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DiaQ: Efficient State-Vector Quantum Simulation

Srikar Chundury, Jiajia Li, In-Saeng Suh, Frank Mueller

TL;DR

DiaQ identifies diagonal sparsity in time-step unitaries of quantum circuits and introduces a diagonal-based sparse format, DiaQ, with a C++ lib and Python wrappers. Integrating DiaQ with SV-Sim yields substantial speedups (up to ~$69\%$) and memory reductions by converting dense $N \times N$ representations to $O(d \cdot N)$, where $d$ is the number of diagonals. The approach accelerates state-vector simulation on multi-core CPUs with SIMD and opens avenues for density-matrix and tensor-network extensions. The work demonstrates practical improvements on benchmarks from SupermarQ and QASMBench, indicating DiaQ's potential for scalable quantum simulations on classical hardware.

Abstract

In the current era of Noisy Intermediate Scale Quantum (NISQ) computing, efficient digital simulation of quantum systems holds significant importance for quantum algorithm development, verification and validation. However, analysis of sparsity within these simulations remains largely unexplored. In this paper, we present a novel observation regarding the prevalent sparsity patterns inherent in quantum circuits. We introduce DiaQ, a new sparse matrix format tailored to exploit this quantum-specific sparsity, thereby enhancing simulation performance. Our contribution extends to the development of libdiaq, a numerical library implemented in C++ with OpenMP for multi-core acceleration and SIMD vectorization, featuring essential mathematical kernels for digital quantum simulations. Furthermore, we integrate DiaQ with SV-Sim, a state vector simulator, yielding substantial performance improvements across various quantum circuits (e.g., ~26.67% for GHZ-28 and ~32.72% for QFT-29 with multi-core parallelization and SIMD vectorization on Frontier). Evaluations conducted on benchmarks from SupermarQ and QASMBench demonstrate that DiaQ represents a significant step towards achieving highly efficient quantum simulations.

DiaQ: Efficient State-Vector Quantum Simulation

TL;DR

DiaQ identifies diagonal sparsity in time-step unitaries of quantum circuits and introduces a diagonal-based sparse format, DiaQ, with a C++ lib and Python wrappers. Integrating DiaQ with SV-Sim yields substantial speedups (up to ~) and memory reductions by converting dense representations to , where is the number of diagonals. The approach accelerates state-vector simulation on multi-core CPUs with SIMD and opens avenues for density-matrix and tensor-network extensions. The work demonstrates practical improvements on benchmarks from SupermarQ and QASMBench, indicating DiaQ's potential for scalable quantum simulations on classical hardware.

Abstract

In the current era of Noisy Intermediate Scale Quantum (NISQ) computing, efficient digital simulation of quantum systems holds significant importance for quantum algorithm development, verification and validation. However, analysis of sparsity within these simulations remains largely unexplored. In this paper, we present a novel observation regarding the prevalent sparsity patterns inherent in quantum circuits. We introduce DiaQ, a new sparse matrix format tailored to exploit this quantum-specific sparsity, thereby enhancing simulation performance. Our contribution extends to the development of libdiaq, a numerical library implemented in C++ with OpenMP for multi-core acceleration and SIMD vectorization, featuring essential mathematical kernels for digital quantum simulations. Furthermore, we integrate DiaQ with SV-Sim, a state vector simulator, yielding substantial performance improvements across various quantum circuits (e.g., ~26.67% for GHZ-28 and ~32.72% for QFT-29 with multi-core parallelization and SIMD vectorization on Frontier). Evaluations conducted on benchmarks from SupermarQ and QASMBench demonstrate that DiaQ represents a significant step towards achieving highly efficient quantum simulations.
Paper Structure (17 sections, 2 equations, 8 figures, 1 table, 3 algorithms)

This paper contains 17 sections, 2 equations, 8 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Quantum Simulations
  4. Benchmark Circuits
  5. Time-Steps in Quantum Circuits
  6. Motivation
  7. Sparsity Patterns in QC
  8. Existing Sparse Representations
  9. DiaQ: A Novel Quantum-Tailored Format
  10. The DiaQ Library
  11. Integrating DiaQ with SV-Sim
  12. Experimental Framework
  13. Results
  14. Quantitative Results
  15. Qualitative Analysis
  16. ...and 2 more sections

Figures (8)

  • Figure 1: Timesteps in Quantum Circuits
  • Figure 2: Sparsity patterns of time-step unitaries in a 4-qubit circuit when a single Hadamard gate is applied to just the (a) first, (b) second, (c) third and (d), or the last qubit. Unitaries represent circuits from Figure \ref{['fig:hadamard_sparsity_patterns']}. Note: The red stars denote non-zeros, black dots denote zeros.
  • Figure 3: Sparsity in SupermarQ benchmarks
  • Figure 4: Memory Savings that DiaQ offers for GHZ circuit's chain of unitaries
  • Figure 5: GHZ Analysis
  • ...and 3 more figures