arXiv subjects

Itay Hen

Publications and source records attributed to Itay Hen.

At least 19 recordsLinked to original sources

arXiv2026

Quantum algorithm for differential equations via permutation matrix representation with application to the Burgers equation

We develop a quantum algorithm for solving the dynamics of the nonlinear viscous Burgers equation. We apply the Carleman linearization procedure on the spatially discretized equation, followed by a padding scheme that allows implementation on qubit registers. Existing Carleman-based quantum algorithms commonly formulate the lifted linear differential equation in an oracle model. Here we decompose the padded generator into diagonal masks and reversible arithmetic permutations using the Permutation Matrix Representation (PMR), which we show to be naturally compatible with the Linear Combination of Hamiltonian Simulations (LCHS) algorithm. Under the assumptions required by LCHS - most importantly positive semidefiniteness of the Hermitian part of the linear generator, possibly after a stabilizing shift - the algorithm prepares a normalized quantum state proportional to the solution of the truncated lifted system; the stabilizing shift introduces an exponential postselection overhead, which we quantify and mitigate through a rescaling scheme. We show that our algorithm scales with the off-diagonal norm of the Carleman generator instead of the matrix norm, which can be advantageous for other generators that are diagonally dominant. We also extend the PMR scheme to general fluid equations that may contain higher-order derivatives or nonlinear terms, or may involve multiple fluid variables or spatial dimensions. The construction illustrates how PMR can serve as a convenient Hamiltonian-simulation primitive for a broader class of LCU-based algorithms.

quant-ph↗

arXiv2026

Dismantling the Stoquastic Dichotomy

We challenge the notion that a stoquastic binary governs fundamental computational boundaries in quantum computing and classical simulation of quantum systems. We argue that vanishing geometric phase (VGP), a geometric condition on the Hamiltonian's transition graph, more adequately captures these boundaries. To distinguish VGP from stoquasticity, we construct VGP 3-local Hamiltonians that are formally hard to stoquastize, yet belong to a family admitting polynomial-time recognition of the VGP property. Without constructing a stoquastizing unitary, we prove that the local Hamiltonian problem is $\mathsf{StoqMA}$-complete under the promise that the input Hamiltonian has VGP, and that a frustration-free variant is in $\mathsf{MA}$ under the same promise. We use this result to argue that non-VGP is necessary for any claimed adiabatic advantage justified by escaping the $\mathsf{StoqMA}$ regime. Further, we identify natural settings where the VGP property can be recognized in polynomial time. In contrast, we show that recognition of VGP is $\mathsf{PSPACE}$-complete in general for geometrically local Hamiltonians. Our results show that the computational boundaries $\mathsf{MA} \subseteq \mathsf{StoqMA} \subseteq \mathsf{QMA}$ traditionally attributed to stoquasticity are better understood as boundaries between vanishing and non-vanishing geometric phase structure.

quant-ph↗

arXiv2026

Planted-Solution Pauli Hamiltonians as a Quantum Benchmarking Primitive

We introduce a construction of Pauli Hamiltonians with exactly known ground-state energies, intended as reference instances for ground-state energy estimation algorithms. The construction embeds a planted block-product state as the simultaneous ground state of a sum of frustration-free local clauses on overlapping supports, exposes the resulting model only as a polynomial-size linear combination of Pauli operators, and admits optional Clifford conjugation that preserves the spectrum. The framework subsumes classical planted constraint-satisfaction problems as a diagonal special case, providing a direct embedding channel through which classical hardness properties can be inherited. Open-source software, certification keys, and example instances are made publicly available.

quant-ph↗

arXiv2026

Permutation Matrix Representation for Quantum Simulation: Comparative Resource Analysis

We present a comparative study of the permutation matrix representation (PMR) method for Hamiltonian simulation alongside other leading quantum algorithms. Our analysis focuses on resource costs for simulating both time-independent and time-dependent Hamiltonians. For the time-independent case, we benchmark PMR against quantum signal processing (QSP) and qubitization, using the Rydberg interaction Hamiltonian as a representative example. For the time-dependent case, we compare the time-dependent extension of PMR with the quantum highly oscillatory protocol (qHOP), applied to a Floquet-driven transverse field Ising model in arbitrary spatial dimensions. In both regimes, we find that PMR offers complementary advantages in resource requirements and exhibits favorable scaling with certain system parameters, suggesting that it may provide practical benefits on resource-constrained quantum hardware.

quant-ph↗

arXiv2026

Planted-solution SAT and Ising benchmarks from integer factorization

We present a family of planted-solution benchmark instances for satisfiability (SAT) solvers and Ising optimization derived from integer factorization. Given two primes $p$ and $q$, the construction encodes the arithmetic constraints of $N = p \times q$ as a conjunctive normal form (CNF) formula whose satisfying assignments correspond to valid factorizations of~$N$. The known pair $(p,q)$ serves as a built-in ground truth, enabling unambiguous verification of solver output. We show that for two $d$-bit primes the total number of carry contractions is on the order of $d^4$. Empirical benchmarks with SAT solvers show that median runtime grows exponentially in the bit-length of the factors over the range tested. The construction provides a scalable, structured, and verifiable benchmark family controlled by a single parameter, accompanied by open-source generation software.

