Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model

TL;DR

This paper explores quantum error mitigation techniques for simulating particle-density correlations in the real-time dynamics of the Schwinger model, combining classical optimization and experimental runs on IBM quantum hardware.

Contribution

It introduces a quantum-classical approach to reduce circuit complexity and implements error mitigation for studying correlations in the Schwinger model.

Findings

Error mitigation improves accuracy of correlation measurements

Optimized circuits reduce the number of three-qubit gates

Experimental results demonstrate feasibility on IBM quantum devices

Abstract

Quantum computing gives direct access to the study of real-time dynamics of quantum many-body systems. In principle, it is possible to directly calculate non-equal-time correlation functions, from which one can detect interesting phenomena, such as the presence of quantum scars or dynamical quantum phase transitions. In practice, these calculations are strongly affected by noise, due to the complexity of the required quantum circuits. As a testbed for the evaluation of real-time evolution of observables and correlations, the dynamics of the Zn Schwinger model in a one dimensional lattice is considered. To control the computational cost, we adopt a quantum-classical strategy that reduces the dimensionality of the system by restricting the dynamics to the Dirac vacuum sector and optimizes the embedding into a qubit model by minimizing the number of three-qubit gates. We derive a digital circuit implementation of the time-evolution of particle-density correlation operators and their correlation, comparing results from exact evolution, bare noisy simulations and simulations with different error mitigation techniques. For the evolution of the particle-density operators we also perform runs on a physical IBM quantum device.