Quantum Many-body Physics Research Articles

Random Quantum Circuits

Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.

Fundamental Limitation on the Detectability of Entanglement.

Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponentially many resources with regard to system size or qubit number, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to evaluate the detection capability of entanglement criteria theoretically. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double exponentially. Furthermore, if multicopy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems. Our results may shed light on why quantum phenomena are difficult to observe in large noisy systems.

Disorder-free localization with Stark gauge protection

Disorder-free localization in translation-invariant gauge theories presents a counterintuitive yet powerful framework of ergodicity breaking in quantum many-body physics. The fragility of this phenomenon in the presence of gauge-breaking errors has recently been addressed, but no scheme has been able to reliably stabilize disorder-free localization through all accessible evolution times while preserving the disorder-free property. Here, we introduce the concept of \textit{Stark gauge protection}, which entails a linear sum in gauge-symmetry local (pseudo)generators weighted by a Stark potential. Using exact diagonalization and Krylov-based methods, we show how this scheme can stabilize or even enhance disorder-free localization against gauge-breaking errors in $\mathrm{U}(1)$ and $\mathbb{Z}_2$ gauge theories up to all accessible evolution times, without inducing \textit{bona fide} Stark many-body localization. We show through a Magnus expansion that the dynamics under Stark gauge protection is described by an effective Hamiltonian where gauge-breaking terms are suppressed locally by the protection strength and additionally by the matter site index, which we argue is the main reason behind stabilizing the localization up to all accessible times. Our scheme is readily feasible in modern ultracold-atom experiments and Rydberg-atom setups with optical tweezers.

Probing Operator Spreading via Floquet Engineering in a Superconducting Circuit.

Operator spreading, often characterized by out-of-time-order correlators (OTOCs), is one of the central concepts in quantum many-body physics. However, measuring OTOCs is experimentally challenging due to the requirement of reversing the time evolution of systems. Here we apply Floquet engineering to investigate operator spreading in a superconducting 10-qubit chain. Floquet engineering provides an effective way to tune the coupling strength between nearby qubits, which is used to demonstrate quantum walks with tunable couplings, reversed time evolution, and the measurement of OTOCs. A clear light-cone-like operator propagation is observed in the system with multiple excitations, and has a nearly equal velocity as the single-particle quantum walk. For the butterfly operator that is nonlocal (local) under the Jordan-Wigner transformation, the OTOCs show distinct behaviors with (without) a signature of information scrambling in the near integrable system.

Entanglement witnessing for lattice gauge theories

Entanglement is assuming a central role in modern quantum many-body physics. Yet, for lattice gauge theories its certification remains extremely challenging. A key difficulty stems from the local gauge constraints underlying the gauge theory, which separate the full Hilbert space into a direct sum of subspaces characterized by different superselection rules. In this work, we develop the theoretical framework of entanglement witnessing for lattice gauge theories that takes this subtlety into account. We illustrate the concept at the example of a U(1) lattice gauge theory in 2+1 dimensions, without and with dynamical fermionic matter. As this framework circumvents costly state tomography, it opens the door to resource-efficient certification of entanglement in theoretical studies as well as in laboratory quantum simulations of gauge theories.

Perturbative Quantum Simulation.

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to 48 qubits only using an 8+1 qubit quantum hardware. We demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.

Quantum nonlinear spectroscopy of single nuclear spins

Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.

Proposal for low-power atom trapping on a GaN-on-sapphire chip

The hybrid photon-atom integrated circuits, which include photonic microcavities and trapped single neutral atom in their evanescent field, are of great potential for quantum information processing. In this platform, the atoms provide the single-photon nonlinearity and long-lived memory, which are complementary to the excellent passive photonics devices in conventional quantum photonic circuits. In this work, we propose a stable platform for realizing the hybrid photon-atom circuits based on an unsuspended photonic chip. By introducing high-order modes in the microring, a feasible evanescent-field trap potential well $\sim0.3\,\mathrm{mK}$ could be obtained by only $10\,\mathrm{mW}$-level power in the cavity, compared with $100\,\mathrm{mW}$-level power required in the scheme based on fundamental modes. Based on our scheme, stable single atom trapping with relatively low laser power is feasible for future studies on high-fidelity quantum gates, single-photon sources, as well as many-body quantum physics based on a controllable atom array in a microcavity.

Codebase release 3.4 for NetKet

We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code.

NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code.

Codebase release 0.3 for ITensor

ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagrams, allowing users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The ITensor interface rules out common programming errors and enables rapid prototyping of algorithms. After discussing the philosophy behind the ITensor approach, we show examples of each part of the interface including Index objects, the ITensor product operator, tensor factorizations, tensor storage types, algorithms for matrix product state (MPS) and matrix product operator (MPO) tensor networks, quantum number conserving block sparse tensors, and the NDTensors library. We also review publications that have used ITensor for quantum many-body physics and for other areas where tensor networks are increasingly applied. To conclude we discuss promising features and optimizations to be added in the future.

