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Explicit decoders using fixed-point amplitude amplification based on QSVT

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Researchers Takeru Utsumi and Yoshifumi Nakata developed two explicit quantum decoders using fixed-point amplitude amplification (FPAA) and quantum singular value transformation (QSVT), enabling reliable quantum information recovery from noisy channels. The decoders work under the decoupling condition, where quantum information is theoretically recoverable, and are compatible with both entanglement-assisted and non-assisted communication settings, making them universally applicable to any noise model. By leveraging QSVT-based FPAA, the team extended prior erasure-noise-only solutions, significantly reducing circuit complexity and computational costs compared to existing explicit decoder implementations. The approach combines a low-probability quantum measurement protocol with amplitude amplification, achieving communication rates arbitrarily close to the quantum capacity by increasing channel uses, addressing a long-standing efficiency challenge. This work bridges quantum algorithms and communication theory, offering potential applications in quantum many-body physics and advancing practical, high-rate quantum information transmission.

Explicit decoders using fixed-point amplitude amplification based on QSVT

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AbstractReliably transmitting quantum information via a noisy quantum channel is a central challenge in quantum information science. While constructing a decoder is crucial to this goal, little was known about quantum circuit implementations of decoders that reach high communication rates. In this paper, we provide two decoders with explicit quantum circuits capable of recovering quantum information when the decoupling condition is satisfied, i.e., when quantum information is in principle recoverable. These are applicable to both entanglement-assisted and non-assisted settings. By developing a technique that relies on a symmetric structure of the decoders, we show that they are applicable to any noise model. As a consequence, for any noisy channel, our decoders can be used to achieve a communication rate arbitrarily close to the quantum capacity by increasing the number of channel uses. To construct the decoders, we employ the fixed-point amplitude amplification (FPAA) based on the quantum singular value transformation (QSVT), extending a previous approach applicable only to erasure noise. Our constructions offer advantages in the computational cost, largely reducing the circuit complexity compared to previous explicit decoders. Through an investigation of the decoding problem, unique advantages of the QSVT-based FPAA are highlighted.Featured image: A diagram of quantum communication, where the boxes represent quantum channels. The purpose of the sender and the receiver is to transmit quantum information via a noisy channel $\mathcal{N}^{C\to D}$. They may share $(\log d_B)$-ebit entanglement in advance, which is used in the encoding and decoding. When $d_B = 1$, this corresponds to the entanglement-non-assisted setting, while $d_B \neq 1$ corresponds to the entanglement-assisted setting with a limited or unlimited amount of entanglement. In this work, we focus on decoding and provide explicit algorithms.Popular summaryQuantum information is easily destroyed by noise. A key technique for protecting it is to encode the information so that it becomes robust to noise and then decode it afterward. While explicitly constructing decoders is crucial, only a few general constructions are known, and all of them are computationally expensive. In this work, we construct two explicit decoders using a recently developed quantum algorithm. These decoders have broad applicability, can achieve high communication rates, and require lower computational cost than previous constructions. Our construction proceeds in two steps. First, we design a protocol based on a quantum measurement that successfully decodes when a desired outcome is obtained, although this typically occurs with small probability. We then amplify the success probability using an amplitude amplification algorithm. While a similar idea was previously proposed in highly restricted settings, we substantially extend it to much broader scenarios by making nontrivial use of the quantum singular value transformation (QSVT), obtaining quantum circuit implementations of decoders for general situations. Our results demonstrate the power of algorithmic approaches to constructing decoders and establish a connection between quantum algorithms and quantum communication theory. In particular, they represent a step toward the long-standing goal of constructing decoders that achieve high communication rates at low computational cost. Furthermore, because decoders are also used in fundamental physics to probe complex quantum many-body systems, our work may contribute to a better understanding of exotic many-body phenomena.► BibTeX data@article{Utsumi2026explicitdecoders, doi = {10.22331/q-2026-03-13-2024}, url = {https://doi.org/10.22331/q-2026-03-13-2024}, title = {Explicit decoders using fixed-point amplitude amplification based on {QSVT}}, author = {Utsumi, Takeru and Nakata, Yoshifumi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2024}, month = mar, year = {2026} }► References [1] Patrick Hayden and John Preskill. ``Black holes as mirrors: quantum information in random subsystems''. J.

