Correcting and extending Trotterized quantum many-body dynamics

TL;DR

This paper introduces a hybrid quantum-classical method for simulating quantum many-body dynamics that mitigates noise, extends system size, and corrects Trotterization errors by combining Trotterized quantum evolution with classical corrections.

Contribution

It proposes a novel hybrid ansatz that corrects Trotterized quantum simulations using classical models, enabling error mitigation and system size extension without variational quantum parameters.

Findings

Avoids SWAP gates by hardware-efficient Hamiltonian terms

Mitigates Trotterization errors effectively

Extends system size with constant qubits on quantum device

Abstract

A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical application is currently limited by noise and restricted scalability. In this work, we address these problems by proposing a hybrid ansatz combining the strengths of quantum and classical computational methods. Using Trotterization, we evolve an initial state on the quantum computer according to a simplified Hamiltonian, focusing on terms that are difficult to simulate classically. A classical model then corrects the simulation by including the terms omitted in the quantum circuit. While the classical ansatz is optimized during the time evolution, the quantum circuit has no variational parameters. Derivatives can thus be calculated purely classically, avoiding challenges arising in the optimization of parameterized quantum circuits. We demonstrate three applications of this hybrid method. First, our approach allows us to avoid SWAP gates in the quantum circuit by restricting the quantum part of the ansatz to hardware-efficient terms of the Hamiltonian. Second, we can mitigate errors arising from the Trotterization of the time evolution unitary. Finally, we can extend the system size while keeping the number of qubits on the quantum device constant by including additional degrees of freedom in the classical ansatz.