Explicit decoders using fixed-point amplitude amplification based on QSVT

• URL: http://arxiv.org/abs/2405.06051v3
• Date: Wed, 09 Oct 2024 22:18:16 GMT
• Title: Explicit decoders using fixed-point amplitude amplification based on QSVT
• Authors: Takeru Utsumi, Yoshifumi Nakata,
• Abstract summary: We provide two explicit decoding quantum circuits capable of recovering quantum information. The decoders are constructed by using the fixed-point amplitude amplification (FPAA) based on the quantum singular value transformation (QSVT)
• Score: 2.3020018305241337
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recovering quantum information from a noisy quantum system is one of the central challenges in quantum information science. The key to this goal is explicitly constructing a decoder. In this paper, we provide two explicit decoding quantum circuits that are both capable of recovering quantum information when a decoupling condition is satisfied, i.e., when quantum information is in principle recoverable. The decoders are constructed by using the fixed-point amplitude amplification (FPAA) based on the quantum singular value transformation (QSVT), which significantly extends a previous approach in a specific noise model to arbitrary noisy models. In our constructions, it is crucial to use the QSVT-based FPAA, demonstrating for the first time the separation between any other amplitude amplification algorithms and the QSVT-based one in the application. We also show that the proposed decoders have high decoding performance and reduce the computational cost compared to a previously known explicit decoder.

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