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Quantum-classical simulation of quantum field theory by quantum circuit learning

Kazuki Ikeda

TL;DR

A hybrid quantum‐classical approach is used to predict quench dynamics, chiral dynamics and jet production in a 1+1‐dimensional model of quantum electrodynamics, finding that its predictions closely align with the results of rigorous classical calculations, exhibiting a high degree of accuracy.

Abstract

We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing the Hamiltonian using Pauli spin matrices. To address this challenge, we leverage quantum circuit learning, employing a compact configuration of qubits and low-depth quantum circuits to predict real-time dynamics in quantum field theories. The key advantage of this approach is that a single-qubit measurement can accurately forecast various physical parameters, including fully-connected operators. To demonstrate the effectiveness of our method, we use it to predict quench dynamics, chiral dynamics and jet production in a 1+1-dimensional model of quantum electrodynamics. We find that our predictions closely align with the results of rigorous classical calculations, exhibiting a high degree of accuracy. This hybrid quantum-classical approach illustrates the feasibility of efficiently simulating large-scale QFTs on cutting-edge quantum devices.

Quantum-classical simulation of quantum field theory by quantum circuit learning

TL;DR

A hybrid quantum‐classical approach is used to predict quench dynamics, chiral dynamics and jet production in a 1+1‐dimensional model of quantum electrodynamics, finding that its predictions closely align with the results of rigorous classical calculations, exhibiting a high degree of accuracy.

Abstract

We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing the Hamiltonian using Pauli spin matrices. To address this challenge, we leverage quantum circuit learning, employing a compact configuration of qubits and low-depth quantum circuits to predict real-time dynamics in quantum field theories. The key advantage of this approach is that a single-qubit measurement can accurately forecast various physical parameters, including fully-connected operators. To demonstrate the effectiveness of our method, we use it to predict quench dynamics, chiral dynamics and jet production in a 1+1-dimensional model of quantum electrodynamics. We find that our predictions closely align with the results of rigorous classical calculations, exhibiting a high degree of accuracy. This hybrid quantum-classical approach illustrates the feasibility of efficiently simulating large-scale QFTs on cutting-edge quantum devices.
Paper Structure (1 section, 20 equations, 4 figures)

This paper contains 1 section, 20 equations, 4 figures.

Table of Contents

  1. The lattice Hamiltonian of the massive Schwinger model

Figures (4)

  • Figure 1: Predictions of the chiral condensate [left] and the electric field [right].
  • Figure 2: Prediction of the real-time dynamics of the axial charge after the quench.
  • Figure 3: Prediction of the real-time evolution of the chiral condensate [left] and energy [right]. g.s., 1st and 2nd mean that the ground, first and second excited states are used as initial states.
  • Figure 4: Behavior of $L_{\mathrm{ext},n}(t)$, where a jet pair is produced at $t_0=0,x_0=N/2$.