The ITensor Software Library for Tensor Network Calculations

ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagrams, allowing users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The ITensor interface rules out common programming errors and enables rapid prototyping of algorithms. After discussing the philosophy behind the ITensor approach, we show examples of each part of the interface including Index objects, the ITensor product operator, tensor factorizations, tensor storage types, algorithms for matrix product state (MPS) and matrix product operator (MPO) tensor networks, quantum number conserving block sparse tensors, and the NDTensors library. We also review publications that have used ITensor for quantum many-body physics and for other areas where tensor networks are increasingly applied. To conclude we discuss promising features and optimizations to be added in the future.

Parameter-free differential evolution algorithm for the analytic continuation of imaginary time correlation functions.

We report on differential evolution for analytic continuation: a parameter-free evolutionary algorithm to generate the dynamic structure factor from imaginary time correlation functions. Our approach to this long-standing problem in quantum many-body physics achieves enhanced spectral fidelity while using fewer compute (CPU) hours. The need for fine-tuning of algorithmic control parameters is eliminated by embedding them within the genome to be optimized for this evolutionary computation-based algorithm. Benchmarks are presented for models where the dynamic structure factor is known exactly and experimentally relevant results are included for quantum Monte Carlo simulations of bulk ^{4}He below the superfluid transition temperature.

Quantum Hall states for Rydberg arrays with laser-assisted dipole-dipole interactions

Rydberg atoms with dipole-dipole interactions provide intriguing platforms to explore exotic quantum many-body physics. Here we propose a novel scheme with laser-assisted dipole-dipole interactions to realize synthetic magnetic field for Rydberg atoms in a two-dimensional array configuration, which gives rise to the exotic bosonic topological states. In the presence of an external effective Zeeman splitting gradient, the dipole-dipole interaction between neighboring Rydberg atoms along the gradient direction is suppressed, but can be assisted when Raman lights are applied to compensate the energy difference. With this scheme we generate a controllable uniform magnetic field for the complex spin-exchange coupling model, which can be mapped to hard core bosons coupling to an external synthetic magnetic field. The highly tunable flat Chern bands of the hard core bosons are then obtained and moreover, the bosonic fractional quantum Hall states can be achieved with experimental feasibility. This work opens an avenue for the realization of the highly-sought-after bosonic topological orders using Rydberg atoms.

Fixed-point quantum Monte Carlo method: A combination of density-matrix quantum Monte Carlo method and stochastic unravellings

We present an alternative approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from density-matrix quantum Monte Carlo in dealing with the sign problem and incorporates additional features. First of all, the dynamics is transferred to the Laplace representation where an exact equation can be derived and solved using an evolution step that, unlike most Monte Carlo methods, is not a priori physically bounded. Moreover, the spawning events are formulated in terms of two-process stochastic unravellings of quantum master equations, a formalism that is particularly useful when working with density matrices. Last, our approach is perturbative in nature, with the free part being integrated exactly and, as such, the convergence is greatly accelerated when the interaction parameter is small. We benchmark our method by applying it to two case studies in condensed-matter physics, perform some ground-state calculations, show its accuracy, and further discuss its efficiency.

Evidence for moiré intralayer excitons in twisted WSe2/WSe2 homobilayer superlattices

Recent advances in twisted van der Waals heterostructure superlattices have emerged as a powerful and attractive platform for exploring novel condensed matter physics due to the interplay between the moiré potential and Coulomb interactions. The moiré superlattices act as a periodic confinement potential in space to capture interlayer excitons (IXs), resulting in moiré exciton arrays, which provide opportunities for quantum emitters and many-body physics. The observation of moiré IXs in twisted transition-metal dichalcogenide (TMD) heterostructures has recently been widely reported. However, the capture and study of the moiré intralayer excitons based on TMD twisted homobilayer (T-HB) remain elusive. Here, we report the observation of moiré intralayer excitons in a WSe2/WSe2 T-HB with a small twist angle by measuring PL spectrum. The multiple split peaks with an energy range of 1.55–1.73 eV are different from that of the monolayer WSe2 exciton peaks. The split peaks were caused by the trapping of intralayer excitons via the moiré potential. The confinement effect of the moiré potential on the moiré intralayer excitons was further demonstrated by the changing of temperature, laser power, and valley polarization. Our findings provide a new avenue for exploring new correlated quantum phenomena and their applications.

