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Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

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Operator ordering in Trotterized unitary coupled cluster (UCC) methods significantly impacts quantum chemistry simulations. Different orderings lead to chemical-scale energy variations, necessitating defined operator sequences for reproducibility and accurate quantum chemical models.

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Quantum algorithms

Background:

  • The Variational Quantum Eigensolver (VQE) is a key near-term quantum algorithm for simulating molecular electronic structures.
  • Unitary Coupled Cluster (UCC) theory is a promising ansatz for VQE, but its quantum implementation requires Suzuki-Trotter decomposition.
  • The nonuniqueness of operator ordering in Trotterized UCC methods has been noted, but its chemical significance is unexplored.

Purpose of the Study:

  • To investigate the impact of operator ordering on Trotterized UCC ansatze, specifically UCCSD and k-UpCCGSD.
  • To determine if operator ordering variations affect simulation energies at the chemical scale.
  • To establish the necessity of defining operator order for quantum chemical model reproducibility.

Main Methods:

  • Exploration of operator ordering effects on Trotterized Unitary Coupled Cluster Singles Doubles (UCCSD) ansatz.
  • Analysis of operator ordering in the k-UpCCGSD ansatz.
  • Comparison of resulting energies across different operator orderings.

Main Results:

  • Significant, system-dependent energy variations were observed due to different operator orderings.
  • These energy variations can reach hundreds of kcal/mol, impacting chemical accuracy.
  • The choice of operator ordering demonstrably affects the computed energies.

Conclusions:

  • Operator ordering in Trotterized UCC methods is crucial and affects results at the chemical scale.
  • Defining a specific operator sequence is essential for reproducible quantum chemical calculations.
  • A strategy for selecting an effective operator ordering is proposed.