Quantum Many-body Systems Research Articles

Many-body quantum chaos in stroboscopically-driven cold atoms

In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform of two-level spectral correlation function, is known to follow random matrix theory (RMT), namely a ‘ramp’ followed by a ‘plateau’ in late times. Recently, a generic early-time deviation from RMT, so-called the ‘bump’, was shown to exist in random quantum circuits as toy models for many-body quantum systems. We demonstrate the existence of ‘bump-ramp-plateau’ behavior in the SFF for a number of paradigmatic and stroboscopically-driven 1D cold-atom models: spinless and spin-1/2 Bose-Hubbard models, and nonintegrable spin-1 condensate with contact or dipolar interactions. We find that the scaling of the many-body Thouless time tTh —the onset of RMT—, and the bump amplitude are more sensitive to variations in atom number than the lattice size regardless of the hyperfine structure, the symmetry classes, or the choice of driving protocol. Moreover, tTh scaling and the increase of the bump amplitude in atom number are significantly slower in spinor gases than interacting bosons in 1D optical lattices, demonstrating the role of locality. We obtain universal scaling functions of SFF which suggest power-law behavior for the bump regime in quantum chaotic cold-atom systems, and propose an interference measurement protocol.

Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout

Quantum many-body systems subjected to unitary evolution with the addition of interspersed measurements exhibit a variety of dynamical phases that do not occur under pure unitary evolution. However, these systems remain challenging to investigate on near-term quantum hardware owing to the need for numerous ancilla qubits or repeated high-fidelity mid-circuit measurements, a capability that has only recently become available. Here we report the realization of a measurement-induced entanglement phase transition with a hybrid random circuit on up to 14 superconducting qubits with mid-circuit readout capability. We directly observe extensive and sub-extensive scaling of entanglement entropy in the volume- and area-law phases, respectively, by varying the rate of the measurements. We also demonstrate phenomenological critical behaviour by performing a data collapse of the measured entanglement entropy. Our work establishes the use of mid-circuit measurement as a powerful resource for quantum simulation on near-term quantum computers. The interplay of quantum measurements and unitary evolution is expected to produce dynamical phases with different entanglement properties. An entanglement phase transition has now been detected with hybrid quantum circuits in a superconducting processor.

Measurement-induced entanglement phase transitions in variational quantum circuits

Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using near-term quantum computers. Prominent challenges associated with this family of quantum-classical hybrid algorithms are the control of quantum entanglement and quantum gradients linked to their classical optimization. Known as the barren plateau phenomenon, these quantum gradients may rapidly vanish in the presence of volume-law entanglement growth, which poses a serious obstacle to the practical utility of VQAs. Inspired by recent studies of measurement-induced entanglement transition in random circuits, we investigate the entanglement transition in variational quantum circuits endowed with intermediate projective measurements. Considering the Hamiltonian Variational Ansatz (HVA) for the XXZ model and the Hardware Efficient Ansatz (HEA), we observe a measurement-induced entanglement transition from volume-law to area-law with increasing measurement rate. Moreover, we provide evidence that the transition belongs to the same universality class of random unitary circuits. Importantly, the transition coincides with a “landscape transition” from severe to mild/no barren plateaus in the classical optimization. Our work may provide an avenue for improving the trainability of quantum circuits by incorporating intermediate measurement protocols in currently available quantum hardware.

Localization properties in disordered quantum many-body dynamics under continuous measurement

We study localization properties of continuously monitored dynamics and associated measurement-induced phase transitions in disordered quantum many-body systems on the basis of the quantum trajectory approach. By calculating the fidelity between random quantum trajectories, we demonstrate that the disorder and the measurement can lead to dynamical properties distinct from each other, although both have a power to suppress the entanglement spreading. In particular, in the large-disorder regime with weak measurement, we elucidate that the fidelity exhibits an anomalous power-law decay before saturating to the steady-state value. Furthermore, we propose a general method to access physical quantities for quantum trajectories in continuously monitored dynamics without resorting to postselection. It is demonstrated that this scheme drastically reduces the cost of experiments. Our results can be tested in ultracold atoms subject to continuous measurement and open the avenue to study dynamical properties of localization, which cannot be understood from the stationary properties of the entanglement entropy.

Transformer Variational Wave Functions for Frustrated Quantum Spin Systems.

