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

International Symposium on Lattice Field Theory (LATTICE)

T-mu phase diagram using classical-quantum hybrid algorithm

Akio Tomiya

Published Jan 6, 2023• 1 citation
Publisher

Abstract

We study the Schwinger model at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt $\beta$-VQE, a classical-quantum hybrid algorithm with a neural network, to evaluate thermal and quantum expectation values and study the phase diagram for the massless Schwinger model along with the temperature and density. By comparing the exact variational free energy, we find that the variational algorithm works for the Schwinger model for $T>0$ and $\mu$>0. As a result, we obtain a qualitative picture of the phase diagram for the massless Schwinger model.

DOI
10.22323/1.430.0039

Related papers

Schwinger model at finite temperature and density with beta VQE

Akio Tomiya

We investigate a quantum gauge theory at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt $β$-VQE to evaluate thermal and quantum expectation values and study the phase diagram for massless Schwinger model along with the temperature and density. By compering the exact variational free energy, we find the variational algorithm work for $T>0$ and $μ>0$ for the Schwinger model. No significant volume dependence of the variational free energy is observed in $μ/g \in[0, 1.4]$. We calculate the chiral condensate and take the continuum extrapolation. As a result, we obtain qualitative picture of the phase diagram for massless Schwinger model.

arXiv:2205.08860•May 18, 2022•3 citations

Variational thermal quantum simulation of the lattice Schwinger model

Xu-Dan Xie, Xingyu Guo, Hongxi Xing +3 more

Confinement of quarks due to the strong interaction and the deconfinement at high temperatures and high densities are a basic paradigm for understanding the nuclear matter. Their simulation, however, is very challenging for classical computers due to the sign problem of solving equilibrium states of finite-temperature quantum chromodynamical systems at finite density. In this paper, we propose a variational approach, using the lattice Schwinger model, to simulate the confinement or deconfinement by investigating the string tension. We adopt an ansatz that the string tension can be evaluated without referring to quantum protocols for measuring the entropy in the free energy. Results of numeral simulation show that the string tension decreases both along the increasing of the temperature and the chemical potential, which can be an analog of the phase diagram of QCD. Through numerical simulations on the classical computer, we demonstrate the potential of exploiting near-term quantum computers for investigating the phase diagram of finite-temperature and finite-density nuclear matters.

arXiv:2205.12767•Physical review. D/Physical review. D.•Sep 21, 2022•27 citations

Quantum Simulation of Finite Temperature Schwinger Model via Quantum Imaginary Time Evolution

Juan W. Pedersen, Etsuko Itou, Rong-Yang Sun +1 more

We study the Schwinger model at finite-temperature regime using a quantum-classical hybrid algorithm. The preparation of thermal state on quantum circuit presents significant challenges. To address this, we adopt the Thermal Pure Quantum (TPQ) state approach and apply the Quantum Imaginary Time Evolution (QITE) algorithm to implement the necessary imaginary time evolution. We first compute the chiral condensate in the massless Schwinger model, verifying its consistency with the analytical solution. We then simulate the massive Schwinger model with non-zero topological $\theta$-term to investigate the temperature and $\theta$-dependence of the chiral condensate. Our method works well even at non-zero $\theta$ regime, while the conventional lattice Monte Carlo method suffers from the sign problem in this system.

arXiv:2311.11616•International Symposium on Lattice Field Theory (LATTICE)•Dec 27, 2023•6 citations

Mixed State Variational Quantum Eigensolver for the Estimation of Expectation Values at Finite Temperature

Giuseppe Clemente

We introduce a novel hybrid quantum-classical algorithm for the near-term computation of expectation values in quantum systems at finite temperatures. This is based on two stages: on the first one, a mixed state approximating a fiducial truncated density matrix is prepared through Variational Quantum Eigensolving (VQE) techniques; this is then followed by a reweighting stage where the expectation values for observables of interest are computed. These two stages can then be iterated again with different hyperparameters to achieve arbitrary accuracy. Resource and time scalability of the algorithm is discussed with a near-term perspective.

arXiv:2401.17194•International Symposium on Lattice Field Theory (LATTICE)•May 4, 2024•1 citation

