Measurement optimization in the variational quantum eigensolver using a minimum clique cover.

Area of Science:

• Quantum computing
• Computational chemistry
• Electronic structure theory

Background:

• The Variational Quantum Eigensolver (VQE) is a key algorithm for solving the electronic structure problem.
• Current quantum hardware limitations necessitate measuring Hamiltonian expectation values in parts, leading to inefficiencies.
• The number of Hamiltonian terms scales as O(N⁴) with system size N, exacerbating measurement challenges.

Purpose of the Study:

• To optimize the measurement process in VQE by grouping commuting Hamiltonian terms.
• To reduce the number of operators required for Hamiltonian expectation value measurement.
• To investigate the effectiveness of heuristic algorithms for the minimum clique cover problem in this context.

Main Methods:

• Representing qubit-wise commutativity of Hamiltonian terms as a graph.
• Formulating the optimal grouping problem as a minimum clique cover (MCC) problem.
• Applying and evaluating polynomial heuristic algorithms for MCC on molecular electronic Hamiltonians.

Main Results:

• Qubit-wise commutativity can be mapped to a graph problem equivalent to MCC.
• Heuristic algorithms provide approximate solutions to the NP-hard MCC problem.
• Grouping qubit-wise commuting terms reduced the number of operators to measure by an average factor of three.

Conclusions:

• Grouping qubit-wise commuting terms is an effective strategy to optimize VQE measurements.
• The graph-based MCC approach offers a practical method for Hamiltonian term grouping.
• This optimization significantly enhances the efficiency of VQE for electronic structure calculations.