arXiv subjects

Oles Shtanko

Publications and source records attributed to Oles Shtanko.

At least 19 recordsLinked to original sources

arXiv2026

Observation of Improved Accuracy over Classical Sparse Ground-State Solvers using a Quantum Computer

Demonstrating quantum advantage over classical algorithms for ground state energy problems is an outstanding open problem in quantum computation. We experimentally demonstrate that a quantum algorithm can outperform classical selected configuration interaction (SCI) methods, a key family of techniques used in computational chemistry and condensed matter physics. We construct a class of local Hamiltonian problems with sparse ground states, and show that SCI fails to find the ground state of a 49-qubit instance. We then show that sample-based Krylov quantum diagonalization, run on an IBM Heron R3 processor, succeeds at the same task. While the problem is solvable classically using iterative solvers designed to target our Hamiltonian construction, this work resolves the question of whether a sample-based quantum diagonalization algorithm can outperform standard SCI heuristics.

quant-ph↗

arXiv2026

Efficient Quantum Gibbs Sampling with Local Circuits

The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing thermal states -- crucial for probing equilibrium behavior -- became available only recently with breakthrough algorithms based on the simulation of well-designed dissipative processes, a quantum-analogue to Markov chain Monte Carlo (MCMC) algorithms. We show a way to implement these algorithms avoiding expensive block encoding and relying only on dense local circuits, akin to Hamiltonian simulation. Specifically, our method leverages spatial truncation and Trotterization of exact quasilocal dissipative processes. We rigorously prove that the approximations we use have little effect on rapid mixing at high temperatures and allow convergence to the thermal state with small bounded error. Moreover, we accompany our analytical results with numerical simulations that show that this method, unlike previously thought, is within the reach of current generation of quantum hardware. These results provide the first provably efficient quantum thermalization protocol implementable on near-term quantum devices, offering a concrete path toward practical simulation of equilibrium quantum phenomena.

quant-ph↗

arXiv2025

Bounds on Autonomous Quantum Error Correction

Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an ``always-on'' decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper bounds and a lower bound on the logical error rate in terms of correction and noise rates. These bounds suggest that, in general, there is always a correction rate, possibly size-dependent, above which autonomous memories exhibit arbitrarily long coherence times. For any given autonomous memory, size dependence of this correction rate is difficult to rule out: we point to common scenarios where autonomous decoders that stochastically implement active error correction must operate at rates that grow with code size. For codes with a threshold, we show that it is possible to achieve faster-than-polynomial decay of the logical error rate with code size by using superlogarithmic scaling of the correction rate. We illustrate our results with several examples. One example is an exactly solvable global dissipative toric code model that can achieve an effective logical error rate that decreases exponentially with the linear lattice size, provided that the recovery rate grows proportionally with the linear lattice size.

quant-ph↗

arXiv2025

Uncovering Local Integrability in Quantum Many-Body Dynamics

Interacting many-body quantum systems and their dynamics, while fundamental to modern science and technology, are formidable to simulate and understand. However, by discovering their symmetries, conservation laws, and integrability one can unravel their intricacies. Here, using up to 124 qubits of a fully programmable quantum computer, we uncover local conservation laws and integrability in one- and two-dimensional periodically-driven spin lattices in a regime previously inaccessible to such detailed analysis. We focus on the paradigmatic example of disorder-induced ergodicity breaking, where we first benchmark the system crossover into a localized regime through anomalies in the one-particle-density-matrix spectrum and other hallmark signatures. We then demonstrate that this regime stems from hidden local integrals of motion by faithfully reconstructing their quantum operators, thus providing a detailed portrait of the system's integrable dynamics. Our results demonstrate a versatile strategy for extracting the hidden dynamical structure from noisy experiments on large-scale quantum computers.

quant-ph↗

arXiv2025

Maximizing free energy gain

Maximizing the amount of work harvested from an environment is important for a wide variety of biological and technological processes, from energy-harvesting processes such as photosynthesisto energy storage systems such as fuels and batteries. Here we consider the maximization of free energy -- and by extension, the maximum extractable work -- that can be gained by a classical or quantum system that undergoes driving by its environment. We consider how the free energy gain depends on the initial state of the system, while also accounting for the cost of preparing the system. We provide simple necessary and sufficient conditions for increasing the gain of free energy by varying the initial state. We also derive simple formulae that relate the free energy gained using the optimal initial state rather than another suboptimal initial state. Finally, we demonstrate that the problem of finding the optimal initial state may have two distinct regimes, one easy and one difficult, depending on the temperatures used for preparation and work extraction. We illustrate our results on a simple model of an information engine.

