Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane

TL;DR

This paper introduces a nearly optimal measurement scheme for molecular Hamiltonians in quantum chemistry, reducing the number of measurements needed and utilizing finite projective planes to improve efficiency on quantum computers.

Contribution

It develops a novel measurement construction based on finite projective planes that significantly reduces measurement complexity compared to previous methods.

Findings

Requires only 2N^2 measurements, improving over 10/3 N^2 scaling.

Constructs sets of measurable operators using finite projective planes.

Each measurement involves an O(N) depth circuit with O(N^2) gates.

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.