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Recent Extensions of the ZKCM Library for Parallel and Accurate MPS Simulation of Quantum Circuits

Akira SaiToh

TL;DR

The paper presents parallel extensions to the ZKCM and ZKCM_QC libraries to enable high-precision, matrix-product-state (MPS) simulations of quantum circuits using OpenMP and NVIDIA CUDA. It demonstrates that OpenMP accelerates Hermitian diagonalization at high precision, which is a key bottleneck in MPS-based simulations, though CUDA gains depend on hardware parity. The work discusses simulated quantum algorithms (notably Deutsch-Jozsa-type circuits) and reviews quantum factoring efforts, arguing that high-precision arithmetic is essential to maintain small Schmidt ranks and accurate time evolution. The findings suggest meaningful performance benefits for large-scale, high-precision simulations and point to future multi-thread, multi-precision advancements to tackle larger quantum circuits. Overall, the extensions position ZKCM and ZKCM_QC as viable tools for scalable, precise classical simulation of quantum circuits.

Abstract

A C++ library ZKCM and its extension library ZKCM_QC have been developed since 2011 for multiple-precision matrix computation and accurate matrix-product-state (MPS) quantum circuit simulation, respectively. In this report, a recent progress in the extensions of these libraries is described, which are mainly for parallel processing with the OpenMP and CUDA frameworks.

Recent Extensions of the ZKCM Library for Parallel and Accurate MPS Simulation of Quantum Circuits

TL;DR

The paper presents parallel extensions to the ZKCM and ZKCM_QC libraries to enable high-precision, matrix-product-state (MPS) simulations of quantum circuits using OpenMP and NVIDIA CUDA. It demonstrates that OpenMP accelerates Hermitian diagonalization at high precision, which is a key bottleneck in MPS-based simulations, though CUDA gains depend on hardware parity. The work discusses simulated quantum algorithms (notably Deutsch-Jozsa-type circuits) and reviews quantum factoring efforts, arguing that high-precision arithmetic is essential to maintain small Schmidt ranks and accurate time evolution. The findings suggest meaningful performance benefits for large-scale, high-precision simulations and point to future multi-thread, multi-precision advancements to tackle larger quantum circuits. Overall, the extensions position ZKCM and ZKCM_QC as viable tools for scalable, precise classical simulation of quantum circuits.

Abstract

A C++ library ZKCM and its extension library ZKCM_QC have been developed since 2011 for multiple-precision matrix computation and accurate matrix-product-state (MPS) quantum circuit simulation, respectively. In this report, a recent progress in the extensions of these libraries is described, which are mainly for parallel processing with the OpenMP and CUDA frameworks.
Paper Structure (10 sections, 2 figures)

This paper contains 10 sections, 2 figures.

Table of Contents

  1. Introduction
  2. Extensions for Parallel Processing
  3. ZKCM_OMP
  4. ZKCM_CUS
  5. Evaluation of Speedup
  6. Usage in an MPS simulation
  7. Simulations of Quantum Algorithms
  8. Deutsch-Jozsa Algorithm
  9. Remarks on Quantum Factoring
  10. Conclusion

Figures (2)

  • Figure 1: Comparison of computing time for Hermitian matrix diagonalization. See the text for explanation.
  • Figure 2: Comparison of computing time for simulating quantum circuits of the Deutsch-Jozsa algorithm for a certain function structure. $n$ stands for the total number of qubits (namely, the circuit width). The bold line indicates the line of ${\rm const} \times n^3$ with fitting to the data points of "OpenMP+CUDA". "single" stands for the case where ZKCM_QC is compiled without parallel processing; "OpenMP" stands for the case with ZKCM_OMP; "CUDA" stands for the case with ZKCM_CUS; "OpenMP+CUDA" stands for the case with both of ZKCM_OMP and ZKCM_CUS.