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arXiv · 2312.11840

Measurement reduction for expectation values via fine-grained commutativity

Ben DalFavero·Rahul Sarkar·Jeremiah Rowland·Daan Camps·Nicolas Sawaya·Ryan LaRose
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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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Ben DalFavero, Rahul Sarkar, Jeremiah Rowland, Daan Camps, Nicolas Sawaya, Ryan LaRose. 2023-12-19. Measurement reduction for expectation values via fine-grained commutativity. https://arxiv.org/abs/2312.11840

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