Compilation of Trotter-Based Time Evolution for Partially Fault-Tolerant Quantum Computing Architecture

TL;DR

This paper introduces an optimized Trotter-based time evolution method for the 2D Hubbard model within a partially fault-tolerant quantum architecture, significantly reducing overhead and resource requirements for quantum simulations.

Contribution

It develops two novel techniques to improve simulation efficiency in the STAR architecture, enabling faster quantum phase estimation with fewer resources.

Findings

Over 10x speedup over naive methods

Approximately 65,000 physical qubits needed for 8x8 Hubbard model

Efficient simulation reduces resource overhead in fault-tolerant quantum computing

Abstract

Achieving practical quantum speedup with limited resources is a crucial challenge in both academic and industrial communities. To address this, a partially fault-tolerant quantum computing architecture called ``space-time efficient analog rotation quantum computing architecture (STAR architecture)'' has been recently proposed. This architecture focuses on minimizing resource requirements while maximizing the precision of non-Clifford gates, essential for universal quantum computation. However, non-deterministic processes such as the repeat-until-success (RUS) protocol and state injection can introduce significant computational overhead. Therefore, optimizing the logical circuit to minimize this overhead by using efficient fault-tolerant operations is essential. This paper presents an efficient method for simulating the time evolution of the 2D Hubbard model Hamiltonian, a promising application of the STAR architecture. We present two techniques, parallel injection protocol and adaptive injection region updating, to reduce unnecessary time overhead specific to our architecture. By integrating these with the existing fSWAP technique, we develop an efficient Trotter-based time evolution operation for the 2D Hubbard model. Our analysis reveals an acceleration of over 10 times compared to naive serial compilation. This optimized compilation enables us to estimate the computational resources required for quantum phase estimation of the 2D Hubbard model. For devices with a physical error rate of $p_{\rm phys} = 10^{-4}$, we estimate that approximately $6.5 \times 10^4$ physical qubits are required to achieve faster ground state energy estimation of the $8\times8$ Hubbard model compared to classical computation.