arXiv subjects

Ryotaro Niwa

Publications and source records attributed to Ryotaro Niwa.

5 recordsLinked to original sources

arXiv2026

Singular value transformation for unknown quantum channels

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 $O(d^3/δ)$ 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 unnormalized 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. Our results establish a general framework for manipulating black-box quantum channels with QSVT and related methods, enabling direct evaluation of the channel's spectral properties without tomography or significant classical post-processing.

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arXiv2026

Asymptotically optimal purification of noisy unitary channels in any dimension

We consider the problem of noisy unitary purification. Given access to an unknown $d$-dimensional unitary channel followed by depolarizing noise of strength $p$, we aim to construct a superchannel that universally purifies the noisy unitary back to the original unknown unitary. We optimize over arbitrary adaptive sequential strategies and analytically derive the optimal fidelity to the leading order in the noise strength and number of channel uses, while also providing a concrete $\mathrm{SU}(d)$-covariant parallel strategy that attains the optimum. Our result implies the query complexity $Θ(d^2p/ε)$ for achieving leading-order infidelity $ε$ in the low-noise regime, which scales better than the naive approach combining optimal state purification and storage-and-retrieval of quantum channels. We also consider the dual problem of noisy unitary conjugation, where the goal is to obtain the best approximation of the complex conjugate of the original unknown unitary from access to noisy queries. We show that the optimal fidelity for this task coincides with that of noisy unitary purification to the leading-order in the low-noise and large-query limit.

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arXiv2026

Scaling-optimal purification of noisy qubit unitary channels

We consider the problem of purifying noisy qubit unitary channels. Given the ability to apply an unknown qubit unitary channel followed by depolarizing noise, we aim to construct a superchannel that purifies the noisy unitary back to the original unknown unitary. We first provide numerical evidence that sequential strategies can strictly outperform parallel strategies when the number of channel uses is finite, highlighting the fundamental distinction from state purification. We then provide a concrete $\mathrm{U}(2)$-covariant parallel protocol based on a novel entanglement-assisted quantum error-correcting code that suppresses the first-order noise strength as $O(1/n)$ with $n$ channel uses and show this scaling is asymptotically optimal in the low-noise regime, even when sequential strategies are allowed.

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arXiv2026

Random dilation superchannel

We present a quantum circuit that implements the random dilation superchannel, transforming parallel queries of an unknown quantum channel into the same number of parallel queries of a randomly chosen dilation isometry of the input channel. This is a natural generalization of the random purification channel, that transforms copies of an unknown mixed state to copies of a randomly chosen purification state. The circuit complexity of our construction is $O(\mathrm{poly}(n, \log d_I, \log d_O))$, where $n$ is the number of queries and $d_I$ and $d_O$ are the input and output dimensions of the input channel, respectively. This random dilation superchannel is extended to the sequential queries approximately, by transforming the parallel random dilation isometry into sequential random dilation unitaries with $O(\mathrm{poly}(d_I))$ overhead in the number of queries. We also show that our results can be further extended to the case of quantum superchannels. On the other hand, we show a no-go theorem on the exact random dilation of sequential queries with $o(\mathrm{poly}(\min\{d_I, d_O\}))$ query overhead, showcasing a fundamental difference between the parallel and sequential cases. As an application, we show an efficient storage-and-retrieval of an unknown quantum channel, which improves the program cost exponentially in the retrieval error $\varepsilon$. For the case where the Kraus rank $r$ is the least possible (i.e., $r = d_I/d_O$), we show quantum circuits that transform $n$ parallel queries of an unknown quantum channel $Λ$ to $Θ(n^α)$ parallel queries of $Λ$ for any $α<2$ approximately, and implement its Petz recovery map for the maximally mixed reference state probabilistically and exactly.

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arXiv2025

Coherent information for CSS codes under decoherence

Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons. Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state. Here we perform a simple analytic calculation of the coherent information for general CSS codes under local incoherent Pauli errors via diagonalization of the density matrices and mapping to classical statistical mechanical (SM) models. Our result establishes a rigorous connection between the decoding transition of the quantum code and the phase transition in the random classical SM model. It is also directly confirmed for CSS codes that exact error correction is possible if and only if the maximum-likelihood (ML) decoder always succeeds in the thermodynamic limit. Thus, the fundamental threshold is saturated by the optimal decoder.

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