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Measurement Optimization Techniques for Excited Electronic States in Near-Term Quantum Computing Algorithms.

Seonghoon Choi1,2, Artur F Izmaylov1,2

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Improving quantum measurement efficiency is key for the variational quantum eigensolver (VQE) algorithm. This study compares measurement techniques for excited-state VQE, finding multistate contraction requires fewer measurements than quantum subspace expansion.

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Quantum algorithms

Background:

  • The variational quantum eigensolver (VQE) is a leading quantum algorithm for electronic structure calculations.
  • Improving quantum measurement efficiency is critical for VQE's practical application.
  • The performance of measurement techniques in excited-state VQE algorithms is not well understood.

Purpose of the Study:

  • To adapt and compare various quantum measurement techniques for two prominent excited-state VQE algorithms: multistate contraction and quantum subspace expansion.
  • To assess the measurement requirements of these techniques in the context of excited-state electronic structure problems.

Main Methods:

  • Adaptation of state-of-the-art quantum measurement techniques.
  • Numerical comparison of measurement requirements for multistate contraction and quantum subspace expansion.
  • Evaluation of measurement strategies based on Hamiltonian data, wave function information, and randomized techniques.

Main Results:

  • For multistate contraction, methods minimizing measurements by utilizing Hamiltonian data and wave function information are most effective.
  • Randomized measurement techniques are better suited for quantum subspace expansion due to the need to measure numerous observables with varying energy scales.
  • Overall, multistate contraction requires significantly fewer measurements than quantum subspace expansion when optimal measurement techniques are employed.

Conclusions:

  • The choice of measurement technique significantly impacts the efficiency of excited-state VQE algorithms.
  • Multistate contraction offers a more measurement-efficient approach for certain excited-state electronic structure problems compared to quantum subspace expansion.
  • Further research into optimizing quantum measurement strategies is essential for advancing near-term quantum algorithms like VQE.