any dimension. These include 1+1D quantum electrodynamics, 2+1D Abelian Chern-Simons theory coupled to fermions, and 2+1D pure Z2 gauge theory. The scheme proposed, along with the optimization protocol applied, will have applications beyond the examples presented in this work, and will enable scalable analog quantum simulation of Heisenberg spin models in any number of dimensions and with arbitrary interaction strengths.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.023015}, url = {https://arxiv.org/abs/1908.03210}, author = {Zohreh Davoudi and Mohammad Hafezi and Christopher Monroe and Guido Pagano and Alireza Seif and Andrew Shaw} } @article {2609, title = {Transport and dynamics in the frustrated two-bath spin-boson model}, year = {2020}, month = {7/7/2020}, abstract = {

We study the strong coupling dynamics as well as transport properties of photons in the two-bath spin-boson model, in which a spin-1/2 particle is frustratingly coupled to two independent Ohmic bosonic baths. Using a combination of numerical and analytical methods, we show that the frustration in this model gives rise to rich physics in a very wide range of energies. This is in contrast to the one-bath spin-boson model, where the non-trivial physics occurs at an energy scale close to the renormalized spin frequency. The renormalized spin frequency in the two-bath spin-boson model is still important, featuring in different observables, including the non-equiblirum dynamics of both the spin and the baths along with the elastic transport properties of a photon. The latter however reveals a much more complex structure. The elastic scattering displays non-monotonic behavior at high frequencies, and is very different in the two channels: intra- and inter-bath scattering. The photon can also be inelastically scattered, a process in which it is split into several photons of smaller energies. We show that such inelastic processes are highly anisotropic, with the outgoing particles being preferentially emitted into only one of the baths. Moreover, the inelastic scattering rate is parameterically larger than in the one-bath case, and can even exceed the total elastic rate. Our results can be verified with state-of-the-art circuit and cavity quantum electrodynamics experiments.\ 

}, url = {https://arxiv.org/abs/2007.03690}, author = {Ron Belyansky and Seth Whitsitt and Rex Lundgren and Yidan Wang and Andrei Vrajitoarea and Andrew A. Houck and Alexey V. Gorshkov} } @article {2337, title = {Thermalization and chaos in QED3}, journal = {Phys. Rev. D }, volume = {99}, year = {2019}, month = {04/11/2019}, abstract = {

We study the real time dynamics of NF flavors of fermions coupled to a U(1) gauge field in 2+1 dimensions to leading order in a 1/NF expansion. For large enough NF, this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in 1/NF. We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance.\ 

}, doi = {https://doi.org/10.1103/PhysRevD.99.076007}, url = {https://arxiv.org/abs/1901.04984}, author = {Julia Steinberg and Brian Swingle} } @article {2392, title = {Toward convergence of effective field theory simulations on digital quantum computers}, year = {2019}, month = {04/18/2019}, abstract = {

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansaetze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of E4=\−2.220\±0.179MeV may be compared with the exact Deuteron ground-state energy \−2.224MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps for the first time. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.\ 

}, url = {https://arxiv.org/abs/1904.04338}, author = {Omar Shehab and Kevin A. Landsman and Yunseong Nam and Daiwei Zhu and Norbert M. Linke and Matthew J. Keesan and Raphael C. Pooser and Christopher R. Monroe} } @article {2401, title = {Towards Bulk Metric Reconstruction from Extremal Area Variations}, year = {2019}, month = {04/09/19}, abstract = {

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension , knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an\textit {explicit} spacetime metric reconstruction.

}, url = {https://arxiv.org/abs/1904.04834}, author = {Ning Bao and ChunJun Cao and Sebastian Fischetti and Cynthia Keeler} } @article {2574, title = {{\textquoteleft}Two Dogmas{\textquoteright} Redux}, year = {2019}, month = {7/14/2019}, publisher = {Springer, Cham}, abstract = {

I revisit the paper \‘Two dogmas about quantum mechanics,\’ co-authored with Itamar Pitowsky, in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Following the analysis by Frauchiger and Renner of \‘encapsulated\’ measurements (where a super-observer, with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures the memory of an observer system after that system measures the spin of a qubit), I show that the Everett interpretation leads to modal contradictions. In this sense, the Everett interpretation is inconsistent.

