Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation

TL;DR

This paper introduces a hybrid quantum-classical algorithm called LSVQC that efficiently compiles quantum circuits for simulating quantum many-body systems, significantly reducing circuit depth and resource requirements compared to traditional methods.

Contribution

The paper presents a novel subspace-based variational compilation method that improves quantum simulation efficiency by localizing optimization, reducing circuit depth, and estimating resource requirements for near-term quantum devices.

Findings

Achieves 95% reduction in circuit depth compared to Trotterization.

Maintains high accuracy with reduced resource requirements.

Estimates gate error thresholds suitable for near-term quantum hardware.

Abstract

Simulation of quantum many-body systems is a promising application of quantum computers. However, implementing the time-evolution operator as a quantum circuit efficiently on near-term devices with limited resources is challenging. Standard approaches like Trotterization often require deep circuits, making them impractical. This paper proposes a hybrid quantum-classical algorithm called Local Subspace Variational Quantum Compilation (LSVQC) for compiling the time-evolution operator. The LSVQC uses variational optimization to reproduce the action of the target time-evolution operator within a physically reasonable subspace. Optimization is performed on small local subsystems based on the Lieb-Robinson bound, allowing for cost function evaluation using small-scale quantum devices or classical computers. Numerical simulations on a spin-lattice model and an $\mathit{\text{ab initio}}$ effective model of strongly correlated material Sr$_2$CuO$_3$ demonstrate the algorithm's effectiveness. It is shown that the LSVQC achieves a 95% reduction in circuit depth compared to Trotterization while maintaining accuracy. The subspace restriction also reduces resource requirements and improves accuracy. Furthermore, we estimate the gate count needed to execute the quantum simulations using the LSVQC on near-term quantum computing architectures in the noisy intermediate-scale or early fault-tolerant quantum computing era. Our estimation suggests that the acceptable physical gate error rate for the LSVQC can be significantly larger than for Trotterization.