Measurement reduction for expectation values via fine-grained commutativity Article Swipe

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Ben DalFavero , Rahul Sarkar , Daan Camps , Nicolas P. D. Sawaya , Ryan LaRose ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2312.11840

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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Pauli Exclusion Principle

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Commutative property Qubit Observable Tensor product Reduction (mathematics) Pauli exclusion principle Mathematics Pure mathematics Discrete mathematics Quantum Quantum mechanics Physics Theoretical physics Geometry

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2312.11840
PDF: https://arxiv.org/pdf/2312.11840
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Cited By: 1
Related Works: 10
OpenAlex ID: https://openalex.org/W4390041826

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DOI: https://doi.org/10.48550/arxiv.2312.11840

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Title: Measurement reduction for expectation values via fine-grained commutativity

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-12-19

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Authors: Ben DalFavero, Rahul Sarkar, Daan Camps, Nicolas P. D. Sawaya, Ryan LaRose

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Landing page: https://arxiv.org/abs/2312.11840

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Concepts: Commutative property, Qubit, Observable, Tensor product, Reduction (mathematics), Pauli exclusion principle, Mathematics, Pure mathematics, Discrete mathematics, Quantum, Quantum mechanics, Physics, Theoretical physics, Geometry

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Cited by: 1

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