Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Many-Body Quantum Teleportation via Operator Spreading in the Traversable Wormhole Protocol
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving
The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Controlling quantum many-body dynamics in driven Rydberg atom arrays
Dynamic stabilization of an array Large-scale systems comprising one-dimensional chains and two-dimensional arrays of excited atoms held in a programmable optical lattice are a powerful platform with which to simulate emergent phenomena. Bluvstein et al. built an array of up to 200 Rydberg atoms and subjected the system to periodic excitation. Under such driven excitation, they found that the array of atoms stabilized, freezing periodically into what looked like time crystals. Understanding and controlling the dynamic interactions in quantum many-body systems lies at the heart of contemporary condensed matter physics and the exotic phenomena that can occur. Science , this issue p. 1355
Science & Technology - Other Topics↗
Time Evolution of Correlation Functions in Quantum Many-Body Systems
We give rigorous analytical results on the temporal behavior of two-point correlation functions—also known as dynamical response functions or Green’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 $\langle$A ( t ) B$\rangle$ β → $\langle$ A$\rangle$ β $\langle$ B$\rangle$ 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 autocorrelation 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 nonintegrable 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.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Preparing quantum many-body scar states on quantum computers
Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Preparing Quantum Many-Body Scar States on Quantum Computers
Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to other eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we propose both a linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we propose a circuit architecture with polynomial depth. We also provide proof of principle implementations of these protocols on superconducting quantum hardware.
Quantum Computing↗
Scalable semidefinite programming approach to variational embedding for quantum many-body problems
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Decoherence in Molecular Electron Spin Qubits: Insights from Quantum Many-Body Simulations
Quantum states are described by wave functions whose phases cannot be directly measured, but which play a vital role in quantum effects such as interference and entanglement. The loss of the relative phase information, termed decoherence, arises from the interactions between a quantum system and its environment. Decoherence is perhaps the biggest obstacle on the path to reliable quantum computing. Here we show that decoherence occurs even in an isolated molecule although not all phase information is lost via a theoretical study of a central electron spin qubit interacting with nearby nuclear spins in prototypical magnetic molecules. The residual coherence, which is molecule-dependent, provides a microscopic rationalization for the nuclear spin diffusion barrier proposed to explain experiments. The contribution of nearby molecules to the decoherence has a non-trivial dependence on separation, peaking at intermediate distances. Molecules that are far away only affect the long-time behavior. Because the residual coherence is simple to calculate and correlates well with the coherence time, it can be used as a descriptor for coherence in magnetic molecules. This work will help establish design principles for enhancing coherence in molecular spin qubits and serve to motivate further theoretical work
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Learning energy-based representations of quantum many-body states
Efficient representation of quantum many-body states on classical computers is a problem of practical importance. An ideal representation of a quantum state combines a succinct characterization informed by the structure and symmetries of the system along with the ability to predict the physical observables of interest. Several machine-learning approaches have been recently used to construct such classical representations, which enable predictions of observables and account for physical symmetries. However, the structure of a quantum state typically gets lost unless a specialized is employed based on prior knowledge of the system. Moreover, most such approaches give no information about what states are easier to learn in comparison with others. Here, we propose a generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the difficulty of learning an energy-based representation of a given class of quantum states when measured in a certain basis. Published by the American Physical Society 2024
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Digital quantum simulation of non-equilibrium quantum many-body systems
Digital quantum simulation uses the capabilities of quantum computers to determine the dynamics of quantum systems, which are beyond the computability of modern classical computers. A notoriously challenging task in this field is the description of non-equilibrium dynamics in quantum many-body systems. In this study, we used the IBM quantum computers to simulate the non-equilibrium dynamics of few spin and fermionic systems. Our results reveal that with a combination of error mitigation, noise extrapolation and optimized initial state preparation, one can tackle the most important drawbacks of modern quantum devices. The systems we simulate demonstrate the potential for large-scale quantum simulations of light–matter interactions in the near future.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Lindblad many-body scars
Quantum many-body scars have received much recent attention for being both intriguing nonergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with 𝑁 fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify 𝑁/2+1 scars for complex fermions due to the 𝑈(1) symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin chain. We also characterize the physical properties of Lindblad scars. First, the operator size is independent of the disorder realization and has a vanishing variance. By contrast, the operator size for nonscarred states, believed to be quantum chaotic, is well described by a distribution centered around a specific size and a finite variance, which could be relevant for a precise definition of the eigenstate thermalization hypothesis in dissipative quantum chaos. Moreover, the entanglement entropy of these scars has distinct features such as a strong dependence on the partition choice and, in certain cases, a large entanglement.
Eigenstate thermalization↗
Preparing quantum many-body scar states on quantum computers
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Gustafson, Erik↗
Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz
Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Quantum many-body scars from Einstein-Podolsky-Rosen states in bilayer systems
Quantum many-body scar states are special eigenstates of nonintegrable models with distinctive entanglement features that give rise to infinitely long-lived coherent dynamics under quantum quenches from certain initial states. Here, we elaborate on a construction of quantum many-body scar states in which they emerge from Einstein-Podolsky-Rosen states in systems with two layers, wherein the two layers are maximally entangled. We apply this construction to spin systems as well as systems of itinerant fermions and bosons and demonstrate how symmetries can be harnessed to enhance its versatility. We show that several well-known examples of quantum many-body scars, including the tower of states in the spin-1 XY model and the η-pairing states in the Fermi-Hubbard model, can be understood within this formalism. We also demonstrate how an infinite tower of many-body scar states can emerge in bilayer Bose-Hubbard models with charge conservation.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Motif magnetism and quantum many-body scars
In this work, we generally expect quantum systems to thermalize and satisfy the eigenstate thermalization hypothesis (ETH), which states that finite-energy-density eigenstates are thermal. However, some systems, such as many-body localized systems and systems with quantum many-body scars, violate ETH and have high-energy athermal eigenstates. In systems with scars, most eigenstates thermalize, but a few atypical scar states do not. Scar states can give rise to a periodic revival when time-evolving particular initial product states, which can be detected experimentally. Recently, a family of spin Hamiltonians was found with magnetically ordered three-colored eigenstates that are quantum many-body scars [Lee et al., Phys. Rev. B 101, 241111(R) (2020)]. These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet. In this paper, we introduce a generalized family of n-colored Hamiltonians with “spiral colored” eigenstates made from n-spin motifs such as polygons or polyhedra. We show how these models can be realized in many different lattice geometries and provide numerical evidence that they can exhibit quantum many-body scars with periodic revivals that can be observed by time-evolving simple product states. The simple structure of these Hamiltonians makes them promising candidates for future experimental studies of quantum many-body scars.
36 MATERIALS SCIENCE↗
Quantum many-body calculations using body-centered cubic lattices
It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this paper we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down neutrons in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy E FG , we find that the ground state energy is E 0 /E FG =0.369(2),0.371(2), using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice [He et al., Phys. Rev. A 101, 063615 (2020)]. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size of lattice artifacts in simulations of continuum quantum many-body systems.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