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

Yutaro Akahoshi1,2,*, Riki Toshio1,2, Jun Fujisaki1,2, Hirotaka Oshima1,2, Shintaro Sato1,2, and Keisuke Fujii2,3,4,5

  • 1Quantum Laboratory, Fujitsu Research, Fujitsu Limited, 4-1-1 Kawasaki, Kanagawa 211-8588, Japan
  • 2Fujitsu Quantum Computing Joint Research Division, Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 565-8531, Japan
  • 3Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
  • 4Center for Quantum Information and Quantum Biology, Osaka University, 560-0043, Japan
  • 5RIKEN Center for Quantum Computing (RQC), Wako Saitama 351-0198, Japan

  • *Contact author: akahoshi.yutaro@fujitsu.com
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PRX Quantum 6, 040319 – Published 28 October, 2025

DOI: https://doi.org/10.1103/93zr-1ykb

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) been recently been proposed. This architecture focuses on minimizing resource requirements while maximizing the precision of non-Clifford gates, essential for universal quantum computation. However, nondeterministic 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 two-dimensional (2D) Hubbard-model Hamiltonian, a promising application of the STAR architecture. We present two techniques, the parallel-injection protocol and adaptive injection-region updating, to reduce unnecessary time overhead specific to our architecture. By integrating these with the existing fermionic swap (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. Based on this optimized compilation, we estimate the computational resources required for the quantum phase estimation of the 2D Hubbard model. For devices with a physical error rate of pphys=10−4, we estimate that approximately 6.2×104 physical qubits are required to achieve faster ground-state energy estimation of the 8×8 Hubbard model compared to classical computation.

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Popular Summary

Quantum computers are expected to drastically accelerate certain computing tasks over classical computers. To perform large-scale quantum computations, we consume many qubits (typically millions of qubits) for quantum error correction (QEC) to protect all operations from quantum noise, which is still far from realization. In our previous study, we proposed a promising approach to reduce the qubit requirement for robust quantum computing, in which quantum operations are partially protected by QEC while minimizing the additional noise. We confirm that our approach surpasses the existing approaches and classical computers in the early fault-tolerant quantum computing era, in which approximately 104 physical qubits would be available. However, the accuracy of the noisy operation is still not enough to perform practical tasks such as simulations of simple physical models of matter.

In this study, we show how our proposed architecture can achieve practical quantum acceleration on a certain task, the quantum simulation of the two-dimensional Hubbard model. This model describes the behavior of electrons in solid matter and is expected to be one of the early practical tasks where quantum computers will surpass their classical counterparts. One important issue in achieving this is the efficient compilation of the quantum circuit to reduce unnecessary overhead uniquely appearing in our architecture. We introduce two improvements in the compilation and achieve about 10 times acceleration over the known compilation method. By using this result and the efficient phase-estimation algorithm recently proposed, we show that our architecture can perform an about 103 times faster simulation compared to the classical algorithm on an 8×8 Hubbard model with 6×104 physical qubits. This result shows the potential utility of our architecture in the early realization of practical quantum advantage.

This study provides a promising approach for the faster realization of useful quantum computations. We continue to investigate where and how our architecture shows an advantage over other existing approaches.

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Outline

Information

PRX Quantum 6, 040319– Published 28 October, 2025
  • Received 21 October 2024
  • Revised 12 February 2025
  • Accepted 29 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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