arXiv subjects

Dmitry A. Abanin

Publications and source records attributed to Dmitry A. Abanin.

At least 19 recordsLinked to original sources

arXiv2026

Local autonomous inference machines for quantum LDPC codes

We introduce a local and distributed framework for decoding quantum LDPC codes. Built atop belief propagation (BP), the architecture combines strictly local processing of syndrome information, local feedback, autonomous operation, and highly parallelized decoding. We establish the framework at two complementary levels. First, we show that any code exhibiting a threshold under iterative BP decoding can be promoted to an autonomous local measurement-and-feedback dynamics while preserving that threshold. We then turn to codes for which naive BP does not itself exhibit threshold behavior. Our key observation is that BP can nevertheless provide sufficiently accurate \emph{local} marginal information: active syndrome defects use these local beliefs to \emph{move}, pair, and annihilate through asynchronous feedback. We demonstrate numerically that this construction exhibits threshold behavior in the point-like sectors of the two- and three-dimensional toric codes, where conventional BP decoding fails. Exploiting the graph-generality of BP, we then study the inference dynamics on the membrane-like sector of the three-dimensional toric code and in a family of bivariate-bicycle quantum LDPC codes.

quant-ph↗

arXiv2026

Multibath Influence Matrices: Universal Scaling from Real-Time Dynamics

Diverging timescales are the hallmark of critical dynamics and the bottleneck to their classical and quantum simulation. To tame this, we compress a spacetime tensor network: temporally into semigroup influence matrices and spatially via matrix-product states. Benchmarking on the two-impurity Anderson model with its four fermionic species, we compute spectral functions to map the evolution from a Kondo resonance, across a non-Fermi-liquid quantum critical point, and into a gapped singlet phase. Resolving transient through asymptotic dynamics in sudden quenches and Kibble-Zurek ramps, we obtain the universal two-channel-Kondo exponent. Together, these results establish multibath influence matrices as a practical tool for real-time dynamics in strongly correlated multi-orbital systems.

cond-mat.str-el↗

arXiv2026

Algorithmic Locality via Provable Convergence in Quantum Tensor Networks

Belief propagation has recently emerged as a powerful framework for evaluating tensor networks in higher dimensions, combining computational efficiency with provable analytical guarantees. In this work, we develop the first end-to-end theory of tensor network belief propagation for a class of projected entangled pair states satisfying \emph{strong injectivity}. We show that when the injectivity parameter exceeds a constant threshold, BP fixed points can be found efficiently, and a cluster-corrected BP algorithm computes physical quantities to $1/\mathrm{poly}(N)$ error in $\mathrm{poly}(N)$ time for an $N$ qubit system. We identify a striking phenomenon we term \emph{algorithmic locality}: local perturbations of the tensor network affect the BP fixed point with an influence decaying rapidly with distance. As a result, updates to the fixed point after a local perturbation can be carried out using only local recomputation. Moreover, through the cluster expansion, this locality extends to observables, implying that local expectation values can be approximated from local data with controlled accuracy. Our results provide the first rigorous guarantee for the effectiveness of tensor-network belief propagation on a wide class of many-body states, bridging a gap between widely used numerical practice and provable algorithmic performance.

quant-ph↗

arXiv2026

Quantum matter is weakly entangled at low energies

We construct upper bounds on entanglement entropies of many-body quantum states that have fixed energy expectation values with respect to geometrically local Hamiltonians. Our focus is on entanglement entropies of subsystems that make up approximately half of the full system. The upper bound on the von Neumann entanglement entropy is half the sum of the thermal entropies of two fictitious systems at the same temperature as one another, with an additional area-law contribution in some systems. The effective temperature is chosen such that the sum of the thermal energies of the two fictitious systems matches the constraint on the energy of the state in the original problem; at subextensive energies, this temperature decreases with increasing system size. Our upper bounds on Rényi entanglement entropies take an analogous form. As a first application we show that ground-state Schmidt ranks in frustration-free (FF) systems are upper bounded by the ground-state degeneracies of Hamiltonians acting on subsystems. Ground-state von Neumann and Rényi entanglement entropies therefore follow an area law when the zero-temperature thermal entropies of subsystems scale with surface areas, rather than with subsystem volumes. This result holds independently of the spectral gap. For physical models of quantum matter, which have well-defined specific heat capacities (and are not necessarily FF), our bounds provide a way to convert this thermodynamic data into constraints on pure-state entanglement at both subextensive and extensive energies. We also show that our upper bounds on half-system entanglement entropies are optimal, up to subleading corrections, in wide varieties of systems. Our results relate physical thermodynamic properties to the structure of many-body Hilbert space at low energies.

