$k$-commutativity and measurement reduction for expectation values

• URL: http://arxiv.org/abs/2312.11840v2
• Date: Wed, 17 Jan 2024 16:34:06 GMT
• Title: $k$-commutativity and measurement reduction for expectation values
• Authors: Ben DalFavero, Rahul Sarkar, Daan Camps, Nicolas Sawaya, Ryan LaRose
• Abstract summary: We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubit-wise commutativity and (full) commutativity. We apply this notion to measuring expectation values of observables in quantum circuits and show a reduction in the number measurements at the cost of increased circuit depth.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubit-wise commutativity and (full) commutativity. We apply this notion, which we call $k$-commutativity, to measuring expectation values of observables in quantum circuits and show a reduction in the number measurements at the cost of increased circuit depth. Last, we discuss the asymptotic measurement complexity of $k$-commutativity for several families of $n$-qubit Hamiltonians, showing examples with $O(1)$, $O(\sqrt{n})$, and $O(n)$ scaling.

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