Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Physical Society of Japan

Local Field Response Method Phenomenologically Introducing Spin Correlations

Tatsuya Tomaru

Published Feb 1, 2018• 1 citation
Publisher

Abstract

The local field response (LFR) method is a way of searching for the ground state in a similar manner to quantum annealing. However, the LFR method operates on a classical machine, and quantum effects are introduced through a priori information and through phenomenological means reflecting the states during the computations. The LFR method has been treated with a one-body approximation, and therefore, the effect of entanglement has not been sufficiently taken into account. In this report, spin correlations are phenomenologically introduced as one of the effects of entanglement, by which multiple tunneling at anticrossing points is taken into account. As a result, the accuracy of solutions for a 128-bit system increases by 31% compared with that without spin correlations.

DOI
10.7566/jpsj.87.034801

Related papers

Entanglement and quantum correlations in many-body systems: a unified approach via local unitary operations

Marco Cianciaruso, S. M. Giampaolo, Wojciech Roga +3 more

Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under least-perturbing local unitary operations is a bona fide measure of quantum entanglement, the so-called entanglement of response, which can be extended to mixed states via the convex roof construction. On the other hand, when defined directly on mixed states perturbed by local unitary operations, such a distance turns out to be a bona fide measure of quantum correlations, the so-called discord of response. Exploiting this unified framework, we perform a detailed comparison between two-body entanglement and two-body quantum discord in infinite XY quantum spin chains both in symmetry-preserving and symmetry-breaking ground states as well as in thermal states at finite temperature. The results of the investigation show that in symmetry-preserving ground states the two-point quantum discord dominates over the two-point entanglement, while in symmetrybreaking ground states the two-point quantum discord is strongly suppressed and the two-point entanglement is essentially unchanged. In thermal states, for certain regimes of Hamiltonian parameters, we show that the pairwise quantum discord and the pairwise entanglement can increase with increasing thermal fluctuations.

arXiv:1412.1054•Dec 2, 2014•1 citation

Local Field Response Method Working as Quasi-Quantum Annealing

Tatsuya Tomaru

The local field response (LFR) method is a method of searching for the ground state in a similar manner to quantum annealing. However, it operates on a classical machine, and quantum effects are phenomenologically introduced: (1) an average quantum effect is incorporated in the response function of the spins to the effective field through a priori information; (2) the effect of linear superposition is introduced by taking two successive time points into account in the spin response, reproducing 〈σz〉 ≈ 0 at band anticrossing points; (3) spin correlations, as an effect of entanglement, are introduced by resequencing the calculation order of the spins at their response to the effective field. In this report, we review these phenomenological methods and their effects.

Journal of the Physical Society of Japan•Mar 1, 2019•0 citations

Improved Local Field Response Method Working as Quasi-Quantum Annealing

Tatsuya Tomaru

The local-field response (LFR) method is a way of searching for the ground state of an Ising spin Hamiltonian. Spins evolve by responding to an effective field consisting of gradually decreasing external transverse fields and spin–spin interactions. The spins are treated as classical variables, but quantum effects are taken into account in the response of the spins. The conventional LFR method takes a quantum effect into account through an a priori determined response function. This report not only uses the response function but also considers quantum effects more directly. (1) The effect of band anticrossing is considered. (2) The interaction term and local term in the effective field are appropriately balanced by renormalizing the local term. (3) The a priori determined response function is modified on the basis of a self-field correction. In addition to these quantum-mechanical improvements, (4) the transverse field is modulated with a saw shape to increase opportunities of finding the global minimum, and all spins are inverted several times in the middle of the process in order to expand the search space. As a result, the false probability, the inaccuracy of the solution, and the average number of steps before reaching the final solution decrease to about one-tenth of the corresponding values for the case without improvements.

Journal of the Physical Society of Japan•Apr 18, 2017•2 citations

Quantum Entanglement States: A Non-Local Theory

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge to classical intuition. This paper explores the potential of extending this peculiar phenomenon to encompass non-local correlations, proposing a novel framework termed "Entanglement Non-Locality" (ENL). The core claim is to establish a theoretical foundation for this non-locality, leveraging the inherent properties of entangled states to simulate quantum information transfer and associate it with classical information transfer. We hypothesize that by embedding entanglement within a non-local field theory, we can achieve enhanced quantum information processing and communication capabilities. This research delves into the design of such a field theory, examining its potential to overcome limitations imposed by classical physics and unlock new avenues for quantum technologies.

•Sep 7, 2026•0 citations

Quasi-Adiabatic Quantum Computing Treated with c-Numbers Using the Local-Field Response

Tatsuya Tomaru

A computational method called the local-field response method is proposed, where spins evolve by responding to an effective field consisting of gradually decreasing external fields and spin–spin interactions, similarly to what is carried out in adiabatic quantum computing (AQC). This method is partly quantum–mechanical. That is, spins are treated as classical variables, but the response function of the spins to the effective field is determined a priori by referring to a quantum–mechanical calculation that was carried out for similar problems. This novel response function improves the performance of the ground state being maintained in the time evolution compared with the case without a priori information. The performance is numerically checked in an eight-qubit system by solving random-interaction problems of finding their ground states. The false probability decreases by about half as a result of using a priori information. The operation of this method is classical, but it has a quantum–mechanical advantage through a priori information. This method is practically useful because obtaining a complete quantum system is difficult as it stands.