cond-mat.stat-mech↗

arXiv2026

Simple slow operators and quantum thermalization

We establish a rigorous relation between the thermalization of typical initial states and the dynamics of local operators. We introduce a concept of simple slow operators (SSOs), defined as operators that have a small commutator with the Hamiltonian and have significant small-sized components. We show that if typical initial states (drawn from a low-complexity state ensemble) do not thermalize on timescale $t$, then SSOs must exist that are approximately conserved up to timescale $t$. Equivalently, the absence of SSOs implies that typical initial states thermalize. We establish these results by introducing the concept of an ensemble variance norm of an operator, defined as the typical magnitude of the expectation value of that operator with respect to states in the ensemble. For low-entanglement ensembles, the norm is related to operator sizes, allowing us to establish a direct link between operator growth and thermalization.

quant-ph↗

arXiv2026

Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits

Belief propagation (BP) provides a scalable heuristic for contracting tensor networks on loopy graphs, but its success in quantum many-body settings has largely rested on empirical evidence. Developing upon a recently introduced cluster-expansion framework for tensor networks, we rigorously study the applicability of BP to many-body quantum systems. For a state represented as a PEPS satisfying a ``loop-decay" condition, we prove that BP supplemented by cluster corrections approximates local observables with exponentially small relative error, and we give explicit formulas expressing local expectation values as BP predictions dressed by connected clusters intersecting the observable region. This representation establishes a direct link between cluster corrections and physical correlation functions. As a result, we show that ``loop-decay" \emph{necessarily implies} exponential decay of connected correlations, yielding sharp, rigorous criteria for when BP can and cannot succeed, and ruling out its validity at critical points. Numerical simulations of the two- and three-dimensional transverse field Ising model at zero and finite temperature confirm our analytical predictions, demonstrating quantitative accuracy deep in gapped phases and systematic failure near criticality.

quant-ph↗

arXiv2026

Quantum thermal state preparation for near-term quantum processors

Preparation of quantum thermal states of many-body systems is a key computational challenge for quantum processors, with applications in physics, chemistry, and classical optimization. We provide a simple and efficient algorithm for thermal state preparation, combining engineered bath resetting and modulated system-bath coupling to derive a quantum channel approximately satisfying quantum detailed balance relations. We show that the fixed point $\hatσ$ of the channel approximates the Gibbs state as $\|\hatσ-\hatσ_β\|\sim θ^2$, where $θ$ is the system-bath coupling and $\hatσ_β\propto e^{-β\hat H_S}$. We provide extensive numerics, for the example of the 2D Quantum Ising model, confirming that the protocol successfully prepares the thermal state throughout the finite-temperature phase diagram, including near the quantum phase transition. Simulations for free-fermion systems provide further evidence for the accuracy of the protocol for large system sizes in the weak-coupling limit. Our algorithm provides a path to efficient quantum simulation of quantum-correlated states at finite temperature with current and near-term quantum processors.

quant-ph↗

arXiv2025

Temporal entanglement transition in chaotic quantum many-body dynamics

Temporal entanglement (TE) of an influence matrix (IM) has been proposed as a measure of complexity of simulating dynamics of local observables in a many-body system. Foligno et al. [Phys. Rev. X 13, 041008 (2023)] recently argued that the TE in chaotic 1d quantum circuits obeys linear (volume-law) scaling with evolution time. To reconcile this apparent high complexity of IM with the rapid thermalization of local observables, here we study the relation between TE, non-Markovianity, and local temporal correlations for chaotic quantum baths. By exactly solving a random-unitary bath model, and bounding distillable entanglement between future and past degrees of freedom, we argue that TE is extensive for low enough bath growth rate, and it reflects genuine non-Markovianity. This memory, however, is entirely contained in highly complex temporal correlations, and its effect on few-point temporal correlators is negligible. An IM coarse-graining procedure, reducing the allowed frequency of measurements of the probe system, results in a transition from volume- to area-law TE scaling. We demonstrate the generality of this TE transition in 1d circuits by analyzing the kicked Ising model analytically at dual-unitary points, as well as numerically away from them. This finding indicates that dynamics of local observables are fully captured by an area-law IM. We provide evidence that the compact IM MPS obtained via standard compression algorithms accurately describes local evolution.

