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Related papers: Ising Machines for Diophantine Problems in Physics

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Critical phenomena at finite temperature underpin a broad range of physical systems, yet their study remains challenging due to computational bottlenecks near phase transitions. Quantum annealers have attracted significant interest as a…

Statistical Mechanics · Physics 2025-07-11 Gianluca Teza , Francesco Campaioli , Marco Avesani , Oren Raz

The dissipative variant of the Ising model in a transverse field is one of the most important models in the analysis of open quantum many-body systems, due to its paradigmatic character for understanding driven-dissipative quantum phase…

Quantum Physics · Physics 2023-11-15 David Roberts , Aashish A. Clerk

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the…

Dynamical Systems · Mathematics 2016-09-06 Anna Litvak Hinenzon , Vered Rom-Kedar

Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…

Number Theory · Mathematics 2021-11-18 Elisa Bellah

Quantum annealing is a contender to solve combinatorial optimization problems based on quantum dynamics. While significant efforts have been undertaken to investigate the quality of the solutions and the required runtimes, much less…

Statistical Mechanics · Physics 2023-06-05 Artem Rakcheev , Andreas M. Läuchli

In this paper we present a novel strategy to solve optimization problems within a hybrid quantum-classical scheme based on quantum annealing, with a particular focus on QUBO problems. The proposed algorithm is based on an iterative…

Quantum Physics · Physics 2020-04-07 Enrico Blanzieri , Davide Pastorello

Critical phenomena in the two-dimensional Ising model with a defect line are studied using boundary conformal field theory on the $c=1$ orbifold. Novel features of the boundary states arising from the orbifold structure, including…

High Energy Physics - Theory · Physics 2011-07-19 Masaki Oshikawa , Ian Affleck

We propose a novel method using a quantum annealer -- an analog quantum computer based on the principles of quantum adiabatic evolution -- to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are…

Quantum Physics · Physics 2013-05-30 Itay Hen , A. P. Young

Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…

Quantum Physics · Physics 2019-07-17 Chia Cheng Chang , Arjun Gambhir , Travis S. Humble , Shigetoshi Sota

Dynamical Ising machines are continuous dynamical systems that evolve from a generic initial state to a state strongly related to the ground state of the classical Ising model. We show that such a machine driven by the V${}_2$ dynamical…

Emerging Technologies · Computer Science 2025-12-30 Mikhail Erementchouk , Aditya Shukla , Pinaki Mazumder

Quantum annealing devices have been subject to various analyses in order to classify their usefulness for practical applications. While it has been successfully proven that such systems can in general be used for solving combinatorial…

Quantum Physics · Physics 2019-03-18 Michael Streif , Florian Neukart , Martin Leib

The spontaneous disentanglement hypothesis is motivated by some outstanding issues in standard quantum mechanics, including the problem of quantum measurement. The current study compares between some possible methods that can be used to…

Quantum Physics · Physics 2026-02-10 Eyal Buks

The 1+1D Ising model is an ideal benchmark for quantum algorithms, as it is very well understood theoretically. This is true even when expanding the model to include complex coupling constants. In this work, we implement quantum algorithms…

Quantum Physics · Physics 2023-12-01 Erik Gustafson , Michael Hite , Jay Hubisz , Bharath Sambasivam , Judah Unmuth-Yockey

Boltzmann sampling is a central component of many computational frameworks, including numerous algorithms in machine learning. Although quantum annealers have been investigated as potential fast Boltzmann samplers, their dependence on…

Statistical Mechanics · Physics 2026-04-15 Ju-Yeon Gyhm , Gilhan Kim , Hyukjoon Kwon , Yongjoo Baek

The model of laminated wave turbulence puts forth a novel computational problem - construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order $10^{12}$ and more. The equations to be solved in…

Mathematical Physics · Physics 2009-11-11 Elena Kartashova , Alexey Kartashov

We demonstrate experimentally the ability of a quantum annealer to distinguish between sets of non-isomorphic graphs that share the same classical Ising spectrum. Utilizing the pause-and-quench features recently introduced into D-Wave…

Quantum Physics · Physics 2020-09-30 Zoe Gonzalez Izquierdo , Ruilin Zhou , Klas Markström , Itay Hen

The photonic Ising machine is a new paradigm of optical computing that takes advantage of the unique properties of light wave propagation, parallel processing, and low-loss transmission. Thus, the process of solving combinatorial…

Emerging Technologies · Computer Science 2025-04-08 Jiayi Ouyang , Yuxuan Liao , Zhiyao Ma , Deyang Kong , Xue Feng , Xiang Zhang , Xiaowen Dong , Kaiyu Cui , Fang Liu , Wei Zhang , Yidong Huang

To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult…

Quantum Physics · Physics 2020-04-17 David Roberts , Lukasz Cincio , Avadh Saxena , Andre Petukhov , Sergey Knysh

We describe a new algorithm for the numerical simulation of quantum spin and boson systems. The method is based on the Trotter decomposition in imaginary time and a decoupling by auxiliary Ising spins. It can be applied, in principle, to…

Disordered Systems and Neural Networks · Physics 2009-10-31 M. Ulmke , R. T. Scalettar