Biexciton-like quartet condensates in an electron-hole liquid

We theoretically study the ground-state properties and the condensations of exciton-like Cooper pairs and biexciton-like Cooper quartets in an electron-hole system. Applying the variational approach associated based on the quartet Bardeen-Cooper-Schrieffer (BCS) model to the four-component fermionic system consisting of spin-1/2 electrons and spin-1/2 holes, we show how Cooper pairs and quartet correlations appear in the equation of state at the thermodynamic limit. The biexciton-like four-body correlations survive even at the high-density regime as a many-body BCS-like state of Cooper quartets. Our results are useful for further understanding of exotic matter in the interdisciplinary context of quantum many-body physics with multiple degrees of freedom.

Fermion Sampling: A Robust Quantum Computational Advantage Scheme Using Fermionic Linear Optics and Magic Input States

Fermionic Linear Optics (FLO) is a restricted model of quantum computation which in its original form is known to be efficiently classically simulable. We show that, when initialized with suitable input states, FLO circuits can be used to demonstrate quantum computational advantage with strong hardness guarantees. Based on this, we propose a quantum advantage scheme which is a fermionic analogue of Boson Sampling: Fermion Sampling with magic input states. We consider in parallel two classes of circuits: particle-number conserving (passive) FLO and active FLO that preserves only fermionic parity and is closely related to Matchgate circuits introduced by Valiant. Mathematically, these classes of circuits can be understood as fermionic representations of the Lie groups $U(d)$ and $SO(2d)$. This observation allows us to prove our main technical results. We first show anticoncentration for probabilities in random FLO circuits of both kind. Moreover, we prove robust average-case hardness of computation of probabilities. To achieve this, we adapt the worst-to-average-case reduction based on Cayley transform, introduced recently by Movassagh, to representations of low-dimensional Lie groups. Taken together, these findings provide hardness guarantees comparable to the paradigm of Random Circuit Sampling. Importantly, our scheme has also a potential for experimental realization. Both passive and active FLO circuits are relevant for quantum chemistry and many-body physics and have been already implemented in proof-of-principle experiments with superconducting qubit architectures. Preparation of the desired quantum input states can be obtained by a simple quantum circuit acting independently on disjoint blocks of four qubits and using 3 entangling gates per block. We also argue that due to the structured nature of FLO circuits, they can be efficiently certified.

Explainable natural language processing with matrix product states

Despite empirical successes of recurrent neural networks (RNNs) in natural language processing (NLP), theoretical understanding of RNNs is still limited due to intrinsically complex non-linear computations. We systematically analyze RNNs’ behaviors in a ubiquitous NLP task, the sentiment analysis of movie reviews, via the mapping between a class of RNNs called recurrent arithmetic circuits (RACs) and a matrix product state. Using the von-Neumann entanglement entropy (EE) as a proxy for information propagation, we show that single-layer RACs possess a maximum information propagation capacity, reflected by the saturation of the EE. Enlarging the bond dimension beyond the EE saturation threshold does not increase model prediction accuracies, so a minimal model that best estimates the data statistics can be inferred. Although the saturated EE is smaller than the maximum EE allowed by the area law, our minimal model still achieves training accuracies in realistic sentiment analysis data sets. Thus, low EE is not a warrant against the adoption of single-layer RACs for NLP. Contrary to a common belief that long-range information propagation is the main source of RNNs’ successes, we show that single-layer RACs harness high expressiveness from the subtle interplay between the information propagation and the word vector embeddings. Our work sheds light on the phenomenology of learning in RACs, and more generally on the explainability of RNNs for NLP, using tools from many-body quantum physics.

Exponential Clustering of Bipartite Quantum Entanglement at Arbitrary Temperatures

Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using long-range entanglement, i.e., entanglement in the macroscopic length scale. The long-range entanglement not only characterizes the novel quantum phases but also serves as a critical resource for quantum computation. Thus, the problem that arises is under which conditions can the long-range entanglement be stable even at room temperatures. Here, we show that bi-partite long-range entanglement is unstable at arbitrary temperatures and exponentially decays with distance. Our theorem provides a no-go theorem on the existence of the long-range entanglement. The obtained results are consistent with the existing observations that long-range entanglement at non-zero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. In the derivation of our result, we introduce a quantum correlation defined by the convex roof of the standard correlation function. We establish an exponential clustering theorem for generic quantum many-body systems for such a quantum correlation at arbitrary temperatures, which yields our main result by relating quantum correlation to quantum entanglement. As a simple application of our analytical techniques, we derived a general limit on the Wigner-Yanase-Dyson skew information and the quantum Fisher information, which will attract significant attention in the field of quantum metrology. Our work reveals novel general aspects of low-temperature quantum physics and sheds light on the characterization of long-range entanglement.