Towards enhancing quantum expectation estimation of matrices through partial Pauli decomposition techniques and post-processing

• URL: http://arxiv.org/abs/2401.17640v2
• Date: Mon, 6 May 2024 06:18:37 GMT
• Title: Towards enhancing quantum expectation estimation of matrices through partial Pauli decomposition techniques and post-processing
• Authors: Dingjie Lu, Yangfan Li, Dax Enshan Koh, Zhao Wang, Jun Liu, Zhuangjian Liu,
• Abstract summary: We introduce an approach for estimating the expectation values of arbitrary $n$-qubit matrices $M in mathbbC2ntimes 2n$ on a quantum computer.
• Score: 7.532969638222725
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce an approach for estimating the expectation values of arbitrary $n$-qubit matrices $M \in \mathbb{C}^{2^n\times 2^n}$ on a quantum computer. In contrast to conventional methods like the Pauli decomposition that utilize $4^n$ distinct quantum circuits for this task, our technique employs at most $2^n$ unique circuits, with even fewer required for matrices with limited bandwidth. Termed the \textit{partial Pauli decomposition}, our method involves observables formed as the Kronecker product of a single-qubit Pauli operator and orthogonal projections onto the computational basis. By measuring each such observable, one can simultaneously glean information about $2^n$ distinct entries of $M$ through post-processing of the measurement counts. This reduction in quantum resources is especially crucial in the current noisy intermediate-scale quantum era, offering the potential to accelerate quantum algorithms that rely heavily on expectation estimation, such as the variational quantum eigensolver and the quantum approximate optimization algorithm.

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