cond-mat.stat-mech↗

arXiv2025

Realization of Two-dimensional Discrete Time Crystals with Anisotropic Heisenberg Coupling

A discrete time crystal (DTC) is the paradigmatic example of a phase of matter that occurs exclusively in systems out of equilibrium. This phenomenon is characterized by the spontaneous symmetry breaking of discrete time-translation and provides a rich playground to study a fundamental question in statistical physics: what mechanism allows for driven quantum systems to exhibit emergent behavior that deviates from their counterparts with time-independent evolution? Unlike equilibrium phases, DTCs exhibit macroscopic manifestations of coherent quantum dynamics, challenging the conventional narrative that thermodynamic behavior universally erases quantum signatures. However, due to the difficulty of simulating these systems with either classical or quantum computers, previous studies have been limited to a set of models with Ising-like couplings -- and mostly only in one dimension -- thus precluding our understanding of the existence (or not) of DTCs in models with interactions that closely align with what occurs in nature. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we are able to demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. Our comprehensive analysis reveals a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, highlighting the tunability of these phases through multiple control parameters. Crucially, our results emphasize the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.

quant-ph↗

arXiv2024

Complexity of Local Quantum Circuits under Nonunital Noise

It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as depolarizing noise. Building on the idea of the "quantum refrigerator" [Ben-Or, Gottesman and Hassidim (2013)], we improve upon previous results and show that geometrically local circuits in the presence of nonunital noise, in any dimension $d\geq 1$, can correct errors without mid-circuit measurements and extend computation to any depth, with only polylogarithmic overhead in the depth and the number of qubits. This implies that local quantum dynamics subjected to sufficiently weak nonunital noise is computationally universal and nearly as hard to simulate as noiseless dynamics. Additionally, we quantify the contraction property of local random circuits in the presence of nonunital noise.

quant-ph↗

arXiv2024

Tensor Network enhanced Dynamic Multiproduct Formulas

Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We introduce a novel algorithm that combines tensor networks and quantum computation to produce results that are more accurate than what could be achieved by either method used in isolation. Our algorithm is based on multiproduct formulas (MPF) - a technique that linearly combines Trotter product formulas to reduce algorithmic error. Our algorithm uses a quantum computer to calculate the expectation values and tensor networks to calculate the coefficients used in the linear combination. We present a detailed error analysis of the algorithm and demonstrate the full workflow on a one-dimensional quantum simulation problem on $50$ qubits using two IBM quantum computers: $ibm\_torino$ and $ibm\_kyiv$.

quant-ph↗

arXiv2024

Advantage of Quantum Neural Networks as Quantum Information Decoders

A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less understood. We study the problem of decoding quantum information encoded in the groundspaces of topological stabilizer Hamiltonians in the presence of generic perturbations, such as quenched disorder. We first prove that the standard stabilizer-based error correction and decoding schemes work adequately well in such perturbed quantum codes by showing that the decoding error diminishes exponentially in the distance of the underlying unperturbed code. We then prove that Quantum Neural Network (QNN) decoders provide an almost quadratic improvement on the readout error. Thus, we demonstrate provable advantage of using QNNs for decoding realistic quantum error-correcting codes, and our result enables the exploration of a wider range of non-stabilizer codes in the near-term laboratory settings.

quant-ph↗

arXiv2023

Observing and braiding topological Majorana modes on programmable quantum simulators

Electrons are indivisible elementary particles, yet paradoxically a collection of them can act as a fraction of a single electron, exhibiting exotic and useful properties. One such collective excitation, known as a topological Majorana mode, is naturally stable against perturbations, such as unwanted local noise, and can thereby robustly store quantum information. As such, Majorana modes serve as the basic primitive of topological quantum computing, providing resilience to errors. However, their demonstration on quantum hardware has remained elusive. Here, we demonstrate a verifiable identification and braiding of topological Majorana modes using a superconducting quantum processor as a quantum simulator. By simulating fermions on a one-dimensional lattice subject to a periodic drive, we confirm the existence of Majorana modes localized at the edges, and distinguish them from other trivial modes. To simulate a basic logical operation of topological quantum computing known as braiding, we propose a non-adiabatic technique, whose implementation reveals correct braiding statistics in our experiments. This work could further be used to study topological models of matter using circuit-based simulations, and shows that long-sought quantum phenomena can be realized by anyone in cloud-run quantum simulations, whereby accelerating fundamental discoveries in quantum science and technology.

