RQC Seminar

238th RQC Seminar

  • Speaker

    Dr. David Herrera-Martí
    ( CEA-List, Grenoble, France )

  • Date

    13:20-14:20 (1:20 p.m.-2:20 p.m.), October 21, 2025 Tuesday

  • Venue

    Hybrid(ZOOM・ Seminar Room 345-347 at Wako Main Research Building / 研究本館3階 セミナー室 (345-347) (C01))

  • Title

    Overcoming Finite Precision Bottlenecks in Classical and Quantum Krylov Methods

  • Inquiries

    norilab_rqc_assist[at]ml.riken.jp

Abstract
The combinatorial problem Max-Cut has become a benchmark in the evaluation of local search heuristics for both quantum and classical optimisers. In contrast to local search, which only provides average-case performance guarantees, the convex semidefinite relaxation of Max-Cut by Goemans and Williamson, provides worst-case guarantees and is therefore suited to both the construction of benchmarks and in applications to performance-critic scenarios. We show how extended floating point precision can be incorporated in algebraic subroutines in convex optimisation, namely in indirect matrix inversion methods like Conjugate Gradient, which are used in Interior Point Methods in the case of very large system sizes. We estimated the expected acceleration of the time to solution for a hardware architecture that runs natively on extended precision. We see that increasing the internal working precision reduces the time to solution by a factor that increases with the system size.

I will also present my current unpublished work on how to circumvent limitations of quantum Krylov methods that arise from measurement noise. A moderate amount of noise (gate noise, fluctuations from finite sampling…) will result in very ill-conditioned matrices, which typically will invalidate the results of the generalised eigenvalue problem in quantum Krylov methods. In particular, I will explain how to use approximation to the ground state energy, like the one that could be obtained from a mean-field calculation, to guide the construction of the Krylov subspace which gives meaningful results.

References:
https://arxiv.org/pdf/2510.02863
https://cea.hal.science/cea-05043041/document


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