Singular value transformation for unknown quantum channels

• URL: http://arxiv.org/abs/2506.24112v2
• Date: Tue, 15 Jul 2025 03:19:48 GMT
• Title: Singular value transformation for unknown quantum channels
• Authors: Ryotaro Niwa, Zane Marius Rossi, Philip Taranto, Mio Murao,
• Abstract summary: We develop a quantum algorithm for transforming a quantum channel's singular values.<n>We show our method applies practically to the problem of learning the $q$-th singular value moments of unknown quantum channels.
• Score: 0.7499722271664144
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Given the ability to apply an unknown quantum channel acting on a $d$-dimensional system, we develop a quantum algorithm for transforming its singular values. The spectrum of a quantum channel as a superoperator is naturally tied to its Liouville representation, which is in general non-Hermitian. Our key contribution is an approximate block-encoding scheme for this representation in a Hermitized form, given only black-box access to the channel; this immediately allows us to apply polynomial transformations to the channel's singular values by quantum singular value transformation (QSVT). We then demonstrate an $O(d^3/\delta)$ upper bound and an $\Omega(d/\delta)$ lower bound for the query complexity of constructing a quantum channel that is $\delta$-close in diamond norm to a block-encoding of the Hermitized Liouville representation. We show our method applies practically to the problem of learning the $q$-th singular value moments of unknown quantum channels for arbitrary $q>2, q\in \mathbb{R}$, which has implications for testing if a quantum channel is entanglement breaking.

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