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arXiv · 2512.24589

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

Grant Davis·James K. Freericks
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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.

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Grant Davis, James K. Freericks. 2025-12-31. Hidden rotation symmetry of the Jordan-Wigner transformation and its application to measurement in quantum computation. https://arxiv.org/abs/2512.24589

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