quant-ph↗

arXiv2025

Temporal Complexity Hierarchies in Solvable Quantum Many-Body Dynamics

The influence matrix (IM) provides a powerful framework for characterizing nonequilibrium quantum many-body dynamics by encoding multitime correlations into tensor-network states. Understanding how its computational complexity relates to underlying dynamics is crucial for both theoretical insight and practical utility, yet remains largely unexplored despite a few case studies. Here, we address this question for a family of brickwork quantum circuits ranging from integrable to chaotic regimes. Using tools from geometric group theory, we identify three qualitatively distinct scalings of temporal entanglement entropy, establishing a hierarchy of computational resources required for accurate tensor-network representations of the IM for these models. We further analyze the memory structure of the IM and distinguish between classical and quantum temporal correlations. In particular, for certain examples, we identify effectively classical IMs that admit an efficient Monte Carlo algorithm for computing multitime correlations. In more generic settings without an explicit classical description of the IM, we introduce an operational measure of quantum memory with an experimental protocol, and discuss examples exhibiting long-time genuinely quantum correlations. Our results establish a new connection between quantum many-body dynamics and group theory, providing fresh insights into the complexity of the IM and its intricate connection to the physical characteristics of the dynamics.

quant-ph↗

arXiv2025

Integrals of motion as slow modes in dissipative many-body operator dynamics

We consider Lindbladian operator dynamics in many-body quantum systems with one or more integrals of motion (IOM), subject to weak local dissipation. We demonstrate that IOMs with small support become slow modes of these dynamics, in the sense that their Frobenius norm decays more slowly compared to generic operators. As a result, the eigenoperators of such Lindbladians with slowest decay rates have a large overlap with the IOMs of the underlying Hamiltonian. We demonstrate this correspondence between slow modes and IOMs numerically for a number of many-body models, and further corroborate it with perturbative arguments. These results open up a new method for the identification of IOMs, and provide insights into the dissipative many-body dynamics.

quant-ph↗

arXiv2025

Diverging conditional correlation lengths in the approach to high temperature

The Markov length was recently proposed as an information-theoretic diagnostic for quantum mixed-state phase transitions [Sang & Hsieh, Phys. Rev. Lett. 134, 070403 (2025)]. Here, we show that the Markov length diverges even under classical stochastic dynamics, when a low-temperature ordered state is quenched into the high temperature phase. Conventional observables do not exhibit growing length scales upon quenching into the high-temperature phase; however, the Markov length grows exponentially in time. Consequently, the state of a system as it heats becomes increasingly non-Gibbsian, and the range of its putative "parent Hamiltonian" must diverge with the Markov length. From this information-theoretic point of view the late-time limit of thermalization is singular. We introduce a numerical technique for computing the Markov length based on matrix-product states, and explore its dynamics under general thermal quenches in the one-dimensional classical Ising model. For all cases, we provide simple information-theoretic arguments that explain our results.

quant-ph↗

arXiv2025

Semi-group influence matrices for non-equilibrium quantum impurity models

We introduce a framework for describing the real-time dynamics of quantum impurity models out of equilibrium which is based on the influence matrix approach. By replacing the dynamical map of a large fermionic quantum environment with an effective semi-group influence matrix (SGIM) which acts on a reduced auxiliary space, we overcome the limitations of previous proposals, achieving high accuracy at long evolution times. This SGIM corresponds to a uniform matrix-product state representation of the influence matrix and can be obtained by an efficient algorithm presented in this paper. We benchmark this approach by computing the spectral function of the single impurity Anderson model with high resolution. Further, the spectrum of the effective dynamical map allows us to obtain relaxation rates of the impurity towards equilibrium following a quantum quench. Finally, for a quantum impurity model with on-site two-fermion loss, we compute the spectral function and confirm the emergence of Kondo physics at large loss rates.

cond-mat.str-el↗

arXiv2025

Steady-state dynamical mean field theory based on influence functional matrix product states

We implement the recently developed influence functional matrix product states approach as impurity solver in equilibrium and nonequilibrium dynamical mean field theory (DMFT) calculations of the single-band Hubbard model. The method yields numerically exact descriptions of metallic states without sharp spectral features, at a moderate numerical cost. Systems with narrow quasiparticle or spin-polaron peaks, as well as low-temperature Mott insulators provide more challenges, since these simulations require long time contours or high bond dimensions. A promising field of application is the DMFT simulation of nonequilibrium steady states, which we demonstrate with results for photo-doped Mott systems with long-lived doublon and holon populations.

cond-mat.str-el↗

arXiv2025

Constructive interference at the edge of quantum ergodic dynamics

Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC$^{(2)}$. In contrast to dynamics without time reversal, OTOC$^{(2)}$ are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC$^{(2)}$ values. This indicates that OTOC$^{(2)}$ is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC$^{(2)}$ with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC$^{(2)}$ measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC$^{(2)}$, our results indicate a viable path to practical quantum advantage.

