Hidden Rotation Symmetry of the Jordan–Wigner Transformation and Its Application to Measurement in Quantum Computation
Abstract
Using a global rotation by θ 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.
Fields of Study & Subjects
Quantum Information and Cryptography
Quantum Mechanics and Non-Hermitian Physics
Quantum Computing Algorithms and Architecture
Publication details
- Journal / source
- Symmetry
- Publisher
- MDPI AG
- Volume
- 18
- Issue
- 2
- Pages
- 251–251
- Publication date
- 30 January 2026
- Language
- EN