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Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver.

Takeshi Yoshikawa1,2, Tomoya Takanashi2, Hiromi Nakai2,3,4

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This summary is machine-generated.

The divide-and-conquer (DC) technique enhances the Unitary Coupled Cluster (UCC) variational quantum eigensolver (VQE) for noisy quantum devices. This DC-qUCC/VQE method reduces qubit requirements and minimizes errors by conserving electron numbers.

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Quantum Algorithms

Background:

  • Noisy Intermediate-Scale Quantum (NISQ) devices face challenges with incoherent errors in variational quantum eigensolver (VQE) algorithms.
  • Shallow or constant-depth quantum circuits are a primary focus for VQE on NISQ hardware.
  • Unitary Coupled Cluster (UCC) ansatz is suitable for quantum computation due to the unitary nature of quantum gates.

Purpose of the Study:

  • To introduce a novel Divide-and-Conquer (DC) approach integrated with UCC-based VQE (DC-qUCC/VQE).
  • To reduce the number of qubits required for quantum simulations.
  • To mitigate incoherent errors in quantum computations on NISQ devices.

Main Methods:

  • Application of the divide-and-conquer (DC) linear scaling technique to fragment a larger system.
  • Implementation of the Unitary Coupled Cluster (UCC) ansatz within the VQE framework.
  • Utilizing quantum-computed density matrices to conserve the total number of electrons in the system.

Main Results:

  • The DC-qUCC/VQE algorithm successfully reduces the number of required qubits.
  • Numerical assessments show a decrease in energy errors when the total electron number is conserved.
  • The algorithm demonstrates a reduction in the number of quantum gates, indicating potential for reduced incoherent errors.

Conclusions:

  • The DC-qUCC/VQE algorithm is a promising method for accurate quantum chemistry simulations on NISQ computers.
  • Conserving electron number via quantum density matrix evaluation effectively reduces energy errors.
  • This approach offers a pathway to more robust and efficient quantum computations by minimizing gate count and errors.