Near-Optimal Parallel Unitary Process Tomography in Diamond Distance
Abstract
Unitary process tomography is the act of learning how an unknown unitary gate acts on a quantum system. It is an essential procedure for realizing a functioning quantum computer. As quantum technologies develop, it is important to understand the computational resources needed to conduct unitary process tomography using a variety of types of circuits. In particular, when measuring error in diamond distance, it is known how to achieve optimal query complexity using a sequential circuit architecture, but it had not been known whether a parallel circuit architecture could achieve the same optimal query complexity. In this work, we prove that unitary process tomography with near-optimal query complexity is indeed possible using a parallel circuit by introducing an explicit, novel parallel procedure. This closes the gap between sequential and parallel circuits up to a logarithmic factor, showing that parallel and sequential strategies are nearly equally capable for this task.
Related
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BibTeX
@misc{scully2026nearoptimal,
title = {{Near-Optimal Parallel Unitary Process Tomography in Diamond Distance}},
author = {Noam Scully and Sisi Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36127},
eprint = {2609.36127},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36127},
}
RIS
TY - UNPB
TI - Near-Optimal Parallel Unitary Process Tomography in Diamond Distance
AU - Noam Scully
AU - Sisi Zhou
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36127
UR - https://arxiv.org/abs/2609.36127
AB - Unitary process tomography is the act of learning how an unknown unitary gate acts on a quantum system. It is an essential procedure for realizing a functioning quantum computer. As quantum technologies develop, it is important to understand the computational resources needed to conduct unitary process tomography using a variety of types of circuits. In particular, when measuring error in diamond distance, it is known how to achieve optimal query complexity using a sequential circuit architecture, but it had not been known whether a parallel circuit architecture could achieve the same optimal query complexity. In this work, we prove that unitary process tomography with near-optimal query complexity is indeed possible using a parallel circuit by introducing an explicit, novel parallel procedure. This closes the gap between sequential and parallel circuits up to a logarithmic factor, showing that parallel and sequential strategies are nearly equally capable for this task.
ER -