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- W4311553681 abstract "Symmetric states of collective angular momentum are good candidates for multi-qubit probe states in quantum sensors because they are easy to prepare and can be controlled without requiring individual addressability. Here, we give quantum error correction protocols for estimating the magnitude of classical fields using symmetric probe states. To achieve this, we first develop a general theory for quantum error correction on the symmetric subspace. This theory, based on the representation theory of the symmetric group, allows us to construct efficient algorithms that can correct any correctible error on any permutation-invariant code. These algorithms involve measurements of total angular momentum, quantum Schur transforms or logical state teleportations, and geometric pulse gates. For deletion errors, we give a simpler quantum error correction algorithm based on primarily on geometric pulse gates. Second, we devise a simple quantum sensing scheme on symmetric probe states that works in spite of a linear rate of deletion errors, and analyze its asymptotic performance. In our scheme, we repeatedly project the probe state onto the codespace while the signal accumulates. When the time spent to accumulate the signal is constant, our scheme can do phase estimation with precision that approaches the best possible in the noiseless setting. Third, we give near-term implementations of our algorithms." @default.
- W4311553681 created "2022-12-27" @default.
- W4311553681 creator A5006250123 @default.
- W4311553681 creator A5068313115 @default.
- W4311553681 date "2022-12-12" @default.
- W4311553681 modified "2023-09-25" @default.
- W4311553681 title "Quantum error correction on symmetric quantum sensors" @default.
- W4311553681 doi "https://doi.org/10.48550/arxiv.2212.06285" @default.
- W4311553681 hasPublicationYear "2022" @default.
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