{"title":"高温量子Ising模型的经典模拟","authors":"Elizabeth Crosson, Samuel Slezak","doi":"10.22331/q-2025-07-09-1788","DOIUrl":null,"url":null,"abstract":"We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo method based on worldline heat-bath updates always mixes to stationarity in time $\\mathcal{O}(n \\log n)$ for an $n$ qubit system, and therefore provides a fully polynomial-time approximation scheme for the partition function. This result holds whenever the temperature is greater than four plus twice the maximum interaction degree (valence) over all qubits, measured in units of the local coupling strength. For example, this implies that the classical simulation of the thermal state of a superconducting device modeling a frustrated quantum Ising model with maximum valence of 6 and coupling strengths of 1 GHz is always possible at temperatures above 800 mK. Despite the quantum system being at high temperature, the classical spin system resulting from the quantum-to-classical mapping contains strong couplings which cause the single-site Glauber dynamics to mix slowly, therefore this result depends on the use of worldline updates (which are a form of cluster updates that can be implemented efficiently). This result places definite constraints on the temperatures required for a quantum advantage in analog quantum simulation with various NISQ devices based on equilibrium states of quantum Ising models.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"9 1","pages":""},"PeriodicalIF":5.1000,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classical Simulation of High Temperature Quantum Ising Models\",\"authors\":\"Elizabeth Crosson, Samuel Slezak\",\"doi\":\"10.22331/q-2025-07-09-1788\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo method based on worldline heat-bath updates always mixes to stationarity in time $\\\\mathcal{O}(n \\\\log n)$ for an $n$ qubit system, and therefore provides a fully polynomial-time approximation scheme for the partition function. This result holds whenever the temperature is greater than four plus twice the maximum interaction degree (valence) over all qubits, measured in units of the local coupling strength. For example, this implies that the classical simulation of the thermal state of a superconducting device modeling a frustrated quantum Ising model with maximum valence of 6 and coupling strengths of 1 GHz is always possible at temperatures above 800 mK. Despite the quantum system being at high temperature, the classical spin system resulting from the quantum-to-classical mapping contains strong couplings which cause the single-site Glauber dynamics to mix slowly, therefore this result depends on the use of worldline updates (which are a form of cluster updates that can be implemented efficiently). This result places definite constraints on the temperatures required for a quantum advantage in analog quantum simulation with various NISQ devices based on equilibrium states of quantum Ising models.\",\"PeriodicalId\":20807,\"journal\":{\"name\":\"Quantum\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":5.1000,\"publicationDate\":\"2025-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.22331/q-2025-07-09-1788\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.22331/q-2025-07-09-1788","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Classical Simulation of High Temperature Quantum Ising Models
We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo method based on worldline heat-bath updates always mixes to stationarity in time $\mathcal{O}(n \log n)$ for an $n$ qubit system, and therefore provides a fully polynomial-time approximation scheme for the partition function. This result holds whenever the temperature is greater than four plus twice the maximum interaction degree (valence) over all qubits, measured in units of the local coupling strength. For example, this implies that the classical simulation of the thermal state of a superconducting device modeling a frustrated quantum Ising model with maximum valence of 6 and coupling strengths of 1 GHz is always possible at temperatures above 800 mK. Despite the quantum system being at high temperature, the classical spin system resulting from the quantum-to-classical mapping contains strong couplings which cause the single-site Glauber dynamics to mix slowly, therefore this result depends on the use of worldline updates (which are a form of cluster updates that can be implemented efficiently). This result places definite constraints on the temperatures required for a quantum advantage in analog quantum simulation with various NISQ devices based on equilibrium states of quantum Ising models.
QuantumPhysics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
9.20
自引率
10.90%
发文量
241
审稿时长
16 weeks
期刊介绍:
Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.