The transformer architecture has become the state-of-art model for natural language processing tasks and, more recently, also for computer vision tasks, thus defining the vision transformer (ViT) architecture. The key feature is the ability to describe long-range correlations among the elements of the input sequences, through the so-called self-attention mechanism. Here, we propose an adaptation of the ViT architecture with complex parameters to define a new class of variational neural-network states for quantum many-body systems, the ViT wave function. We apply this idea to the one-dimensional J_{1}-J_{2} Heisenberg model, demonstrating that a relatively simple parametrization gets excellent results for both gapped and gapless phases. In this case, excellent accuracies are obtained by a relatively shallow architecture, with a single layer of self-attention, thus largely simplifying the original architecture. Still, the optimization of a deeper structure is possible and can be used for more challenging models, most notably highly frustrated systems in two dimensions. The success of the ViT wave function relies on mixing both local and global operations, thus enabling the study of large systems with high accuracy.

Polarons and bipolarons in a two-dimensional square lattice

Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.

Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains

Many-body interactions give rise to the appearance of exotic phases in Hermitian physics. Despite their importance, many-body effects remain an open problem in non-Hermitian physics due to the complexity of treating many-body interactions. Here, we present a family of exact and numerical phase diagrams for non-Hermitian interacting Kitaev chains. In particular, we establish the exact phase boundaries for the dimerized Kitaev-Hubbard chain with complex-valued Hubbard interactions. Our results reveal that some of the Hermitian phases disappear as non-Hermiticty is enhanced. Based on our analytical findings, we explore the regime of the model that goes beyond the solvable regime, revealing regimes where non-Hermitian topological degeneracy remains. The combination of our exact and numerical phase diagrams provides an extensive description of a family of non-Hermitian interacting models. Our results provide a stepping stone toward characterizing non-Hermitian topology in realistic interacting quantum many-body systems.

Quantum Language Model With Entanglement Embedding for Question Answering.

Quantum language models (QLMs) in which words are modeled as a quantum superposition of sememes have demonstrated a high level of model transparency and good post-hoc interpretability. Nevertheless, in the current literature, word sequences are basically modeled as a classical mixture of word states, which cannot fully exploit the potential of a quantum probabilistic description. A quantum-inspired neural network (NN) module is yet to be developed to explicitly capture the nonclassical correlations within the word sequences. We propose a NN model with a novel entanglement embedding (EE) module, whose function is to transform the word sequence into an entangled pure state representation. Strong quantum entanglement, which is the central concept of quantum information and an indication of parallelized correlations among the words, is observed within the word sequences. The proposed QLM with EE (QLM-EE) is proposed to implement on classical computing devices with a quantum-inspired NN structure, and numerical experiments show that QLM-EE achieves superior performance compared with the classical deep NN models and other QLMs on question answering (QA) datasets. In addition, the post-hoc interpretability of the model can be improved by quantifying the degree of entanglement among the word states.

Many body density of states of a system of non interacting spinless fermions

The modeling of out-of-equilibrium many-body quantum systems requires to go beyond low-energy physics and single or few bodies densities of states. Many-body localization, presence or lack of thermalization and quantum chaos are examples of phenomena in which states at different energy scales, including highly excited ones, contribute to dynamics and therefore affect the system’s properties. Quantifying these contributions requires the many-body density of states (MBDoS), a function whose calculation becomes challenging even for non-interacting identical particles due to the difficulty to enumerate accessible states while enforcing the exchange symmetry. In the present work, we introduce a new approach to evaluate the MBDoS in the general case of non-interacting systems of identical quantum particles. The starting point of our method is the principal component analysis of a filling matrix F describing how N particles can be distributed into L single-particle energy levels. We show that the many body spectrum can be expanded as a weighted sum of singular vectors of the filling matrix. The weighting coefficients only involve renormalized energies obtained from the single body spectrum. We illustrate our method in two classes of problems that are mapped into spinless fermions : (i) non-interacting electrons in a homogeneous tight-binding model in 1D and 2D, and (ii) interacting spins in a chain under a transverse field.