}, url = {https://arxiv.org/abs/1907.06240}, author = {Jeffrey Bub} } @article {2412, title = {Two-qubit entangling gates within arbitrarily long chains of trapped ions}, year = {2019}, month = {05/28/2019}, abstract = {

Ion trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals, simplifying the scaling of ion trap quantum computers. To this end, we present analytical work that determines how parallel entangling gates produce a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also show experimental work demonstrating entangling gates on a fully-connected chain of seventeen 171Yb+ ions with fidelities as high as 97(1)\%.

}, url = {https://arxiv.org/abs/1905.10421}, author = {Kevin A. Landsman and Yukai Wu and Pak Hong Leung and Daiwei Zhu and Norbert M. Linke and Kenneth R. Brown and Luming Duan and Christopher R. Monroe} } @article {2270, title = {Tabletop experiments for quantum gravity: a user{\textquoteright}s manual}, year = {2018}, abstract = {

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

}, url = {https://arxiv.org/abs/1807.11494}, author = {Daniel Carney and Philip C. E. Stamp and J. M. Taylor} } @article {2204, title = {Tabletop experiments for quantum gravity: a user{\textquoteright}s manual}, year = {2018}, abstract = {

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

}, url = {https://arxiv.org/abs/1807.11494}, author = {Daniel Carney and Philip C. E. Stamp and J. M. Taylor} } @article {2507, title = {Thermal management and non-reciprocal control of phonon flow via optomechanics}, journal = {Nat. Commun.}, volume = {9(1)}, year = {2018}, month = {2018/3/23}, abstract = {

Engineering phonon transport in physical systems is a subject of interest in the study of materials and plays a crucial role in controlling energy and heat transfer. Of particular interest are non-reciprocal phononic systems, which in direct analogy to electric diodes, provide a directional flow of energy. Here, we propose an engineered nanostructured material, in which tunable non-reciprocal phonon transport is achieved through optomechanical coupling. Our scheme relies on breaking time-reversal symmetry by a spatially varying laser drive, which manipulates low-energy acoustic phonons. Furthermore, we take advantage of recent developments in the manipulation of high-energy phonons through controlled scattering mechanisms, such as using alloys and introducing disorder. These combined approaches allow us to design an acoustic isolator and a thermal diode. Our proposed device will have potential impact in phonon-based information processing, and heat management in low temperatures.\ 

}, doi = {https://doi.org/10.1038/s41467-018-03624-y}, url = {https://arxiv.org/abs/1710.08967}, author = {Alireza Seif and Wade DeGottardi and Keivan Esfarjani and Mohammad Hafezi} } @article {2118, title = {Time-reversal of rank-one quantum strategy functions}, journal = {Quantum }, volume = {2}, year = {2018}, month = {2018/01/25}, abstract = {

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators on a certain space. This time-reversal property states that the maximum value obtained by such a function over all valid quantum strategies is also obtained when the direction of time for the function is reversed, despite the fact that the strategies themselves are generally not time reversible. An application of this fact is an alternative proof of a known relationship between the conditional min- and max-entropy of bipartite quantum states, along with generalizations of this relationship.

}, doi = {https://doi.org/10.22331/q-2018-10-04-98}, url = {https://arxiv.org/abs/1801.08491}, author = {Yuan Su and John Watrous} } @book {2249, title = {Totally random: why nobody understands quantum mechanics (a serious comic on entanglement)}, year = {2018}, publisher = {Princeton University Press}, organization = {Princeton University Press}, author = {Jeffrey Bub and Tanya Bub} } @article {2220, title = {Toward the first quantum simulation with quantum speedup}, journal = {Proceedings of the National Academy of Sciences}, volume = {115 }, year = {2018}, pages = {9456-9461}, abstract = {

With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

}, doi = {https://doi.org/10.1073/pnas.1801723115}, url = {https://arxiv.org/abs/1711.10980}, author = {Andrew M. Childs and Dmitri Maslov and Yunseong Nam and Neil J. Ross and Yuan Su} } @article {2463, title = {Two-Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory}, year = {2018}, abstract = {
We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of non-vanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of non-vanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term R2, where R is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cut-off ε2 under a constant boundary dilaton field and the non-vanishing cosmological constant by identifying the lattice spacing a of a lattice Schwarzian theory with the boundary cut-off ε of the two-dimensional dilaton gravity theory.\ 
}, url = {https://arxiv.org/abs/1802.04599}, author = {Su-Kuan Chu and Chen-Te Ma and Chih-Hung Wu} } @article {2100, title = {Thermodynamic Analysis of Classical and Quantum Search Algorithms}, year = {2017}, month = {2017/09/29}, abstract = {

