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A quantum computing view on unitary coupled cluster theory.

Abhinav Anand1, Philipp Schleich2,3,4, Sumner Alperin-Lea1

  • 1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. abhinav.anand@mail.utoronto.ca.

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This review explores Unitary Coupled Cluster (UCC) and related quantum computing ansätze for solving electronic structure problems. It covers their classical origins, quantum implementation, and future challenges for quantum chemistry.

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Electronic structure theory

Background:

  • Coupled Cluster (CC) methods are foundational in classical computational chemistry for accurate electronic structure calculations.
  • Classical CC methods face scalability challenges, motivating the exploration of quantum computing approaches.
  • Unitary Coupled Cluster (UCC) is a prominent quantum ansatz adapted from classical CC theory.

Purpose of the Study:

  • To provide a comprehensive review of the Unitary Coupled Cluster (UCC) ansatz and related quantum algorithms.
  • To bridge the gap between classical Coupled Cluster theory and its quantum computing implementations.
  • To offer a unified perspective on quantum ansätze for electronic structure problems and identify future research directions.

Main Methods:

  • Review of historical development and theoretical formulation of Coupled Cluster methods.
  • Detailed discussion of the Unitary Coupled Cluster (UCC) ansatz and its quantum computational implementation.
  • Analysis of quantum-specific ansätze derived from or related to UCC.

Main Results:

  • The review elucidates the formulation and quantum implementation of the UCC ansatz.
  • It highlights various related ansätze tailored for quantum computation.
  • A unified framework for these quantum ansätze is proposed.

Conclusions:

  • The UCC ansatz and its variants are key for quantum computation of electronic structure.
  • Understanding their classical roots is crucial for effective quantum algorithm development.
  • Open challenges remain in unifying these ansätze and advancing their application.