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Statistical errors in reduced density matrices (RDMs) from quantum simulations increase with RDM order and for excited states. Fewer shots are needed for higher-order RDMs, enabling efficient multireference theory calculations.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Quantum computing

Background:

  • Accurate electronic structure calculations are crucial for understanding molecular properties.
  • Quantum circuit simulations offer a promising approach for these calculations.
  • Statistical errors in reduced density matrices (RDMs) can impact the accuracy of multireference theories.

Purpose of the Study:

  • To analyze statistical errors in RDMs obtained from quantum circuit simulations.
  • To investigate the impact of these errors on multireference theories like CASCI and CASPT2.
  • To determine the relationship between RDM errors, number of shots, and electronic state characteristics.

Main Methods:

  • Detailed analysis of statistical errors in sampled RDMs from active space wavefunctions.
  • Analytical derivation of expected squared errors using a multinomial distribution model.
  • Benchmark calculations on short polyenes (C4H6, C6H8) and a metalloenzyme model complex.

Main Results:

  • RDM errors increase with RDM order and are larger for excited states than ground states.
  • Standard deviation of CASCI energies scales with N_shot^-1/2; CASPT2 energies also show N_shot dependence.
  • Fewer shots are required for higher-order RDMs (e.g., 3-RDM) compared to lower-order ones (e.g., 1,2-RDM).

Conclusions:

  • The study quantifies statistical errors in sampled RDMs and their impact on quantum chemical calculations.
  • Optimized sampling strategies can be developed based on RDM order and state properties.
  • Efficient calculation of multireference energies is achievable by understanding and managing RDM statistical errors.