We analyze the performance of classical and quantum search algorithms from a thermodynamic perspective, focusing on resources such as time, energy, and memory size. We consider two examples that are relevant to post-quantum cryptography: Grover\’s search algorithm, and the quantum algorithm for collisionfinding. Using Bennett\’s \“Brownian\” model of low-power reversible computation, we show classical algorithms that have the same asymptotic energy consumption as these quantum algorithms. Thus, the quantum advantage in query complexity does not imply a reduction in these thermodynamic resource costs. In addition, we present realistic estimates of the resource costs of quantum and classical search, for near-future computing technologies. We find that, if memory is cheap, classical exhaustive search can be surprisingly competitive with Grover\’s algorithm.

}, url = {https://arxiv.org/abs/1709.10510}, author = {Ray Perlner and Yi-Kai Liu} } @article {2055, title = {Thermodynamic limits for optomechanical systems with conservative potentials}, journal = {Physical Review B}, volume = {96}, year = {2017}, month = {2017/11/13}, pages = {184106}, abstract = {

The mechanical force from light \– radiation pressure \– provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a function of external parameters. This non-analyticity, a key feature of thermodynamic phase transitions, suggests that there could be an effective thermodynamic description of optomechanical systems. Here we explicitly define the thermodynamic limit for optomechanical systems and derive a set of sufficient constraints on the system parameters as the mechanical system grows large. As an example, we show how these constraints can be satisfied in a system with Z2 symmetry and derive a free energy, allowing us to characterize this as an equilibrium phase transition.

}, doi = {10.1103/PhysRevB.96.184106}, url = {https://arxiv.org/abs/1707.05771}, author = {Stephen Ragole and Haitan Xu and John Lawall and J. M. Taylor} } @article {2152, title = {Threshold Dynamics of a Semiconductor Single Atom Maser}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/08/31}, pages = {097702}, abstract = {

