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Quantum Algorithms

Measurement reduction for expectation values via fine-grained commutativity

arXiv
Authors: Ben DalFavero, Rahul Sarkar, Jeremiah Rowland, Daan Camps, Nicolas Sawaya, Ryan LaRose

Year

2023

Paper ID

53326

Status

Preprint

Abstract Read

~2 min

Abstract Words

87

Citations

N/A

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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  • It adds a 2023 reference point for readers tracking recent quantum research.
  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2312.11840 [2] arXiv https://arxiv.org/abs/2312.11840 [3] Publisher https://arxiv.org/abs/2312.11840

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