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Quantum Computing Approach to Fixed-Node Monte Carlo Using Classical Shadows.

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Electronic structure theory

Background:

  • Quantum Monte Carlo (QMC) methods offer high accuracy for electronic structure problems.
  • Trial wave function precision limits QMC accuracy.
  • Previous work used quantum computers with auxiliary-field QMC (AFQMC) but faced exponential post-processing.

Purpose of the Study:

  • To develop a quantum Monte Carlo method that avoids exponential scaling.
  • To investigate a fixed-node Monte Carlo approach for improved efficiency.
  • To compare the performance and robustness of AFQMC and fixed-node methods.

Main Methods:

  • Employed a fixed-node Monte Carlo method based on full configuration interaction QMC.
  • Applied the method to the local unitary cluster Jastrow ansatz.
  • Tested on H4, ferrocene, and benzene molecules using up to 12 qubits, considering circuit-level noise.

Main Results:

  • The new fixed-node method avoids the exponential scaling of previous quantum-assisted AFQMC.
  • Auxiliary-field QMC (AFQMC) demonstrated greater robustness to errors than the fixed-node approach.
  • Extrapolations of fixed-node energy reduced the discrepancy between methods.
  • Achieving chemical accuracy requires high sampling costs, even for small systems.

Conclusions:

  • The developed fixed-node method offers an alternative to quantum-assisted AFQMC by avoiding exponential scaling.
  • Despite potential for chemical accuracy, high sampling costs present a challenge for practical applications.
  • Further research is needed to assess the feasibility of outperforming conventional QMC methods.