Variational quantum simulation of the quantum critical regime

Zhi-Quan Shi, Xu-Dan Xie, Dan-Bo Zhang

The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures. While it is of great physical interest, simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity. Herein, we propose a variational approach, which minimizes the variational free energy, to simulate and locate the quantum critical regime on a quantum computer. The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state, in which the entropy can be analytically obtained from the initial state, and thus the free energy can be accessed conveniently. With numeral simulation, using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line. Moreover, the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states. Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.

arXiv:2302.07438•Chinese Physics B•Apr 7, 2023•0 citations

Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits

Jin-Guo Liu, Liang Mao, Pan Zhang +1 more

Abstract We extend the ability of an unitary quantum circuit by interfacing it with a classical autoregressive neural network. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit to solve quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a byproduct, the algorithm also gives access to low energy excitation states. We demonstrate applications of the approach to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.

arXiv:1912.11381•Machine Learning Science and Technology•Jul 1, 2020•57 citations
We study the Schwinger model at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt β\betaβ-VQE, a classical-quantum hybrid algorithm with a neural network, to evaluate thermal and quantum expectation values and study the phase diagram for the massless Schwinger model along with the temperature and density. By comparing the exact variational free energy, we find that the variational algorithm works for the Schwinger model for T>0T>0T>0 and μ\muμ>0. As a result, we obtain a qualitative picture of the phase diagram for the massless Schwinger model.
We investigate a quantum gauge theory at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt βββ-VQE to evaluate thermal and quantum expectation values and study the phase diagram for massless Schwinger model along with the temperature and density. By compering the exact variational free energy, we find the variational algorithm work for T>0T>0T>0 and μ>0μ>0μ>0 for the Schwinger model. No significant volume dependence of the variational free energy is observed in μ/g∈[0,1.4]μ/g \in[0, 1.4]μ/g∈[0,1.4]. We calculate the chiral condensate and take the continuum extrapolation. As a result, we obtain qualitative picture of the phase diagram for massless Schwinger model.
Confinement of quarks due to the strong interaction and the deconfinement at high temperatures and high densities are a basic paradigm for understanding the nuclear matter. Their simulation, however, is very challenging for classical computers due to the sign problem of solving equilibrium states of finite-temperature quantum chromodynamical systems at finite density. In this paper, we propose a variational approach, using the lattice Schwinger model, to simulate the confinement or deconfinement by investigating the string tension. We adopt an ansatz that the string tension can be evaluated without referring to quantum protocols for measuring the entropy in the free energy. Results of numeral simulation show that the string tension decreases both along the increasing of the temperature and the chemical potential, which can be an analog of the phase diagram of QCD. Through numerical simulations on the classical computer, we demonstrate the potential of exploiting near-term quantum computers for investigating the phase diagram of finite-temperature and finite-density nuclear matters.
We study the Schwinger model at finite-temperature regime using a quantum-classical hybrid algorithm. The preparation of thermal state on quantum circuit presents significant challenges. To address this, we adopt the Thermal Pure Quantum (TPQ) state approach and apply the Quantum Imaginary Time Evolution (QITE) algorithm to implement the necessary imaginary time evolution. We first compute the chiral condensate in the massless Schwinger model, verifying its consistency with the analytical solution. We then simulate the massive Schwinger model with non-zero topological θ\thetaθ-term to investigate the temperature and θ\thetaθ-dependence of the chiral condensate. Our method works well even at non-zero θ\thetaθ regime, while the conventional lattice Monte Carlo method suffers from the sign problem in this system.
We introduce a novel hybrid quantum-classical algorithm for the near-term computation of expectation values in quantum systems at finite temperatures. This is based on two stages: on the first one, a mixed state approximating a fiducial truncated density matrix is prepared through Variational Quantum Eigensolving (VQE) techniques; this is then followed by a reweighting stage where the expectation values for observables of interest are computed. These two stages can then be iterated again with different hyperparameters to achieve arbitrary accuracy. Resource and time scalability of the algorithm is discussed with a near-term perspective.
The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures. While it is of great physical interest, simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity. Herein, we propose a variational approach, which minimizes the variational free energy, to simulate and locate the quantum critical regime on a quantum computer. The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state, in which the entropy can be analytically obtained from the initial state, and thus the free energy can be accessed conveniently. With numeral simulation, using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line. Moreover, the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states. Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.
Abstract We extend the ability of an unitary quantum circuit by interfacing it with a classical autoregressive neural network. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit to solve quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a byproduct, the algorithm also gives access to low energy excitation states. We demonstrate applications of the approach to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.