Systolic Array Acceleration of Diagonal-Optimized Sparse-Sparse Matrix Multiplication for Efficient Quantum Simulation

TL;DR

The first diagonal-optimized quantum simulation accelerator is presented, which exploits the diagonal structure commonly found in problem-Hamiltonian (Hermitian) matrices and leverages a restructured systolic array dataflow to transform diagonally sparse matrices into dense computations, enabling high utilization and performance.

Abstract

Hamiltonian simulation is a key workload in quantum computing, enabling the study of complex quantum systems and serving as a critical tool for classical verification of quantum devices. However, it is computationally challenging because the Hilbert space dimension grows exponentially with the number of qubits. The growing dimensions make matrix exponentiation, the key kernel in Hamiltonian simulations, increasingly expensive. Matrix exponentiation is typically approximated by the Taylor series, which contains a series of matrix multiplications. Since Hermitian operators are often sparse, sparse matrix multiplication accelerators are essential for improving the scalability of classical Hamiltonian simulation. Yet, existing accelerators are primarily designed for machine learning workloads and tuned to their characteristic sparsity patterns, which differ fundamentally from those in Hamiltonian simulations that are often dominated by structured diagonals. In this work, we present \name, the first diagonal-optimized quantum simulation accelerator. It exploits the diagonal structure commonly found in problem-Hamiltonian (Hermitian) matrices and leverages a restructured systolic array dataflow to transform diagonally sparse matrices into dense computations, enabling high utilization and performance. Through detailed cycle-level simulation of diverse benchmarks in HamLib, \name{} demonstrates average performance improvements of $10.26\times$, $33.58\times$, and $53.15\times$ over SIGMA, Outer Product, and Gustavson's algorithm, respectively, with peak speedups up to $127.03\times$ while reducing energy consumption by an average of $471.55\times$ and up to $4630.58\times$ compared to SIGMA.

Figures (13)

• Figure 1: A diagonal matrix in dense format vs. DiaQ format. Each diagonal in DiaQ can have a different length (deduced from the matrix dimensions and the offset), which eliminates the need for padding and saves space compared to the traditional DIA format.
• Figure 2: Diagonal Sparse Matrix Decomposition.
• Figure 3: Overview of DIAMOND.
• Figure 4: Microarchitecture of DPE.
• Figure 5: Minkowski-Sum Mapping.