Implementation of Measurement Reduction for the Variational Quantum Eigensolver

Abstract

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware.

arXiv commentRevised order of paper, and further background details about the LCU method added. A unary implementation of LCU is also explored. Results unchanged

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• A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz
• Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver
• Representation of the Fermionic Boundary Operator
• Policy Gradient Approach to Compilation of Variational Quantum Circuits