quant-ph↗

arXiv2025

Exponential divided differences via Chebyshev polynomials

Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically stable evaluation of high-order exponential divided differences for dynamically evolving node sets remains a significant computational challenge. We present a Chebyshev-polynomial-based algorithm that addresses this problem by combining the Chebyshev-Bessel expansion of the exponential function with a direct recurrence for Chebyshev divided differences. The method achieves a computational cost of ${\cal O}(qN)$, where $q$ is the divided-difference order and $N$ is the Chebyshev truncation length. We show that $N$ scales linearly with the spectral width through the decay of modified Bessel coefficients, while the dependence on $q$ enters only through structural polynomial constraints. We further develop an incremental update scheme for dynamic node sets that enables the insertion or removal of a single node in ${\cal O}(N)$ time when the affine mapping interval is held fixed. A full \texttt{C++} reference implementation of the algorithms described in this work is publicly available.

physics.comp-ph↗

arXiv2025

Inequalities, identities, and bounds for divided differences of the exponential function

Let $\exp[x_0,x_1,\dots,x_n]$ denote the divided difference of the exponential function. (i) We prove that exponential divided differences are log-submodular. (ii) We establish the four-point inequality $ \exp[a,a,b,c]\,\exp[d,d,b,c]+\exp[b,b,a,d]\,\exp[c,c,a,d]-\exp[a,b,c,d]^2 \ge 0 $ for all $ a,b,c,d \in \mathbb{R} $. (iii) We obtain sharp two-sided bounds for $\exp[x_0,\dots,x_n]$ at fixed mean and variance; as a consequence, we derive their large-input asymptotics. (iv) We present closed-form identities for divided differences of the exponential function, including a convolution identity and summation formulas for repeated arguments.

math.CA↗

arXiv2025

Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach

In a typical finite temperature quantum Monte Carlo (QMC) simulation, estimators for simple static observables such as specific heat and magnetization are known. With a great deal of system-specific manual labor, one can sometimes also derive more complicated non-local or even dynamic observable estimators. Within the permutation matrix representation (PMR) flavor of QMC, however, we show that one can derive formal estimators for arbitrary static observables. We also derive exact, explicit estimators for general imaginary-time correlation functions and non-trivial integrated susceptibilities thereof. We demonstrate the practical versatility of our method by estimating various non-local, random observables for the transverse-field Ising model on a square lattice.

cond-mat.stat-mech↗

arXiv2025

A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians

We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a previously developed PMR-QMC method for spin-1/2 Hamiltonians [Phys. Rev. Research 6, 013281 (2024)]. Because it does not rely on a local bond decomposition, the method applies equally well to models with arbitrary connectivities, long-range and multi-spin interactions, and its closed-walk formulation allows a natural analysis of sign-problem conditions in terms of cycle weights. To demonstrate its applicability and versatility, we apply our method to spin-1 and spin-3/2 quantum Heisenberg models on the square lattice, as well as to randomly generated high-spin Hamiltonians. Additionally, we show how the approach naturally extends to general Hamiltonians involving mixtures of particle species, including bosons and fermions. We have made our program code freely accessible on GitHub.

physics.comp-ph↗

arXiv2024

A simple quantum simulation algorithm with near-optimal precision scaling

Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer from suboptimal scaling with respect to simulation precision, existing simulation techniques are, for the most part, too intricate to implement on early fault-tolerant quantum hardware. We propose a quantum Hamiltonian dynamics simulation algorithm that aims to be both straightforward to implement and, at the same time, have near-optimal scaling in simulation precision.

quant-ph↗

arXiv2024

A universal black-box quantum Monte Carlo approach to quantum phase transitions

We derive exact, universal, closed-form quantum Monte Carlo estimators for finite-temperature energy susceptibility and fidelity susceptibility, applicable to essentially arbitrary Hamiltonians. Combined with recent advancements in Monte Carlo, our approach enables a black-box framework for studying quantum phase transitions--without requiring prior knowledge of an order parameter or the manual design of model-specific ergodic quantum Monte Carlo update rules. We demonstrate the utility of our method by applying a single implementation to the transverse-field Ising model, the XXZ model, and an ensemble of models related by random unitaries.

cond-mat.stat-mech↗

arXiv2024

ClassiFIM: An Unsupervised Method To Detect Phase Transitions

Estimation of the Fisher Information Metric (FIM-estimation) is an important task that arises in unsupervised learning of phase transitions, a problem proposed by physicists. This work completes the definition of the task by defining rigorous evaluation metrics distMSE, distMSEPS, and distRE and introduces ClassiFIM, a novel machine learning method designed to solve the FIM-estimation task. Unlike existing methods for unsupervised learning of phase transitions, ClassiFIM directly estimates a well-defined quantity (the FIM), allowing it to be rigorously compared to any present and future other methods that estimate the same. ClassiFIM transforms a dataset for the FIM-estimation task into a dataset for an auxiliary binary classification task and involves selecting and training a model for the latter. We prove that the output of ClassiFIM approaches the exact FIM in the limit of infinite dataset size and under certain regularity conditions. We implement ClassiFIM on multiple datasets, including datasets describing classical and quantum phase transitions, and find that it achieves a good ground truth approximation with modest computational resources. Furthermore, we independently implement two alternative state-of-the-art methods for unsupervised estimation of phase transition locations on the same datasets and find that ClassiFIM predicts such locations at least as well as these other methods. To emphasize the generality of our method, we also propose and generate the MNIST-CNN dataset, which consists of the output of CNNs trained on MNIST for different hyperparameter choices. Using ClassiFIM on this dataset suggests there is a phase transition in the distribution of image-prediction pairs for CNNs trained on MNIST, demonstrating the broad scope of FIM-estimation beyond physics.

