Showing papers in "Physical Review X in 2018"
TL;DR: In this paper, a coherent framework of topological phases of non-Hermitian Hamiltonians was developed, and the K-theory was applied to systematically classify all the topology phases in the Altland-Zirnbauer classes in all dimensions.
Abstract: Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi-)edge modes. We then apply the K-theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify a Z2 topological index for arbitrary quantum channels. Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.
543 citations
TL;DR: In this paper, a new theory describes how both insulating and superconducting behavior arises from sheets of graphene stacked and twisted at a particular ''magic'' angle, and the theory is used to explain the behavior of superconductivity.
Abstract: A new theory describes how both insulating and superconducting behavior arises from sheets of graphene stacked and twisted at a particular ``magic'' angle.
525 citations
TL;DR: In this article, a model of the electronic properties of twisted bilayer graphene was proposed to understand the effects of electron correlation and superconductivity in these systems, and the model provided a less complex tool for understanding the effects.
Abstract: A new model of the electronic properties of twisted bilayer graphene provides a less complex tool for understanding the effects of electron correlation and superconductivity in these systems.
522 citations
TL;DR: In this article, the authors show that the spreading of operators in random circuits is described by a hydrodynamical equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (e.g., no conserved energy).
Abstract: Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (“spin chains”), quantum field theory, and holography. We tackle this problem in 1D spin chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs) and entanglement growth in this setting. These results follow from the observation that the spreading of operators in random circuits is described by a “hydrodynamical” equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (e.g., no conserved energy). In this hydrodynamic picture, quantum information travels in a front with a “butterfly velocity” vB that is smaller than the light-cone velocity of the system, while the front itself broadens diffusively in time. The OTOC increases sharply after the arrival of the light cone, but we do not observe a prolonged exponential regime of the form ∼eλL(t-x/v) for a fixed Lyapunov exponent λL. We find that the diffusive broadening of the front has important consequences for entanglement growth, leading to an entanglement velocity that can be significantly smaller than the butterfly velocity. We conjecture that the hydrodynamical description applies to more generic Floquet ergodic systems, and we support this idea by verifying numerically that the diffusive broadening of the operator wavefront also holds in a more traditional nonrandom Floquet spin chain. We also compare our results to Clifford circuits, which have less rich hydrodynamics and consequently trivial OTOC behavior, but which can nevertheless exhibit linear entanglement growth and thermalization.
500 citations
TL;DR: In this article, a trapped-ion implementation of one such hybrid algorithm is used to solve a quantum chemistry problem, which is a promising approach for near-term practical applications of quantum computers.
Abstract: Quantum-classical hybrid algorithms are a promising approach for near-term practical applications of quantum computers. A new experiment demonstrates how a trapped-ion implementation of one such algorithm solves a quantum chemistry problem.
445 citations
TL;DR: In this article, the authors provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries in both 1+1D and higher dimensions.
Abstract: Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1+1D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1+1D, we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed vB. We find that in 1+1D, the “front” of the OTOC broadens diffusively, with a width scaling in time as t1/2. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1/3 in 2+1D and as t0.240 in 3+1D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2+1D. We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2+1D, our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1+1D, we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly. We also use this mapping to give exact results for entanglement growth in 1+1D circuits.
435 citations
TL;DR: In this paper, a new quantum model explores the emergence of irreversible macroscopic behavior from reversible microscopic dynamics, and the model is used to model the evolution of macroscopy behavior.
Abstract: A new quantum model explores the emergence of irreversible macroscopic behavior from reversible microscopic dynamics.
425 citations
TL;DR: An extended protocol based on a quantum subspace expansion (QSE) is used to apply the QSE approach to the H2 molecule, extracting both ground and excited states without the need for auxiliary qubits or additional minimization and can mitigate the effects of incoherent errors.
Abstract: © 2018 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite coherent lifetimes. Hybrid algorithms, such as the variational quantum eigensolver (VQE), leverage classical resources to reduce the required number of quantum gates. Experimental demonstrations of VQE have resulted in calculation of Hamiltonian ground states, and a new theoretical approach based on a quantum subspace expansion (QSE) has outlined a procedure for determining excited states that are central to dynamical processes. We use a superconducting-qubit-based processor to apply the QSE approach to the H2 molecule, extracting both ground and excited states without the need for auxiliary qubits or additional minimization. Further, we show that this extended protocol can mitigate the effects of incoherent errors, potentially enabling larger-scale quantum simulations without the need for complex error-correction techniques.
405 citations
TL;DR: A new analysis of quantum error mitigation, which attempts to limit the effects of errors in near-term quantum computers, shows that two proposed techniques can work in small systems without the need for extra qubits or peripheral devices.
Abstract: A new analysis of quantum error mitigation, which attempts to limit the effects of errors in near-term quantum computers, shows that two proposed techniques can work in small systems without the need for extra qubits or peripheral devices.
396 citations
TL;DR: In this paper, a quantum Boltzmann Machine (QBM) was proposed for machine learning, a quantum extension of a classical neural network, paving the way for quantum approaches to machine learning.
