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Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and

Xiaoxiao Xiao1, Hewang Zhao1, Jiajun Ren1

  • 1Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China.

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We developed a new physics-constrained approach for designing hardware-efficient ansätze (HEA) for quantum computers. This method ensures accuracy and scalability for complex quantum many-body problems.

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Area of Science:

  • Quantum computing
  • Computational physics
  • Quantum chemistry

Background:

  • Variational wave function ansätze are crucial for solving quantum many-body problems.
  • Existing hardware-efficient ansätze (HEA) often lack theoretical rigor and scalability.
  • Previous HEA designs overlooked critical concepts like size-consistency.

Purpose of the Study:

  • To introduce a physics-constrained approach for designing HEA with theoretical guarantees.
  • To ensure HEA are universal, systematically improvable, and size-consistent.
  • To enhance the accuracy and scalability of quantum many-body simulations on quantum computers.

Main Methods:

  • Imposed fundamental physics constraints (universality, systematic improvability, size-consistency) on HEA design.
  • Extended the concept of size-consistency to hardware-efficient ansätze.
  • Developed a concrete HEA realization requiring only linear qubit connectivity.

Main Results:

  • The physics-constrained HEA demonstrates superior accuracy and scalability compared to heuristic designs.
  • Restoring size-consistency significantly reduces the number of layers needed for desired accuracy.
  • Heuristic HEA struggle with scalability beyond 10 qubits due to constraint violations.

Conclusions:

  • Incorporating physical constraints is vital for designing efficient HEA.
  • The developed physics-constrained HEA offers a robust framework for tackling quantum many-body problems.
  • This approach advances the practical application of quantum computing in physics and chemistry.