Explicit decoders using quantum singular value transformation
- URL: http://arxiv.org/abs/2405.06051v2
- Date: Thu, 6 Jun 2024 09:44:42 GMT
- Title: Explicit decoders using quantum singular value transformation
- Authors: Takeru Utsumi, Yoshifumi Nakata,
- Abstract summary: We provide two explicit decoding quantum circuits capable of recovering quantum information.
The proposed decoding circuits reduce the computational cost compared to a previously known explicit decoder.
- 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 and fundamental physics. 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 algorithm based on the quantum singular value transformation, which significantly extends an approach by Yoshida and Kitaev in a specific noise model to general situations. We also show that the proposed decoding circuits reduce the computational cost compared to a previously known explicit decoder. Our constructions not only show an intriguing intersection between decoders and quantum algorithms but also reveal the power of an algorithmic approach to recovering quantum information.
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