Journal of the Physical Society of Japan•Feb 10, 2016•3 citations

Quantum Entanglement Analysis: A Precise Computational Approach to Non-Locality

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge to our classical understanding of space and time. Its non-local nature – the seemingly instantaneous correlation between entangled particles, regardless of distance – has captivated physicists and philosophers alike. This research investigates a novel computational method designed to rigorously analyze entanglement, specifically focusing on its non-locality. The core mechanism centers on leveraging the unique properties of entangled states to precisely calculate the non-locality, offering a potential pathway towards a deeper understanding of entanglement's fundamental nature. The paper outlines a method that utilizes a bespoke mathematical framework to isolate and quantify the non-local correlations inherent within entangled systems. We demonstrate the effectiveness of this approach through rigorous analysis and preliminary results, suggesting a significant advancement in the field of quantum entanglement analysis.

•Aug 31, 2026•0 citations
The local field response (LFR) method is a way of searching for the ground state in a similar manner to quantum annealing. However, the LFR method operates on a classical machine, and quantum effects are introduced through a priori information and through phenomenological means reflecting the states during the computations. The LFR method has been treated with a one-body approximation, and therefore, the effect of entanglement has not been sufficiently taken into account. In this report, spin correlations are phenomenologically introduced as one of the effects of entanglement, by which multiple tunneling at anticrossing points is taken into account. As a result, the accuracy of solutions for a 128-bit system increases by 31% compared with that without spin correlations.
Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under least-perturbing local unitary operations is a bona fide measure of quantum entanglement, the so-called entanglement of response, which can be extended to mixed states via the convex roof construction. On the other hand, when defined directly on mixed states perturbed by local unitary operations, such a distance turns out to be a bona fide measure of quantum correlations, the so-called discord of response. Exploiting this unified framework, we perform a detailed comparison between two-body entanglement and two-body quantum discord in infinite XY quantum spin chains both in symmetry-preserving and symmetry-breaking ground states as well as in thermal states at finite temperature. The results of the investigation show that in symmetry-preserving ground states the two-point quantum discord dominates over the two-point entanglement, while in symmetrybreaking ground states the two-point quantum discord is strongly suppressed and the two-point entanglement is essentially unchanged. In thermal states, for certain regimes of Hamiltonian parameters, we show that the pairwise quantum discord and the pairwise entanglement can increase with increasing thermal fluctuations.
The local field response (LFR) method is a method of searching for the ground state in a similar manner to quantum annealing. However, it operates on a classical machine, and quantum effects are phenomenologically introduced: (1) an average quantum effect is incorporated in the response function of the spins to the effective field through a priori information; (2) the effect of linear superposition is introduced by taking two successive time points into account in the spin response, reproducing 〈σz〉 ≈ 0 at band anticrossing points; (3) spin correlations, as an effect of entanglement, are introduced by resequencing the calculation order of the spins at their response to the effective field. In this report, we review these phenomenological methods and their effects.
The local-field response (LFR) method is a way of searching for the ground state of an Ising spin Hamiltonian. Spins evolve by responding to an effective field consisting of gradually decreasing external transverse fields and spin–spin interactions. The spins are treated as classical variables, but quantum effects are taken into account in the response of the spins. The conventional LFR method takes a quantum effect into account through an a priori determined response function. This report not only uses the response function but also considers quantum effects more directly. (1) The effect of band anticrossing is considered. (2) The interaction term and local term in the effective field are appropriately balanced by renormalizing the local term. (3) The a priori determined response function is modified on the basis of a self-field correction. In addition to these quantum-mechanical improvements, (4) the transverse field is modulated with a saw shape to increase opportunities of finding the global minimum, and all spins are inverted several times in the middle of the process in order to expand the search space. As a result, the false probability, the inaccuracy of the solution, and the average number of steps before reaching the final solution decrease to about one-tenth of the corresponding values for the case without improvements.
Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge to classical intuition. This paper explores the potential of extending this peculiar phenomenon to encompass non-local correlations, proposing a novel framework termed "Entanglement Non-Locality" (ENL). The core claim is to establish a theoretical foundation for this non-locality, leveraging the inherent properties of entangled states to simulate quantum information transfer and associate it with classical information transfer. We hypothesize that by embedding entanglement within a non-local field theory, we can achieve enhanced quantum information processing and communication capabilities. This research delves into the design of such a field theory, examining its potential to overcome limitations imposed by classical physics and unlock new avenues for quantum technologies.
A computational method called the local-field response method is proposed, where spins evolve by responding to an effective field consisting of gradually decreasing external fields and spin–spin interactions, similarly to what is carried out in adiabatic quantum computing (AQC). This method is partly quantum–mechanical. That is, spins are treated as classical variables, but the response function of the spins to the effective field is determined a priori by referring to a quantum–mechanical calculation that was carried out for similar problems. This novel response function improves the performance of the ground state being maintained in the time evolution compared with the case without a priori information. The performance is numerically checked in an eight-qubit system by solving random-interaction problems of finding their ground states. The false probability decreases by about half as a result of using a priori information. The operation of this method is classical, but it has a quantum–mechanical advantage through a priori information. This method is practically useful because obtaining a complete quantum system is difficult as it stands.
Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge to our classical understanding of space and time. Its non-local nature – the seemingly instantaneous correlation between entangled particles, regardless of distance – has captivated physicists and philosophers alike. This research investigates a novel computational method designed to rigorously analyze entanglement, specifically focusing on its non-locality. The core mechanism centers on leveraging the unique properties of entangled states to precisely calculate the non-locality, offering a potential pathway towards a deeper understanding of entanglement's fundamental nature. The paper outlines a method that utilizes a bespoke mathematical framework to isolate and quantify the non-local correlations inherent within entangled systems. We demonstrate the effectiveness of this approach through rigorous analysis and preliminary results, suggesting a significant advancement in the field of quantum entanglement analysis.