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

• URL: http://arxiv.org/abs/2512.24589v1
• Date: Wed, 31 Dec 2025 03:27:15 GMT
• Title: Hidden rotation symmetry of the Jordan-Wigner transformation and its application to measurement in quantum computation
• Abstract summary: 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.<n>This adds a global complex phase to fermionic quantum states that have a fixed number of particles.<n>We 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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