Quantum Error Correction

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Christopher Chamberland - One of the best experts on this subject based on the ideXlab platform.

Kyungjoo Noh - One of the best experts on this subject based on the ideXlab platform.

Atsushi Okamoto - One of the best experts on this subject based on the ideXlab platform.

  • Tracking Quantum Error Correction
    Physical Review A, 2018
    Co-Authors: Kosuke Fukui, Akihisa Tomita, Atsushi Okamoto
    Abstract:

    To implement fault-tolerant Quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large-scale Quantum computation with the GKP qubit [Phys. Rev. X 8, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large-scale Quantum computation, we propose the tracking Quantum Error Correction, where the logical-qubit-level Quantum Error Correction is partially substituted by the single-qubit-level Quantum Error Correction. In the proposed method, the analog Quantum Error Correction is utilized to make the performances of the single-qubit-level Quantum Error Correction almost identical to those of the logical-qubit-level Quantum Error Correction in a practical noise level. The numerical results show that the proposed tracking Quantum Error Correction reduces the number of qubits during a Quantum Error-Correction process by the reduction rate ${2(n\ensuremath{-}1){4}^{l\ensuremath{-}1}\ensuremath{-}n+1}/(2n\ifmmode\times\else\texttimes\fi{}{4}^{l\ensuremath{-}1})$ for $n$-cycles of the Quantum Error-Correction process using Knill's ${C}_{4}/{C}_{6}$ code with the concatenation level $l$. Hence, the proposed tracking Quantum Error Correction has great advantage in reducing the required number of physical qubits, and will open a new way to expoloit the advantages of the GKP qubits in practical Quantum computation.

Gunnar Björk - One of the best experts on this subject based on the ideXlab platform.

  • Fidelity as a figure of merit in Quantum Error Correction
    arXiv: Quantum Physics, 2016
    Co-Authors: Jonas Almlöf, Gunnar Björk
    Abstract:

    We discuss the fidelity as a figure of merit in Quantum Error Correction schemes. We show that when identifiable but uncorrectable Errors occur as a result of the action of the channel, a common strategy that improves the fidelity actually decreases the transmitted mutual information. The conclusion is that while the fidelity is simple to calculate and therefore often used, it is perhaps not always a recommendable figure of merit for Quantum Error Correction. The reason is that while it roughly speaking encourages optimisation of the "mean probability of success", it gives no incentive for a protocol to indicate exactly where the Errors lurk. For small Error probabilities, the latter information is more important for the integrity of the information than optimising the mean probability of success.

  • Combating entanglement sudden death with non-local Quantum-Error Correction
    arXiv: Quantum Physics, 2008
    Co-Authors: Isabel Sainz, Gunnar Björk
    Abstract:

    We study the possibility of preventing finite-time disentanglement caused by dissipation by making use of "non-local Quantum Error Correction. This is made in comparison of previous results, where was shown that "local" Quantum Error Correction can delay disentanglement, but can also cause entanglement sudden death when is not originally present.

  • Quantum Error Correction may delay, but also cause, entanglement sudden death
    Physical Review A, 2008
    Co-Authors: Isabel Sainz, Gunnar Björk
    Abstract:

    Dissipation may cause two initially entangled qubits to evolve into a separable state in a finite time. This behavior is called entanglement sudden death (ESD). We study to what extent Quantum Error Correction can combat ESD. We find that in some cases Quantum Error Correction can delay entanglement sudden death but in other cases Quantum Error Correction may cause ESD for states that otherwise do not suffer from it. Our analysis also shows that fidelity may not be the best measure to compare the efficiency of different Error Correction codes since the fidelity is not directly coupled to a state's remaining entanglement.

Yuichiro Fujiwara - One of the best experts on this subject based on the ideXlab platform.

  • Ability of stabilizer Quantum Error Correction to protect itself from its own imperfection
    Physical Review A, 2014
    Co-Authors: Yuichiro Fujiwara
    Abstract:

    The theory of stabilizer Quantum Error Correction allows us to actively stabilize Quantum states and simulate ideal Quantum operations in a noisy environment. It is critical to correctly diagnose noise from its syndrome and nullify it accordingly. However, hardware that performs Quantum Error Correction itself is inevitably imperfect in practice. Here, we show that stabilizer codes possess a built-in capability to correct Errors not only on Quantum information but also on faulty syndromes extracted by themselves. Shor's syndrome extraction for fault-tolerant Quantum computation is naturally improved. This opens a path to realizing the potential of stabilizer Quantum Error Correction hidden within an innocent-looking choice of generators and stabilizer operators that have been deemed redundant.

  • Quantum Error Correction via less noisy qubits.
    Physical review letters, 2013
    Co-Authors: Yuichiro Fujiwara
    Abstract:

    Known Quantum Error Correction schemes are typically able to take advantage of only a limited class of classical Error-correcting codes. Entanglement-assisted Quantum Error Correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help correct Quantum Errors on noisy qubits, which can be too severe an assumption. We prove that a more relaxed and realistic assumption is sufficient by presenting encoding and decoding operations assisted by qubits on which Quantum Errors of one particular kind may occur. As in entanglement assistance, our scheme can import any binary or quaternary linear codes. If the auxiliary qubits are noiseless, our codes become entanglement-assisted codes, and saturate the Quantum Singleton bound when the underlying classical codes are maximum distance separable.

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