A gauge-invariant theory of small Markovian errors in quantum gate sets

Abstract:Noisy logic operations on a quantum computational register -- e.g., one or more qubits -- can be described by transfer matrices (a.k.a. CPTP maps or superoperators) that act linearly on the density matrix representing the register's quantum state. Collectively, these operations form a gate set. Gate sets have a gauge freedom; many gate sets that appear different actually predict the same experimental outcomes. A property of a gate set can be observable (and thus physically relevant) only if it is gauge-invariant. Unfortunately, no good gauge-invariant parameterizations of gate sets are known. We introduce the next best thing, a perturbative gauge-invariant parameterization of small Markovian errors in gate sets. We construct vector spaces of properties that are first-order gauge-invariant (FOGI). We show how to construct and understand FOGI properties, how to use them as coordinates to parameterize gate sets without gauge freedom, and how to extract approximately gauge-invariant error metrics.

arXiv:2608.14891 [quant-ph]

(or arXiv:2608.14891v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.14891 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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