Hidden rotation symmetry of the Jordan-Wigner transformation and its application to measurement in quantum computation

TL;DR

This paper uncovers a hidden rotational symmetry in the Jordan-Wigner transformation that can optimize measurement strategies in quantum simulations of fermionic systems, reducing computational effort.

Contribution

It derives a new symmetry in the Jordan-Wigner transformation and demonstrates its application to improve measurement efficiency in quantum simulations of physical and chemical systems.

Findings

Symmetry relates expectation values of different Pauli string products.

Application reduces the number of measurements in fermionic quantum simulations.

Enhances measurement circuit efficiency in variational ground state algorithms.

Abstract

Using a global rotation by theta about the z-axis in the spin sector of the Jordan-Wigner transformation rotates Pauli matrices X and Y in the x-y-plane, while it adds a global complex phase to fermionic quantum states that have a fixed number of particles. With the right choice of angles, this relates expectation values of Pauli strings containing products of X and Y to different products, which can be employed to reduce the number of measurements needed when simulating fermionic systems on a quantum computer. Here, we derive this symmetry and show how it can be applied to systems in Physics and Chemistry that involve Hamiltonians with only single-particle (hopping) and two-particle (interaction) terms. We also discuss the consequences of this for finding efficient measurement circuits in variational ground state preparation.