arXiv subjects

Alexander Yosifov

Publications and source records attributed to Alexander Yosifov.

9 recordsLinked to original sources

arXiv2026

Quantum-classical crossover in fault-tolerant quantum dynamics simulation

While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

quant-ph↗

arXiv2026

Entanglement-facilitated macroscopic cluster formation in quantum many-body dynamics

Metastable quantum many-body dynamics could facilitate the organisation of microscopic degrees of freedom into macroscopic structures. However, the conditions under which this occurs are not well understood. Here we study false-vacuum decay in a 2D quantum Ising model and show that the initial correlation structure can qualitatively change this behaviour. Compared with product-state initialisations, correlated false-vacuum states suppress the proliferation of small true-vacuum domains and favour the formation of macroscopic connected clusters. Tree tensor network simulations of lattices up to $25 \times 25$ further reveal that nucleation proceeds predominantly from the boundary. Finite-size scaling demonstrates the dominant connected cluster remains an extensive fraction of the system even as its size increases. By suppressing this edge-assisted nucleation pathway through boundary pinning, we generate large magnetisation fluctuations consistent with macroscopic superposition. This mechanism relies on the 2D nucleation barrier and is absent in 1D systems or product-state quenches. Our results identify correlated state preparation and boundary engineering as complementary techniques for controlling metastable quantum dynamics.

quant-ph↗

arXiv2026

Hysteretic squashed entanglement in many-body quantum systems

Entanglement in many-body quantum systems is distributed across spatial regions, where its structure often dictates the information-processing capabilities of the state. Yet, characterizing the entanglement structure, especially for mixed states, remains a challenge. In this work, we propose hysteretic squashed entanglement $T_{sq}$, a conditional entanglement monotone that measures the genuine quantum correlations between two subregions, conditioned on a third region, in a many-body quantum state. $T_{sq}$ is upper bounded by the convex-roof extension of quantum conditional mutual information and exhibits several desirable properties like monogamy, convexity, asymptotic continuity, faithfulness, and additivity for tensor-product states. We study the conditional entanglement generation in a one-dimensional transverse-field Ising model under quench, where we show that $T_{sq}$ effectively squashes classical contributions and can detect genuine quantum correlations across both adjacent and long-range subsystems. We elucidate the utility of this measure as a robust quantifier of topological entanglement entropy for mixed states. This opens new operational resource-theoretic avenues for probing topological order and criticality.

quant-ph↗

arXiv2025

Direct probing of the simulation complexity of open quantum many-body dynamics

Simulating open quantum systems is key to understanding non-equilibrium processes, as persistent influence from the environment induces dissipation and can give rise to steady-state phase transitions. A common strategy is to embed the system-environment into a larger unitary framework, but this obscures the intrinsic complexity of the reduced system dynamics. Here, we investigate the computational complexity of simulating open quantum systems, focusing on two physically relevant parameters -- correlation length and mixing time -- and explore whether it can be comparable (or even lower) to that of simulating their closed counterparts. In particular, we study the role of dissipation in simulating open-system dynamics using both quantum and classical methods, where the classical complexity is characterised by the bond dimension and operator entanglement entropy. Our results show that dissipation affects correlation length and mixing time in distinct ways at intermediate and long timescales. Moreover, we observe numerically that in classical tensor network simulations, classical complexity does not decrease with stronger dissipation, revealing a separation between quantum and classical resource scaling.

quant-ph↗

arXiv2025

On the emergence of quantum memory in non-Markovian dynamics

The emergence of memory is a hallmark feature of non-Markovian dynamics. However, the type of memory -- classical or quantum -- required to realize certain dynamics remains unknown. We study the quantum homogenizer as a minimal model of non-Markovian evolution and identify the physical conditions under which genuinely quantum memory becomes necessary. Using entanglement measures and relying only on the local dynamics as a witness, we prove both analytically and numerically the type of memory depends not merely on the dynamics itself, but also on the reservoir's initial entanglement structure, and in particular the propagation of non-classical correlations within it. For different bi- or multi-partite reservoir initializations, we establish a correspondence between interaction strength and entanglement generation. We provide physical criteria and an activation lower bound for the onset of quantum memory. The results may inform us how environmental correlations govern the transition from classical to quantum memory in open quantum systems.