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

}, doi = {10.1103/PhysRevLett.119.097702}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.097702}, author = {Liu, Y.-Y. and Stehlik, J. and Eichler, C. and Mi, X. and Hartke, T. R. and Michael Gullans and J. M. Taylor and Petta, J. R.} } @article {1689, title = {Tomography is necessary for universal entanglement detection with single-copy observables}, journal = {Physical Review Letters}, volume = {116}, year = {2016}, month = {2016/06/07}, pages = {230501}, abstract = {Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.}, doi = {10.1103/PhysRevLett.116.230501}, url = {http://arxiv.org/abs/1511.00581}, author = {Dawei Lu and Tao Xin and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Guilu Long and Jonathan Baugh and Xinhua Peng and Bei Zeng and Raymond Laflamme} } @article {1191, title = {Topological phases with long-range interactions}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/01/08}, pages = {041102}, abstract = { Topological phases of matter are primarily studied in quantum many-body systems with short-range interactions. Whether various topological phases can survive in the presence of long-range interactions, however, is largely unknown. Here we show that a paradigmatic example of a symmetry-protected topological phase, the Haldane phase of an antiferromagnetic spin-1 chain, surprisingly remains intact in the presence of arbitrarily slowly decaying power-law interactions. The influence of long-range interactions on the topological order is largely quantitative, and we expect similar results for more general systems. Our conclusions are based on large-scale matrix-product-state simulations and two complementary effective-field-theory calculations. The striking agreement between the numerical and analytical results rules out finite-size effects. The topological phase considered here should be experimentally observable in a recently developed trapped-ion quantum simulator. }, doi = {10.1103/PhysRevB.93.041102}, url = {http://arxiv.org/abs/1505.03146}, author = {Zhe-Xuan Gong and Mohammad F. Maghrebi and Anzi Hu and Michael L. Wall and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1785, title = {Tensor network non-zero testing}, journal = {Quantum Information \& Computation}, volume = {15}, year = {2015}, month = {2015/07/01}, pages = {885-899}, abstract = {Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network non-zero testing (TNZ): Given a tensor network T, does T represent a non-zero vector? We show that TNZ is not in the Polynomial-Time Hierarchy unless the hierarchy collapses. We next show (among other results) that the special cases of TNZ on non-negative and injective tensor networks are in NP. Using this, we make a simple observation: The commuting variant of the MA-complete stoquastic k-SAT problem on D-dimensional qudits is in NP for logarithmic k and constant D. This reveals the first class of quantum Hamiltonians whose commuting variant is known to be in NP for all (1) logarithmic k, (2) constant D, and (3) for arbitrary interaction graphs.}, url = {http://arxiv.org/abs/1406.5279}, author = {Sevag Gharibian and Zeph Landau and Seung Woo Shin and Guoming Wang} } @article {1339, title = {Tunable Spin Qubit Coupling Mediated by a Multi-Electron Quantum Dot}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/06/04}, pages = {226803}, abstract = {We present an approach for entangling electron spin qubits localized on spatially separated impurity atoms or quantum dots via a multi-electron, two-level quantum dot. The effective exchange interaction mediated by the dot can be understood as the simplest manifestation of Ruderman-Kittel-Kasuya-Yosida exchange, and can be manipulated through gate voltage control of level splittings and tunneling amplitudes within the system. This provides both a high degree of tuneability and a means for realizing high-fidelity two-qubit gates between spatially separated spins, yielding an experimentally accessible method of coupling donor electron spins in silicon via a hybrid impurity-dot system. }, doi = {10.1103/PhysRevLett.114.226803}, url = {http://arxiv.org/abs/1312.1711v3}, author = {V. Srinivasa and H. Xu and J. M. Taylor} } @article {1402, title = {Testing quantum expanders is co-QMA-complete}, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/4/15}, abstract = { A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is co-QMA-complete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems. }, doi = {10.1103/PhysRevA.87.042317}, url = {http://arxiv.org/abs/1210.0787v2}, author = {Adam D. Bookatz and Stephen P. Jordan and Yi-Kai Liu and Pawel Wocjan} } @article {1258, title = {A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates}, year = {2013}, month = {2013/02/28}, abstract = { We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n^{5/7}), matching the best known upper bound (obtained via learning graphs) up to log factors. Furthermore, our algorithm has time complexity ~O(n^{5/7}), improving the previous ~O(n^{3/4}). }, url = {http://arxiv.org/abs/1302.7316v1}, author = {Andrew M. Childs and Stacey Jeffery and Robin Kothari and Frederic Magniez} } @article {1184, title = {Topological phases in ultracold polar-molecule quantum magnets}, journal = {Physical Review B}, volume = {87}, year = {2013}, month = {2013/2/26}, abstract = { We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S >= 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases -- previously studied only in the nearest-neighbor case -- survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed. }, doi = {10.1103/PhysRevB.87.081106}, url = {http://arxiv.org/abs/1210.5518v2}, author = {Salvatore R. Manmana and E. M. Stoudenmire and Kaden R. A. Hazzard and Ana Maria Rey and Alexey V. Gorshkov} } @article {1197, title = {Topologically Protected Quantum State Transfer in a Chiral Spin Liquid}, journal = {Nature Communications}, volume = {4}, year = {2013}, month = {2013/3/12}, pages = {1585}, abstract = { Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. }, doi = {10.1038/ncomms2531}, url = {http://arxiv.org/abs/1110.3788v1}, author = {Norman Y. Yao and Chris R. Laumann and Alexey V. Gorshkov and Hendrik Weimer and Liang Jiang and J. Ignacio Cirac and Peter Zoller and Mikhail D. Lukin} } @article {1201, title = {Topological Flat Bands from Dipolar Spin Systems}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/12/26}, abstract = { We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered. }, doi = {10.1103/PhysRevLett.109.266804}, url = {http://arxiv.org/abs/1207.4479v3}, author = {Norman Y. Yao and Chris R. Laumann and Alexey V. Gorshkov and Steven D. Bennett and Eugene Demler and Peter Zoller and Mikhail D. Lukin} } @article {1198, title = {Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules }, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/9/8}, abstract = { By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and novel density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method (DMRG) to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally. }, doi = {10.1103/PhysRevLett.107.115301}, url = {http://arxiv.org/abs/1106.1644v1}, author = {Alexey V. Gorshkov and Salvatore R. Manmana and Gang Chen and Jun Ye and Eugene Demler and Mikhail D. Lukin and Ana Maria Rey} } @article {1489, title = {Temperature driven structural phase transition for trapped ions and its experimental detection }, journal = {Physical Review Letters}, volume = {105}, year = {2010}, month = {2010/12/29}, abstract = { A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system{\textquoteright}s temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology. }, doi = {10.1103/PhysRevLett.105.265703}, url = {http://arxiv.org/abs/1009.0089v1}, author = {Zhe-Xuan Gong and G. -D. Lin and L. -M. Duan} } @article {1849, title = {Thesis: Novel Systems and Methods for Quantum Communication, Quantum Computation, and Quantum Simulation}, journal = {Harvard University Physics Department}, volume = {Ph.D. Thesis}, year = {2010}, author = {Alexey V. Gorshkov} } @article {1850, title = {Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms}, journal = {Nature Phys.}, volume = {6}, year = {2010}, pages = {289}, url = {http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html}, author = {Alexey V. Gorshkov and Hermele, M and Gurarie, V and Xu, C and Julienne, P S and Ye, J and Zoller, P and Demler, E and Lukin, M D and Rey, A M} } @article {1404, title = {Theoretical analysis of perfect quantum state transfer with superconducting qubits }, journal = {Physical Review B}, volume = {78}, year = {2008}, month = {2008/9/24}, abstract = { Superconducting quantum circuits, fabricated with multiple layers, are proposed to implement perfect quantum state transfer between nodes of a hypercube network. For tunable devices such as the phase qubit, each node can transmit quantum information to any other node at a constant rate independent of the distance between qubits. The physical limits of quantum state transfer in this network are theoretically analyzed, including the effects of disorder, decoherence, and higher-order couplings. }, doi = {10.1103/PhysRevB.78.094516}, url = {http://arxiv.org/abs/0708.0577v3}, author = {Frederick W. Strauch and Carl J. Williams} } @article {1292, title = {Tunneling phase gate for neutral atoms in a double-well lattice}, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/5/12}, abstract = { We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atoms in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the {\textquoteleft}{\textquoteleft}tilt{\textquoteright}{\textquoteright}). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity. }, doi = {10.1103/PhysRevA.77.050304}, url = {http://arxiv.org/abs/0712.1856v1}, author = {Frederick W. Strauch and Mark Edwards and Eite Tiesinga and Carl J. Williams and Charles W. Clark} } @article {1276, title = {Two-body transients in coupled atomic-molecular BECs}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/3/3}, abstract = { We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms. }, doi = {10.1103/PhysRevLett.100.093001}, url = {http://arxiv.org/abs/0707.2963v2}, author = {Pascal Naidon and Eite Tiesinga and Paul S. Julienne} } @article {1323, title = {Two dogmas about quantum mechanics}, year = {2007}, month = {2007/12/27}, abstract = { We argue that the intractable part of the measurement problem -- the {\textquoteright}big{\textquoteright} measurement problem -- is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell{\textquoteright}s assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the {\textquoteright}truthmaker{\textquoteright} for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the {\textquoteright}big{\textquoteright} measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, we accept that measurements have definite outcomes. By contrast with the Bohmians and the GRW {\textquoteright}collapse{\textquoteright} theorists who add structure to the theory and propose dynamical solutions to the {\textquoteright}big{\textquoteright} measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events. }, url = {http://arxiv.org/abs/0712.4258v2}, author = {Jeffrey Bub and Itamar Pitowsky} } @article {1252, title = {Two-way quantum communication channels}, journal = {International Journal of Quantum Information}, volume = {04}, year = {2006}, month = {2006/02/01}, pages = {63 - 83}, abstract = { We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel. }, doi = {10.1142/S0219749906001621}, url = {http://arxiv.org/abs/quant-ph/0506039v1}, author = {Andrew M. Childs and Debbie W. Leung and Hoi-Kwong Lo} } @article {1371, title = {Time Reversal and n-qubit Canonical Decompositions}, journal = {Journal of Mathematical Physics}, volume = {46}, year = {2005}, month = {2005/01/01}, pages = {062104}, abstract = { For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner{\textquoteright}s axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers{\textquoteright} nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians. }, doi = {10.1063/1.1900293}, url = {http://arxiv.org/abs/quant-ph/0402051v2}, author = {Stephen S. Bullock and Gavin K. Brennen and Dianne P. O{\textquoteright}Leary} }