2025/06/30 by Ryotaro Niwa, Niwa, Ryotaro, Zane M. Rossi +5 · 2 citations
Computer Science · #FOS: Physical sciences #Polynomial and algebraic computation #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2506.24112
openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(d3/δ) upper bound and an Ω(d/δ) lower bound for the query complexity of constructing a quantum channel that is δ-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∈ ℝ, which has implications for testing if a quantum channel is entanglement breaking.