quant-ph↗

arXiv2025

Quasiparticle cooling algorithms for quantum many-body state preparation

Probing correlated states of many-body systems is one of the central tasks for quantum simulators and processors. A promising approach to state preparation is to realize desired correlated states as steady states of engineered dissipative evolution. A recent experiment with a Google superconducting quantum processor [X. Mi et al., Science 383, 1332 (2024)] demonstrated a cooling algorithm utilizing auxiliary degrees of freedom that are periodically reset to remove quasiparticles from the system, thereby driving it towards its ground state. In this work, we develop a kinetic theory framework to describe quasiparticle cooling dynamics, and employ it to compare the efficiency of different cooling algorithms. In particular, we introduce a protocol where coupling to auxiliaries is modulated in time to minimize heating processes, and demonstrate that it allows a high-fidelity preparation of ground states in different quantum phases. We verify the validity of the kinetic theory description by an extensive comparison with numerical simulations for the examples of a 1d transverse-field Ising model, the transverse-field Ising model with an additional integrability-breaking field, and a non-integrable antiferromagnetic Heisenberg spin ladder. In all cases we are able to efficiently cool into the many-body ground state. The effects of noise, which limits efficiency of variational quantum algorithms in near-term quantum processors, are investigated through the lens of the kinetic theory: we show how the steady state quasiparticle populations depend on the noise rate, and we establish maximum noise values for achieving high-fidelity ground states. This work establishes quasiparticle cooling algorithms as a practical, robust method for many-body state preparation on near-term quantum processors.

quant-ph↗

arXiv2024

Theory of robust quantum many-body scars in long-range interacting systems

Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special non-equilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work we demonstrate that long-range interacting quantum spin systems generically host robust QMBS. We analyze spectral properties upon raising the power-law decay exponent $α$ of spin-spin interactions from the solvable permutationally-symmetric limit $α=0$. First, we numerically establish that despite spectral signatures of chaos appear for infinitesimal $α$, the towers of $α=0$ energy eigenstates with large collective spin are smoothly deformed as $α$ is increased, and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor non-linearly coupled to an extensive set of bosonic modes. We analitycally solve for the eigenstates of this interacting impurity model by means of a novel polaron-type canonical transformation, and show their self-consistent localization in large-spin sectors of the original Hamiltonian for $0<α<d$ (with $d$ = spatial dimension of the lattice). Our theory unveils the stability mechanism of such QMBS for arbitrary system size and predicts instances of its breakdown, e.g. near dynamical critical points or in presence of semiclassical chaos, which we verify numerically in long-range quantum Ising chains. As a byproduct, we find a predictive criterion for presence or absence of heating under periodic driving for $0<α<d$, beyond existing Floquet-prethermalization theorems.

cond-mat.str-el↗

arXiv2024

Efficient Pseudomode Representation and Complexity of Quantum Impurity Models

Out-of-equilibrium fermionic quantum impurity models (QIM), describing a small interacting system coupled to a continuous fermionic bath, play an important role in condensed matter physics. Solving such models is a computationally demanding task, and a variety of computational approaches are based on finding approximate representations of the bath by a finite number of modes. In this paper, we formulate the problem of finding efficient bath representations as that of approximating a kernel of the bath's Feynman-Vernon influence functional by a sum of complex exponentials, with each term defining a fermionic pseudomode. Under mild assumptions on the analytic properties of the bath spectral density, we provide an analytic construction of pseudomodes, and prove that their number scales polylogarithmically with the maximum evolution time $T$ and the approximation error $\varepsilon$. We then demonstrate that the number of pseudomodes can be significantly reduced by an interpolative matrix decomposition (ID). Furthermore, we present a complementary approach, based on constructing rational approximations of the bath's spectral density using the ``AAA'' algorithm, followed by compression with ID. The combination of two approaches yields a pseudomode count scaling as $N_\text{ID} \sim \log(T)\log(1/\varepsilon)$, and the agreement between the two approches suggests that the result is close to optimal. Finally, to relate our findings to QIM, we derive an explicit Liouvillian that describes the time evolution of the combined impurity-pseudomodes system. These results establish bounds on the computational resources required for solving out-of-equilibrium QIMs, providing an efficient starting point for tensor-network methods for QIMs.

cond-mat.str-el↗

arXiv2024

Corrections to diffusion in interacting quantum systems

Transport and the approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor $\langle n(x,t)n\rangle$, in the presence of a single $U(1)$ or $SU(2)$ charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1d Floquet systems with conserved magnetization. We find a qualitative agreement with EFT which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore non-linear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the non-linear phenomena present in thermalizing systems.

cond-mat.stat-mech↗