Memory-Scalable and Hardware-Adaptive Matrix-Free Quantum Simulation

• URL: http://arxiv.org/abs/2606.31598v1
• Date: Tue, 30 Jun 2026 12:45:48 GMT
• Title: Memory-Scalable and Hardware-Adaptive Matrix-Free Quantum Simulation
• Abstract summary: We present a memory-scalable, hardware-adaptive matrix-free framework for applying large operators on vectors.<n>For quantum simulation, it provides the core kernel for quantum operations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The core step in quantum simulations is typically matrix vector multiplication $φ= \Hmat ψ$. Executing this step is limited by memory requirement to store the Hamiltonian. We present a memory-scalable, hardware-adaptive matrix-free framework for applying large operators on vectors without materializing the full matrix on a single accelerator. The operator is represented through a block-procedural interface: blocks may be generated, loaded, cached, distributed, or applied directly only when their action is needed. For quantum simulation, it provides the core kernel for quantum operations. An adaptive planner selects block size, cache strategy, GPU grouping, row distribution, and task parallelization from memory and workload estimates. We describe analytic, measured, and learned planning strategies that choose between procedural generation, partial caching, full caching, and row-distributed caching. The method removes the requirement that the full dense matrix fit in the accelerator memory. This shifts large simulations from a fixed memory barrier to a tunable balance between block generation, cache reuse, data movement, parallel scheduling, and numerical accuracy.

Related papers

• Orkan: Cache-friendly simulation of quantum operations on hermitian operators [0.0]
  I introduce emphOrkan, a simulation library that uses a tiled memory layout storing only the lower triangle of the hermitian matrix at tile granularity.<n>The implementation treats any hermitian operator uniformly and is agnostic to whether the Schrdinger or Heisenberg picture is used.<n> Benchmarks against Qiskit Aer, QuEST, and Qulacs show consistent wall-clock speedups of $2$-$4times$ partly attributable to the reduced memory footprint.
  arXiv  Detail & Related papers  (2026-04-17T07:08:53Z)
• Space Filling Curves is All You Need: Communication-Avoiding Matrix Multiplication Made Simple [42.09057806159106]
  General Matrix multiplication is the cornerstone of Deep Learning and HPC workloads.<n>Modern platforms with matrix multiplication accelerators exhibit high FLOP/Byte machine balance.<n>In this work we revisit space filling curves (SFC) to alleviate the problem of this cumbersome tuning.<n>We obtain platform-oblivious and shape-oblivious matrix-multiplication schemes that exhibit inherently high degree of data locality.
  arXiv  Detail & Related papers  (2026-01-22T19:56:16Z)
• Learning Grouped Lattice Vector Quantizers for Low-Bit LLM Compression [57.54335545892155]
  We introduce a Grouped Lattice Vector Quantization (GLVQ) framework that assigns each group of weights a customized lattice codebook.<n>Our approach achieves a better trade-off between model size and accuracy compared to existing post-training quantization baselines.
  arXiv  Detail & Related papers  (2025-10-23T20:19:48Z)
• Scaling Probabilistic Circuits via Monarch Matrices [109.65822339230853]
  Probabilistic Circuits (PCs) are tractable representations of probability distributions.<n>We propose a novel sparse and structured parameterization for the sum blocks in PCs.
  arXiv  Detail & Related papers  (2025-06-14T07:39:15Z)
• BitStack: Any-Size Compression of Large Language Models in Variable Memory Environments [53.71158537264695]
  Large language models (LLMs) have revolutionized numerous applications, yet their deployment remains challenged by memory constraints on local devices.<n>We introduce textbfBitStack, a novel, training-free weight compression approach that enables megabyte-level trade-offs between memory usage and model performance.
  arXiv  Detail & Related papers  (2024-10-31T13:26:11Z)
• Fast Matrix Multiplications for Lookup Table-Quantized LLMs [58.11584672945781]
  FLUTE is a flexible lookup table engine for LUT-quantized LLMs.<n>At batch sizes 32 and quantization group size of 128, the FLUTE kernel can be 2-4x faster than existing GEMM kernels.
  arXiv  Detail & Related papers  (2024-07-15T17:55:42Z)
• Memory-Efficient Differentiable Programming for Quantum Optimal Control of Discrete Lattices [1.5012666537539614]
  Quantum optimal control problems are typically solved by gradient-based algorithms such as GRAPE. QOC reveals that memory requirements are a barrier for simulating large models or long time spans. We employ a nonstandard differentiable programming approach that significantly reduces the memory requirements at the cost of a reasonable amount of recomputation.
  arXiv  Detail & Related papers  (2022-10-15T20:59:23Z)
• Reducing Memory Requirements of Quantum Optimal Control [0.0]
  gradient-based algorithms such as GRAPE suffer from exponential growth in storage with increasing number of qubits and linear growth in memory requirements with increasing number of time steps. We have created a nonstandard automatic differentiation technique that can compute gradients needed by GRAPE by exploiting the fact that the inverse of a unitary matrix is its conjugate transpose. Our approach significantly reduces the memory requirements for GRAPE, at the cost of a reasonable amount of recomputation.
  arXiv  Detail & Related papers  (2022-03-23T20:42:54Z)
• 8-bit Optimizers via Block-wise Quantization [57.25800395197516]
  Statefuls maintain statistics over time, e.g., the exponentially smoothed sum (SGD with momentum) or squared sum (Adam) of past values. This state can be used to accelerate optimization compared to plain gradient descent but uses memory that might otherwise be allocated to model parameters. In this paper, we develop first gradients that use 8-bit statistics while maintaining the performance levels of using 32-bit gradient states.
  arXiv  Detail & Related papers  (2021-10-06T15:43:20Z)
• Cache Blocking Technique to Large Scale Quantum Computing Simulation on Supercomputers [0.0]
  We apply a cache blocking technique by inserting swap gates in quantum circuits to decrease data movements. We implemented this technique in the open source simulation framework Qiskit Aer.
  arXiv  Detail & Related papers  (2021-02-05T02:03:44Z)
• Leveraging Automated Mixed-Low-Precision Quantization for tiny edge microcontrollers [76.30674794049293]
  This paper presents an automated mixed-precision quantization flow based on the HAQ framework but tailored for the memory and computational characteristics of MCU devices. Specifically, a Reinforcement Learning agent searches for the best uniform quantization levels, among 2, 4, 8 bits, of individual weight and activation tensors. Given an MCU-class memory bound to 2MB for weight-only quantization, the compressed models produced by the mixed-precision engine result as accurate as the state-of-the-art solutions.
  arXiv  Detail & Related papers  (2020-08-12T06:09:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.