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Pauli String Partitioning Algorithm with the Ising Model for Simultaneous Measurements.

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We developed an efficient algorithm to group Pauli strings for quantum computing measurements. This method significantly reduces the number of measurements needed for quantum chemistry simulations, improving computational efficiency.

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Area of Science:

  • Quantum Computing
  • Quantum Chemistry
  • Computational Optimization

Background:

  • Variational quantum eigensolvers (VQEs) require efficient measurement strategies for quantum chemistry.
  • Partitioning Pauli strings into measurable groups is crucial for reducing measurement overhead.

Purpose of the Study:

  • To propose an efficient algorithm for partitioning Pauli strings into simultaneously measurable subgroups.
  • To reduce the number of measurements in VQEs for quantum chemistry applications.
  • To develop an algorithm applicable to large-scale problems exceeding Ising machine capacity.

Main Methods:

  • Algorithm based on Ising model optimization solved using an Ising machine.
  • Iterative application of the algorithm for problems larger than Ising machine capacity (n_bit).
  • Performance evaluation using a Digital Annealer with up to 65535 Pauli strings.

Main Results:

  • Demonstrated time complexity of O(N) for N <= n_bit and O(N^2) for N > n_bit.
  • Achieved a maximum reduction factor of 200 (number of Pauli strings / number of partitions).
  • Algorithm shows improved time complexity and solution optimality compared to existing methods.

Conclusions:

  • The proposed algorithm efficiently partitions Pauli strings, significantly reducing measurement requirements for quantum computing.
  • The method is scalable to large problem sizes and offers superior performance for quantum chemistry simulations.
  • This work advances the practical application of quantum computing in scientific discovery.