quant-ph↗

arXiv2023

Preparing thermal states on noiseless and noisy programmable quantum processors

Nature is governed by precise physical laws, which can inspire the discovery of new computer-run simulation algorithms. Thermal states are the most ubiquitous for they are the equilibrium states of matter. Simulating thermal states of quantum matter has applications ranging from quantum machine learning to better understanding of high-temperature superconductivity and quantum chemistry. The computational complexity of this task is hopelessly hard for classical computers. The existing quantum algorithms come with caveats: most either require quantum phase estimation rendering them impractical for current noisy hardware, or are variational which face obstacles such as initialization, barren plateaus, and a general lack of provable guarantee. We provide two quantum algorithms with provable guarantees to prepare thermal states on (near-term) quantum computers that avoid these drawbacks. The first algorithm is inspired by the natural thermalization process where the ancilla qubits act as the infinite thermal bath. This algorithm can potentially run in polynomial time to sample thermal distributions of ergodic systems -- the vast class of physical systems that equilibrate in isolation with respect to local observables. The second algorithm works for any system and in general runs in exponential time. However, it requires significantly smaller quantum resources than previous such algorithms. In addition, we provide an error mitigation technique for both algorithms to fight back decoherence, which enables us to run our algorithms on the near-term quantum devices. To illustration, we simulate the thermal state of the hardcore Bose-Hubbard model on the latest generation of available quantum computers.

quant-ph↗

arXiv2022

Tight bounds on the convergence of noisy random circuits to the uniform distribution

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work.

quant-ph↗

arXiv2022

Monitoring-induced Entanglement Entropy and Sampling Complexity

The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.

quant-ph↗

arXiv2022

Kramers' degeneracy for open systems in thermal equilibrium

Kramers' degeneracy theorem underpins many interesting effects in quantum systems with time-reversal symmetry. We show that the generator of dynamics for Markovian open fermionic systems can exhibit an analogous degeneracy, protected by a combination of time-reversal symmetry and the microreversibility (detailed balance) property of systems at thermal equilibrium -- the degeneracy is lifted if either condition is not met. We provide simple examples of this phenomenon and show that the degeneracy is reflected in the single-particle Green's functions. Furthermore, we show that certain experimental signatures of topological edge modes in open many-body systems can be protected by microreversibility in the same way. Our results highlight the importance of detailed balance in characterizing open topological matter.

cond-mat.mes-hall↗

arXiv2021

Discovering hydrodynamic equations of many-body quantum systems

Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum systems often admit a simplified description, which involves a small set of physical observables and requires only a few parameters such as sound velocity or viscosity. Unveiling the relationship between these hydrodynamic equations and the underlying microscopic theory usually requires a great effort by condensed matter theorists. In the present paper, we develop a new machine-learning framework for automated discovery of effective equations from a limited set of available data, thus bypassing complicated analytical derivations. The data can be generated from numerical simulations or come from experimental quantum simulator platforms. Using integrable models, where direct comparisons can be made, we reproduce previously known hydrodynamic equations, strikingly discover novel equations and provide their derivation whenever possible. We discover new hydrodynamic equations describing dynamics of interacting systems, for which the derivation remains an outstanding challenge. Our approach provides a new interpretable method to study properties of quantum materials and quantum simulators in non-perturbative regimes.

quant-ph↗

arXiv2021

Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.

quant-ph↗

arXiv2020

Unitary Subharmonic Response and Floquet Majorana Modes

Detection and manipulation of excitations with non-Abelian statistics, such as Majorana fermions, are essential for creating topological quantum computers. To this end, we show the connection between the existence of such localized particles and the phenomenon of unitary subharmonic response (SR) in periodically driven systems. In particular, starting from highly nonequilibrium initial states, the unpaired Majorana modes exhibit spin oscillations with twice the driving period, are localized, and can have exponentially long lifetimes in clean systems. While the lifetime of SR is limited in translationally invariant systems, we show that disorder can be engineered to stabilize the subharmonic response of Majorana modes. A viable observation of this phenomenon can be achieved using modern multiqubit hardware, such as superconducting circuits and cold atomic systems.

cond-mat.str-el↗

arXiv2020

Classical Models of Entanglement in Monitored Random Circuits

The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth Rényi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-Rényi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.

cond-mat.dis-nn↗