Abstract: A new machine-learning algorithm demonstrates the performance of a quantum Boltzmann machine, a quantum extension of a popular classical neural network, paving the way for quantum approaches to machine learning.
330 citations
TL;DR: In this article, the authors measured an energy loss in the postcollision electron spectrum that is correlated with the detected signal of hard photons (gamma rays), consistent with a quantum description of radiation reaction.
Abstract: The dynamics of energetic particles in strong electromagnetic fields can be heavily influenced by the energy loss arising from the emission of radiation during acceleration, known as radiation reaction. When interacting with a high-energy electron beam, today's lasers are sufficiently intense to explore the transition between the classical and quantum radiation reaction regimes. We present evidence of radiation reaction in the collision of an ultrarelativistic electron beam generated by laser-wakefield acceleration (epsilon > 500 MeV) with an intense laser pulse (a(0) > 10). We measure an energy loss in the postcollision electron spectrum that is correlated with the detected signal of hard photons (gamma rays), consistent with a quantum description of radiation reaction. The generated gamma rays have the highest energies yet reported from an all-optical inverse Compton scattering scheme, with critical energy epsilon(crit) > 30 MeV.
TL;DR: In this paper, an error was reported in the implementation of the code of the LIGO Scientific and Virgo Collaborations (LVC) as used in gravitational-wave-based estimations of possible deviations from the post-Newtonian (PN) terms expected in general relativity.
Abstract: We report an error found in the implementation of the code of the LIGO Scientific and Virgo Collaborations (LVC) as used in gravitational-wave-based estimations of possible deviations from the post-Newtonian (PN) terms expected in general relativity. The error concerned the 0.5 PN term and affected the results previously published for GW150914 [1] in Ref. [2], for GW151226 [3] in [4], and for GW170104 in Ref. [5]. We corrected the error and present the reproduced results here, as well as in the respective Refs. [6,7]. The main conclusion, that the results are consistent with general relativity, remains. The test for the parametrized post-Newtonian [8] deviations from the expected GR values relied on creating non-GR waveforms [2,9–13] and using them as potential matches for the observed waveforms [14–17]. In these waveforms, implemented in the frequency domain, freedom was introduced by allowing the phase coefficients describing different powers of the post-Newtonian parameter (equivalently, powers of the frequency) to assume a range of values not only the particular values prescribed by GR. However, a coding bug was introduced, identically zeroing the deviations at 0.5 PN in the inspiral regime (as in GR). Hence, the 0.5 PN deviations were absent in the phasing formula, though not in the junction conditions that relate the inspiral regime to the intermediate regime. Any constraints obtained in Refs. [2,4,5] only resulted from the latter.
TL;DR: In this article, a theoretical analysis explores the nature and origin of the superconducting and insulating phases recently seen in twisted bilayer graphene, and a new theoretical model is proposed to explain them.
Abstract: A new theoretical analysis explores the nature and origin of the superconducting and insulating phases recently seen in twisted bilayer graphene.
TL;DR: In this paper, a dual form of the plane wave basis is proposed to obtain a Hamiltonian representation with O(N^2) second-quantized terms for condensed phase materials.
Abstract: Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using N Gaussian orbitals, leading to Hamiltonians with O(N^4) second-quantized terms. We avoid this overhead and extend methods to condensed phase materials by utilizing a dual form of the plane wave basis which diagonalizes the potential operator, leading to a Hamiltonian representation with O(N^2) second-quantized terms. Using this representation, we can implement single Trotter steps of the Hamiltonians with linear gate depth on a planar lattice. Properties of the basis allow us to deploy Trotter- and Taylor-series-based simulations with respective circuit depths of O(N^(7/2)) and O(N^(8/3)) for fixed charge densities. Variational algorithms also require significantly fewer measurements in this basis, ameliorating a primary challenge of that approach. While our approach applies to the simulation of arbitrary electronic structure problems, the basis sets explored in this work will be most practical for treating periodic systems, such as crystalline materials, in the near term. We conclude with a proposal to simulate the uniform electron gas (jellium) using a low-depth variational ansatz realizable on near-term quantum devices. From these results, we identify simulations of low-density jellium as a promising first setting to explore quantum supremacy in electronic structure.
TL;DR: In this article, a new model of electron motion in twisted bilayer graphene was proposed, which sets the stage for exploring these connections further and shows that superconducting and insulating properties of twisted bilayers suggest deep connections between these phases.
Abstract: Superconducting and insulating behaviors in twisted bilayer graphene suggest deep connections between these phases. A new model of electron motion in these systems sets the stage for exploring these connections further.
TL;DR: In this article, a Gaussian approximation potential for silicon is presented, which can accurately reproduce density-functional-theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects.
Abstract: The success of first-principles electronic-structure calculation for predictive modeling in chemistry, solid-state physics, and materials science is constrained by the limitations on simulated length scales and timescales due to the computational cost and its scaling. Techniques based on machine-learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations remains a challenging goal. Here, we present a Gaussian approximation potential for silicon that achieves this milestone, accurately reproducing density-functional-theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations such as finite-temperature phase-boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture, all of which are very expensive with a first-principles method. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential’s accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material on the atomic scale and serves as a template for the development of such models in the future.
