Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane

Abstract

We propose an efficient and almost optimal scheme for measuring molecular Hamiltonians in quantum chemistry on quantum computers, which requires $2N^2$ distinct measurements in the leading order with $N$ being the number of molecular orbitals. It achieves the state-of-the-art by improving a previous proposal by Bonet-Monroig et al. [Phys. Rev. X 10, 031064 (2020)] which exhibits $\frac{10}{3}{N}^2$ scaling in the leading order. We develop a novel method based on a finite projective plane to construct sets of simultaneously-measurable operators contained in molecular Hamiltonians. Each measurement only requires a depth-$O(N)$ circuit consisting of $O(N^2)$ one- and two-qubit gates under the Jordan-Wigner and parity mapping, assuming the linear connectivity of qubits on quantum hardwares. Because evaluating expectation values of molecular Hamiltonians is one of the major bottlenecks in the applications of quantum devices to quantum chemistry, our finding is expected to accelerate such applications.

20 pages, 6 figures

References in corpus (7)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Efficient quantum computation of molecular forces and other energy gradients
• Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values
• Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver
• Improving quantum measurements by introducing "ghost" Pauli products
• Quantum expectation-value estimation by computational basis sampling
• Perturbation theory with quantum signal processing

Cited by in corpus (2)

• Accelerated variational quantum eigensolver with joint Bell measurement
• A quantum eigenvalue solver based on tensor networks