Quantized Simulated Bifurcation Machine with Sparse Tile Row-flag Matrix Format

Kosuke Tatsumura, Masaya Yamasaki, Hayato Goto

Zhanghao Zhouyin, Hong Guo

Modern atomistic simulations increasingly employ localized orbitals to represent quantum operators, yielding sparse block matrices whose block shapes vary with chemical species and basis choice. Conventional scalar sparse formats store the entries of each block individually, obscuring this local structure and limiting the use of efficient block algorithms. We present VBCSR, a distributed sparse matrix library that preserves variable-size atomic blocks and accelerates the core linear algebra of large-scale atomistic simulations. A unified interface automatically maps scalar, uniform-basis, and multispecies operators to compressed sparse row (CSR), block sparse row (BSR), or variable-block compressed sparse row (VBCSR). Our advanced acceleration method groups blocks of equal shape and dispatches them to optimized dense kernels. In the reported benchmarks, VBCSR outperforms the tested Python-accessible reference implementations for several block-sparse benchmarks. We further demonstrate VBCSR in an InP nanoparticle application containing more than \(10^6\) atoms.

Jakub Pawłowski, Paweł Tarasiuk, Jan Tuziemski +2 more

We introduce Simulated Bifurcation Quantum Annealing (SBQA), a quantum-inspired optimization algorithm that extends simulated bifurcation by incorporating inter-replica interactions to mimic quantum tunneling. SBQA retains the efficiency and parallelism of simulated bifurcation while improving performance on sparse and rugged energy landscapes. We derive its equations of motion, analyze parameter dependence, and propose a lightweight auto-tuning strategy. A comprehensive benchmarking study on both large-scale problems and smaller instances relevant for current quantum hardware shows that SBQA systematically improves on SBM in the sparse and rugged regimes where SBM is known to struggle, while remaining competitive and versatile across a diverse set of tested problem families. These results position SBQA as a practical quantum-inspired optimization heuristic and a stronger classical baseline for the sparse and rugged regimes studied here.

Taro Kanao, Masaru Suzuki, Kosuke Tatsumura +1 more

Wei Li, Yi-Lun Du, Nan Su +3 more

Sohei Shimomai, Kei Ueda, Shinji Kimura

Recently, Quantum Annealing (QA) has attracted attention as an efficient algorithm for combinatorial optimization problems. In QA, the input data size becomes large and its reduction is important for the hardware emulation since its usable memory size and its bandwidth are limited. As an improved Coordinate (COO) format for a sparse matrix, Compressed Sparse Row (CSR) has been proposed [1]. We have checked CSR on an Ising model but found that the compression efficiency is not high.