TL;DR: This work implements cutting-edge Reinforcement Learning techniques and shows that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in non-integrable many-body quantum systems of interacting qubits.
Abstract: New experiments show that reinforcement learning algorithms, a cutting-edge technique for machine learning, can quickly and accurately learn to prepare a desired quantum state despite no knowledge of quantum mechanics.
TL;DR: In this paper, two bands of excitation for spin waves in the insulating honeycomb ferromagnet CrI${}_{3} showed promise for potential spintronic applications.
Abstract: New experiments reveal two bands of excitation for spin waves in the insulating honeycomb ferromagnet CrI${}_{3}$, showing promise for potential spintronic applications.
TL;DR: Substantial energy loss in an electron beam passing through a high-intensity laser provides clear evidence of the radiation reaction, shedding light on how electrons interact with extreme electromagnetic fields.
Abstract: Substantial energy loss in an electron beam passing through a high-intensity laser provides clear evidence of the radiation reaction, shedding light on how electrons interact with extreme electromagnetic fields.
TL;DR: The results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of String-Bond States as a tool in more traditional machine-learning applications.
Abstract: Two tools show great promise in approximating low-temperature, condensed-matter systems: Tensor-network states and artificial neural networks. A new analysis builds a bridge between these techniques, opening the way to a host of powerful approaches to understanding complex quantum systems.
TL;DR: In this paper, the authors apply conservation laws to quantum systems to change the timescale over which information is lost, and show that applying conservation laws on quantum systems changes the timescales of information loss.
Abstract: Applying conservation laws to quantum systems changes the timescale over which information is lost.
TL;DR: In this paper, a minimal model for an ergodic phase in a spatially extended quantum many-body system is proposed, which consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution.
Abstract: We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span a q-dimensional Hilbert space, and time evolution for a pair of sites is generated by a q2 × q2 random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbor on one side during the first half of the evolution period and to its neighbor on the other side during the second half of the period. We show how dynamical behavior averaged over realizations of the random matrices can be evaluated using diagrammatic techniques and how this approach leads to exact expressions in the large-q limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth, and operator spreading.
TL;DR: In this paper, a new metasurface design offers a simple, practical approach to redirecting electromagnetic waves in an arbitrary manner with near perfect power efficiency over a wide range of angles and frequencies.
Abstract: A new metasurface design offers a simple, practical approach to redirecting electromagnetic waves in an arbitrary manner with near perfect power efficiency over a wide range of angles and frequencies.
TL;DR: A method for distributing encryption keys in a quantum network surpasses current limits and is immune to all detection attacks, potentially offering a new standard for future implementations of quantum key distribution as mentioned in this paper.
Abstract: A method for distributing encryption keys in a quantum network surpasses current limits and is immune to all detection attacks, potentially offering a new standard for future implementations of quantum key distribution.
TL;DR: In this paper, two new methods for detecting quantum entanglement successfully do so in a system of 20 qubits, the largest fully controllable entangled system to date, and they successfully detect the quantum link between two qubits.
Abstract: Two new methods for detecting quantum entanglement---a critical ingredient for useful quantum technologies---successfully do so in a system of 20 qubits, the largest fully controllable entangled system to date.
TL;DR: This work shows how a network-based "agent" can discover complete quantum-error-correction strategies, protecting a collection of qubits against noise, and develops two ideas: two-stage learning with teacher/student networks and a reward quantifying the capability to recover the quantum information stored in a multi-qubit system.
Abstract: An artificial neural network can discover algorithms for quantum error correction without human guidance.
TL;DR: In this paper, it was shown that Majorana zero modes (quasiparticles with potential quantum computing applications) can persist in topological superconductors, despite previous difficulties in doing so.
Abstract: New experiments find that Majorana zero modes---quasiparticles with potential quantum computing applications---can persist in topological superconductors, despite previous difficulties in doing so.
TL;DR: In this article, a unified theory for topological crystalline insulators is proposed, connecting spatial symmetries, sample geometry, and surface behavior, which places the enormous variety of surface states seen in topological topological insulators into a unified framework.
Abstract: A new theory places the enormous variety of surface states seen in topological crystalline insulators into a unified framework, connecting spatial symmetries, sample geometry, and surface behavior.
TL;DR: In this article, the effect of quenched disorder on spin-1/2 quantum magnets was analyzed and a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids was proposed.
Abstract: We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1/2 per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology of YbMgGaO4, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO4 and related materials.
TL;DR: In this article, the first experimental demonstration of topologically protected helical edge modes, a robust approach to manipulating vibrations, with potential applications in sensing-signal processing and wave guiding.
Abstract: Elastic plates patterned with triangular and circular holes provide the first experimental demonstration of topologically protected helical edge modes, a robust approach to manipulating vibrations, with potential applications in sensing-signal processing and wave guiding.