Enhancing the accuracy and efficiency of sample-based quantum diagonalization with phaseless auxiliary-field quantum Monte Carlo

• URL: http://arxiv.org/abs/2503.05967v1
• Date: Fri, 07 Mar 2025 22:38:22 GMT
• Title: Enhancing the accuracy and efficiency of sample-based quantum diagonalization with phaseless auxiliary-field quantum Monte Carlo
• Authors: Don Danilov, Javier Robledo-Moreno, Kevin J. Sung, Mario Motta, James Shee,
• Abstract summary: We show that a non-perturbative approach, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can recover a substantial amount of correlation energy.<n> Extrapolation of the ph-AFQMC energy versus the energy variance of the SQD trial wavefunctions has the potential to further improve the energy accuracy.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum Selected Configuration Interaction (QSCI) and an extended protocol known as Sample-based Quantum Diagonalization (SQD) have emerged as promising algorithms to solve the electronic Schr\"odinger equation with noisy quantum computers. In QSCI/SQD a quantum circuit is repeatedly prepared on the quantum device, and measured configurations form a subspace of the many-body Hilbert space in which the Hamiltonian is diagonalized classically. For the dissociation of N$_2$ and a model $\mathrm{[2Fe-2S]}$ cluster (correlating 10 electrons in 26 orbitals and 30 electrons in 20 orbitals, respectively) we show that a non-perturbative stochastic approach, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), using truncated SQD trial wavefunctions obtained from quantum hardware can recover a substantial amount (e.g., O(100) mHa) of correlation energy and alleviate the possible sampling redundancy of the QSCI/SQD procedure. Extrapolation of the ph-AFQMC energy versus the energy variance of the SQD trial wavefunctions has the potential to further improve the energy accuracy.

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