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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Quantum algorithms

Background:

  • Variational quantum eigensolver (VQE) performance is limited by measurement costs.
  • Estimating complex observables like molecular Hamiltonians requires partitioning into commutative Pauli product fragments.
  • Current methods sum fragment variances, directly impacting total measurement count.

Purpose of the Study:

  • To develop a novel method for reducing the number of measurements in VQE.
  • To decrease individual fragment variances without altering the total observable expectation value.
  • To enhance the efficiency of quantum algorithms for chemical simulations.

Main Methods:

  • Introducing "ghost" Pauli products compatible with multiple fragments.
  • Ensuring the sum of coefficients for each "ghost" Pauli product across fragments is zero to maintain the total expectation value.
  • Minimizing individual fragment variances using a classically efficient approximation of the quantum wavefunction.

Main Results:

  • The "ghost" Pauli algorithm effectively lowers individual fragment variances.
  • Numerical tests on molecular electronic Hamiltonians show significant reductions in measurement requirements.
  • Achieved several-fold reductions in measurements compared to existing techniques.

Conclusions:

  • The proposed "ghost" Pauli algorithm offers a substantial improvement in VQE efficiency.
  • This method makes VQE more competitive with classical algorithms for complex problems.
  • Enables more accurate and efficient quantum simulations of molecular systems.