Energy dynamics, information and heat flow in quenched cooling and the crossover from quantum to classical thermodynamics

The dynamics when a hot many-body quantum system is brought into instantaneous contact with a cold many-body quantum system can be understood as a combination of early time quantum correlation (von Neumann entropy) gain and late time energy relaxation. We show that at the shortest timescales there is an energy increase in each system linked to the entropy gain, even though equilibrium thermodynamics does not apply. This energy increase is of quantum origin and results from the collective binding energy between the two systems. Counter-intuitively, this implies that also the hotter of the two systems generically experiences an initial energy increase when brought into contact with the other colder system. In the limit where the energy relaxation overwhelms the (quantum) correlation build-up, classical energy dynamics emerges where the energy in the hot system decreases immediately upon contact with a cooler system. We use both strongly correlated SYK systems and weakly correlated mixed field Ising chains to exhibit these characteristics, and comment on its implications for both black hole evaporation and quantum thermodynamics.

Symmetry-resolved entanglement in critical non-Hermitian systems

The study of entanglement in the symmetry sectors of a theory has recently attracted a lot of attention since it provides better understanding of some aspects of quantum many-body systems. In this paper, we extend this analysis to the case of non-Hermitian models, in which the reduced density matrix $\rho_A$ may be non-positive definite and the entanglement entropy negative or even complex. Here we examine in detail the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point, a model that preserves particle number and whose scaling limit is a $bc$-ghost non-unitary CFT. By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of $\rho_A$ and $|\rho_A|$. From them, we can understand the origin of the non-positiveness of $\rho_A$ and naturally define a positive-definite reduced density matrix in each charge sector, which gives a well-defined symmetry-resolved entanglement entropy. As byproduct, we also obtain the analytical distribution of the critical entanglement spectrum.

Maximum-likelihood-estimate Hamiltonian learning via efficient and robust quantum likelihood gradient

Given the recent developments in quantum techniques, modeling the physical Hamiltonian of a target quantum many-body system is becoming an increasingly practical and vital research direction. Here, we propose an efficient quantum strategy that mingles maximum-likelihood-estimate state and supervised machine learning. Given the measurement outcomes, we optimize the target model Hamiltonian and density operator via a series of quantum descent, which we prove is negative semi-definite with respect to the negative-log-likelihood function. In addition to such optimization efficiency, supervised Hamiltonian learning respects the locality of a given quantum system, therefore, extends readily to larger systems. Compared with previous approaches, it also exhibits better accuracy and overall stability toward noises, fluctuations, and temperature ranges, which we demonstrate with various examples.

Emergence of prethermal states in a driven dissipative system through cross-correlated dissipation

Periodically driven closed quantum many-body systems are known to exhibit prethermal or quasi-steady-state dynamics. In this work, we theoretically show that such prethermal phases can appear in the dynamics of a dipolar two-spin-1/2 system coupled to a heat bath if the cross terms between the drive and dipolar interactions are taken into consideration. To this end, we use our recently reported fluctuation-regulated quantum master equation (Chakrabarti A. and Bhattacharyya R., Phys. Rev. A 97 (2018) 063837), to show that the predicted dynamics can successfully explain the experimentally observed features of the transient and prethermal regime.

Enhancing some separability criteria in many-body quantum systems

Quantum measurements based on mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete positive operator valued measurements, which are commonly used in quantum information and quantum computation. In this paper, by a broad class of informationally complete symmetric measurements and correlation matrices, some separability criteria are proposed for different quantum systems that are more robust and comprehensive than the corresponding criteria previously introduced L M Lai, T Li, S M Fei, and Z X Wang, (2018 Quantum Inf. Process., 17, 314); J W Shang, A Asadian, and H J Zhu, (2018 Phys. Rev. A 98, 022309). Furthermore, we extend the separability criteria of tripartite quantum systems to many-body systems. The proposed entanglement criteria may further enrich the relationship between quantum entanglement and measurement.

Low-dimensional quantum gases in curved geometries

Atomic gases confined in curved geometries are characterized by distinctive features that are absent in their flat counterparts, such as periodic boundaries, local curvature and nontrivial topologies. The recent experiments with shell-shaped quantum gases and the study of ring-shaped superfluids point out that the manifold of a quantum gas could soon become a controllable feature, thus enabling the fundamental study of curved many-body quantum systems. In this Perspective article, we review the main geometries realized in the experiments, analysing the theoretical and experimental status on their phase transitions and on the superfluid dynamics. As our outlook, we delineate the study of vortices, the few-body physics and the search for analogue models in various curved geometries as the most promising research areas. Atomic gases, usually confined in flat geometries, are now experimentally realized also in curved settings. This Perspective article analyses their many-body physics in the available geometries of rings and shells and discusses the open research questions.

Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States.

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a Z_{N} generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wave function deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the Z_{N} model we find a family of (weakly) first-order fracton confinement transitions that in the limit of N→∞ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the N→∞ limit, appears to coexist with a gapless deconfined fracton state.

Dicke Superradiance Requires Interactions beyond Nearest Neighbors.

Photon-mediated interactions within an excited ensemble of emitters can result in Dicke superradiance, where the emission rate is greatly enhanced, manifesting as a high-intensity burst at short times. The superradiant burst is most commonly observed in systems with long-range interactions between the emitters, although the minimal interaction range remains unknown. Here, we put forward a new theoretical method to bound the maximum emission rate by upper bounding the spectral radius of an auxiliary Hamiltonian. We harness this tool to prove that for an arbitrary ordered array with only nearest-neighbor interactions in all dimensions, a superradiant burst is not physically observable. We show that Dicke superradiance requires minimally the inclusion of next-nearest-neighbor interactions. For exponentially decaying interactions, the critical coupling is found to be asymptotically independent of the number of emitters in all dimensions, thereby defining the threshold interaction range where the collective enhancement balances out the decoherence effects. Our findings provide key physical insights to the understanding of collective decay in many-body quantum systems, and the designing of superradiant emission in physical systems for applications such as energy harvesting and quantum sensing.

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Equilibrium quantum many-body systems in the vicinity of phase transitions generically manifest universality. In contrast, limited knowledge has been gained on possible universal characteristics in the non-equilibrium evolution of systems in quantum critical phases. In this context, universality is generically attributed to the insensitivity of observables to the microscopic system parameters and initial conditions. Here, we present such a universal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian – a paradigmatic system of disordered, all-to-all interacting fermions that has been designed as a phenomenological description of quantum critical regions. We drive the system far away from equilibrium by performing a global quench, and track how its ensemble average relaxes to a steady state. Employing state-of-the-art numerical simulations for the exact evolution, we reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information and low-order moments of local operators, exhibit within numerical resolution a universal equilibration process. Under a straightforward rescaling, data that correspond to different initial states collapse onto a universal curve, which can be well approximated by a Gaussian throughout large parts of the evolution. To reveal the physics behind this process, we formulate a general theoretical framework based on the Novikov–Furutsu theorem. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution, and can have applications beyond this work. The exact non-Markovian evolution of the SYK ensemble is very well captured by Bourret–Markov approximations, which contrary to common lore become justified thanks to the extreme chaoticity of the system, and universality is revealed in a spectral analysis of the corresponding Liouvillian.

Growth of entanglement of generic states under dual-unitary dynamics

Dual-unitary circuits are a class of locally interacting quantum many-body systems displaying unitary dynamics also when the roles of space and time are exchanged. These systems have recently emerged as a remarkable framework where certain features of many-body quantum chaos can be studied exactly. In particular, they admit a class of ``solvable'' initial states for which, in the thermodynamic limit, one can access the full nonequilibrium dynamics. This reveals a surprising property: when a dual-unitary circuit is prepared in a solvable state the quantum entanglement between two complementary spatial regions grows at the maximal speed allowed by the local structure of the evolution. Here we investigate the fate of this property when the system is prepared in a generic pair-product state. We show that in this case, the entanglement increment during a time step is submaximal for finite times, however, it approaches the maximal value in the infinite-time limit. This statement is proven rigorously for dual-unitary circuits generating high enough entanglement, while it is argued to hold for the entire class.

Local integrals of motion in quasiperiodic many-body localized systems

Local integrals of motion play a central role in the understanding of many-body localization in many-body quantum systems in one dimension subject to a random external potential, but the question of how these local integrals of motion change in a deterministic quasiperiodic potential is one that has received significantly less attention. Here we develop a powerful new implementation of the continuous unitary transform formalism and use this method to directly compute both the effective Hamiltonian and the local integrals of motion for many-body quantum systems subject to a quasiperiodic potential. We show that the effective interactions between local integrals of motion retain a strong fingerprint of the underlying quasiperiodic potential, exhibiting sharp features at distances associated with the incommensurate wavelength used to generate the potential. Furthermore, the local integrals of motion themselves may be expressed in terms of an operator expansion which allows us to estimate the critical strength of quasiperiodic potential required to lead to a localization/delocalization transition, by means of a finite size scaling analysis.