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High Energy Phys. 2020, 1–14 (2020). https://doi.org/10.1007/JHEP01(2020)168Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-13 11:35:51: Could not fetch cited-by data for 10.22331/q-2026-03-13-2024 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-13 11:35:58: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractReliably transmitting quantum information via a noisy quantum channel is a central challenge in quantum information science. While constructing a decoder is crucial to this goal, little was known about quantum circuit implementations of decoders that reach high communication rates. In this paper, we provide two decoders with explicit quantum circuits capable of recovering quantum information when the decoupling condition is satisfied, i.e., when quantum information is in principle recoverable. These are applicable to both entanglement-assisted and non-assisted settings. By developing a technique that relies on a symmetric structure of the decoders, we show that they are applicable to any noise model. As a consequence, for any noisy channel, our decoders can be used to achieve a communication rate arbitrarily close to the quantum capacity by increasing the number of channel uses. To construct the decoders, we employ the fixed-point amplitude amplification (FPAA) based on the quantum singular value transformation (QSVT), extending a previous approach applicable only to erasure noise. Our constructions offer advantages in the computational cost, largely reducing the circuit complexity compared to previous explicit decoders. Through an investigation of the decoding problem, unique advantages of the QSVT-based FPAA are highlighted.Featured image: A diagram of quantum communication, where the boxes represent quantum channels. The purpose of the sender and the receiver is to transmit quantum information via a noisy channel $\mathcal{N}^{C\to D}$. They may share $(\log d_B)$-ebit entanglement in advance, which is used in the encoding and decoding. When $d_B = 1$, this corresponds to the entanglement-non-assisted setting, while $d_B \neq 1$ corresponds to the entanglement-assisted setting with a limited or unlimited amount of entanglement. In this work, we focus on decoding and provide explicit algorithms.Popular summaryQuantum information is easily destroyed by noise. A key technique for protecting it is to encode the information so that it becomes robust to noise and then decode it afterward. While explicitly constructing decoders is crucial, only a few general constructions are known, and all of them are computationally expensive. In this work, we construct two explicit decoders using a recently developed quantum algorithm. These decoders have broad applicability, can achieve high communication rates, and require lower computational cost than previous constructions. Our construction proceeds in two steps. First, we design a protocol based on a quantum measurement that successfully decodes when a desired outcome is obtained, although this typically occurs with small probability. We then amplify the success probability using an amplitude amplification algorithm. While a similar idea was previously proposed in highly restricted settings, we substantially extend it to much broader scenarios by making nontrivial use of the quantum singular value transformation (QSVT), obtaining quantum circuit implementations of decoders for general situations. Our results demonstrate the power of algorithmic approaches to constructing decoders and establish a connection between quantum algorithms and quantum communication theory. In particular, they represent a step toward the long-standing goal of constructing decoders that achieve high communication rates at low computational cost. Furthermore, because decoders are also used in fundamental physics to probe complex quantum many-body systems, our work may contribute to a better understanding of exotic many-body phenomena.► BibTeX data@article{Utsumi2026explicitdecoders, doi = {10.22331/q-2026-03-13-2024}, url = {https://doi.org/10.22331/q-2026-03-13-2024}, title = {Explicit decoders using fixed-point amplitude amplification based on {QSVT}}, author = {Utsumi, Takeru and Nakata, Yoshifumi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2024}, month = mar, year = {2026} }► References [1] Patrick Hayden and John Preskill. ``Black holes as mirrors: quantum information in random subsystems''. J.

High Energy Phys. 2007, 120 (2007). https://doi.org/10.1088/1126-6708/2007/09/120 [2] Daniel Harlow and Patrick Hayden. ``Quantum computation vs. firewalls''. J.

High Energy Phys. 2015, 1–55 (2015). https://doi.org/10.1007/JHEP06(2015)149 [5] Ahmed Almheiri, Xi Dong, and Daniel Harlow. ``Bulk locality and quantum error correction in AdS/CFT''. J.

High Energy Phys. 2016, 1–49 (2016). https://doi.org/10.1007/JHEP02(2016)004 [10] Daniel A. Roberts and Beni Yoshida. ``Chaos and complexity by design''. J.

High Energy Phys. 02, 017 (2021). https://doi.org/10.1007/JHEP02(2021)017 [97] Chi-Fang Chen, Geoffrey Penington, and Grant Salton. ``Entanglement wedge reconstruction using the Petz map''. J.

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