Demonstrates a symmetry that reduces measurement needs in quantum measurements for fermionic systems, implying greater efficiency in quantum computation.
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.
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Davis et al. (2026) studied this question.
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