cs.LG↗

arXiv2024

Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs

We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is the Hamiltonian. By working out expressions for the partition function and transition amplitudes of discretized versions of continuous-variable quantum systems, and then taking the continuum limit, we explicitly recover Feynman's continuous-variable path integrals. We also discuss the implications of our result.

quant-ph↗

arXiv2024

Accounting for gauge symmetries in CHSH experiments

We re-examine the CHSH experiment, which we abstract here as a multi-round game played between two parties with each party reporting a single binary outcome at each round. We explore in particular the role that symmetries, and the spontaneous breaking thereof, play in determining the maximally achievable correlations between the two parties. We show, with the help of an explicit statistical model, that the spontaneous breaking of rotational symmetry allows for stronger correlations than those that can be achieved in its absence. We then demonstrate that spontaneous symmetry breaking may lead to a violation of the renowned CHSH inequality. We believe that the ideas presented in this paper open the door to novel research avenues that have the potential to deepen our understanding of the quantum formalism and the physical reality that it describes.

quant-ph↗

arXiv2023

Exploiting Maximally Mixed States for Spectral Estimation by Time Evolution

We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the Hamiltonian of interest and collecting specific time-series measurements to estimate its spectrum. We demonstrate the advantage of our technique over currently used classical statistical sampling methods. We showcase our approach by experimentally estimating the spectral decomposition of a 2-qubit Heisenberg Hamiltonian on an IBM Quantum backend. For this purpose, we develop a hardware-efficient decomposition that controls $n$-qubit Pauli rotations against the physically closest qubit alongside expressing two-qubit rotations in terms of the native entangling interaction. This substantially reduced the accumulation of errors from noisy two-qubit operations in time evolution simulation protocols. We conclude by discussing the potential impact of our work and the future directions of research it opens.

quant-ph↗

arXiv2023

A quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs

We propose a quantum Monte Carlo algorithm capable of simulating the Bose-Hubbard model on arbitrary graphs, obviating the need for devising lattice-specific updates for different input graphs. We show that with our method, which is based on the recently introduced Permutation Matrix Representation Quantum Monte Carlo [Gupta, Albash and Hen, J. Stat. Mech. (2020) 073105], the problem of adapting the simulation to a given geometry amounts to generating a cycle basis for the graph on which the model is defined, a procedure that can be carried out efficiently and and in an automated manner. To showcase the versatility of our approach, we provide simulation results for Bose-Hubbard models defined on two-dimensional lattices as well as on a number of random graphs.

cond-mat.stat-mech↗

arXiv2023

A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians

We present a universal parameter-free quantum Monte Carlo (QMC) algorithm designed to simulate arbitrary spin-$1/2$ Hamiltonians. To ensure the convergence of the Markov chain to equilibrium for every conceivable case, we devise a clear and simple automated protocol that produces QMC updates that are provably ergodic and satisfy detailed balance. We demonstrate the applicability and versatility of our method by considering several illustrative examples, including the simulation of the XY model on a triangular lattice, the toric code, and random $k$-local Hamiltonians. We have made our program code freely accessible on GitHub.

physics.comp-ph↗

arXiv2022

Localization transition induced by programmable disorder

We investigate the occurrence of many-body localization (MBL) on a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph with random exchange interactions and longitudinal fields. We observe a transition from an ergodic phase to a non-thermal phase for individual energy eigenstates induced by a critical disorder strength for the Ising parameters. Our result follows from the analysis of both the mean half-system block entanglement and the energy level statistics. We identify the critical point associated with this transition using the maximum variance of the block entanglement over the disorder ensemble as a function of the disorder strength. The calculated energy density phase diagram shows the existence of a mobility edge in the energy spectrum. In terms of the energy level statistics, the system changes from the Gaussian orthogonal ensemble for weak disorder to a Poisson distribution limit for strong randomness, which implies localization behavior. We then realize the time-independent disordered Ising Hamiltonian experimentally using a reverse annealing quench-pause-quench protocol on a D-Wave 2000Q programmable quantum annealer. We characterize the transition from the thermal to the localized phase through magnetization measurements at the end of the annealing dynamics, and the results are compatible with our theoretical prediction for the critical point. However, the same behavior can be reproduced using a classical spin-vector Monte Carlo simulation, which suggests that genuine quantum signatures of the phase transition remain out of reach using this experimental platform and protocol.

quant-ph↗