quant-ph↗

arXiv2024

Dissipation-induced Quantum Homogenization for Temporal Information Processing

Quantum reservoirs have great potential as they utilize the complex real-time dissipative dynamics of quantum systems for information processing and target time-series generation without precise control or fine-tuning of the Hamiltonian parameters. Nonetheless, their realization is challenging as quantum hardware with appropriate dynamics, robustness to noise, and ability to produce target steady states is required. To that end, we propose the disordered quantum homogenizer as an alternative platform, and prove it satisfies the necessary and sufficient conditions - stability and contractivity - of the reservoir dynamics, necessary for solving machine learning tasks with time-series input data streams. The results indicate that the quantum homogenization protocol, physically implementable as either nuclear magnetic resonance ensemble or a photonic system, can potentially function as a reservoir computer.

quant-ph↗

arXiv2024

Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware

Quantum homogenization is a reservoir-based quantum state approximation protocol, which has been successfully implemented in state transformation on quantum hardware. In this work we move beyond that and propose the homogenization as a novel platform for quantum state stabilization and information protection. Using the Heisenberg exchange interactions formalism, we extend the standard quantum homogenization protocol to the dynamically-equivalent ($\mathtt{SWAP}$)$^α$ formulation. We then demonstrate its applicability on available noisy intermediate-scale quantum (NISQ) processors by presenting a shallow quantum circuit implementation consisting of a sequence of $\mathtt{CNOT}$ and single-qubit gates. In light of this, we employ the Beny-Oreshkov generalization of the Knill-Laflamme (KL) conditions for near-optimal recovery channels to show that our proposed ($\mathtt{SWAP}$)$^α$ quantum homogenization protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable. Therefore, the protocol protects quantum information contained in a subsystem of the reservoir Hilbert space under CPTP dynamics.

quant-ph↗

arXiv2024

Efficient Digital Quadratic Unconstrained Binary Optimization Solvers for SAT Problems

Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT decision problems or Max k-SAT optimization problems, with conflict-driven (CDCL) solvers being the most prominent. Despite their ability to handle large instances, CDCL-based solvers have fundamental scalability limitations. In light of this, we propose recently-developed quadratic unconstrained binary optimization (QUBO) solvers as an alternative platform for 3-SAT problems. To utilize them, we implement a 2-step [3-SAT]-[Max 2-SAT]-[QUBO] conversion procedure and present a rigorous proof to explicitly calculate the number of both satisfied and violated clauses of the original 3-SAT instance from the transformed Max 2-SAT formulation. We then demonstrate, through numerical simulations on several benchmark instances, that digital QUBO solvers can achieve state-of-the-art accuracy on 78-variable 3-SAT benchmark problems. Our work facilitates the broader use of quantum annealers on noisy intermediate-scale quantum (NISQ) devices, as well as their quantum-inspired digital counterparts, for solving 3-SAT problems.

math.OC↗

arXiv2020

Holographic Interpretation of Relative State Complexity

We investigate a large-$N$ CFT in a high-energy pure state coupled to a small auxiliary system of $M$ weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an effective low-energy notion of computational cost in the bulk, \textit{i.e.} to the minimal depth of the quantum circuit required to decode its gravitational dual. In light of this, using Nielsen's approach, a new measure of quantum chaos in terms of the evolution of circuit complexity is proposed. It suggests that studying the evolution of circuit complexity of the auxiliary system can teach us about the chaotic properties of the large-$N$ CFT. This new diagnostic for quantum chaos has important implications for the interior dynamics of evaporating black holes as it implies the radiated Hawking cloud is pseudorandom.

hep-th↗