Topic
Steane code
About: Steane code is a research topic. Over the lifetime, 63 publications have been published within this topic receiving 2357 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, a quantum error correction code is proposed to protect a qubit of information against general one qubit errors, which can then be restored by a simple unitary transformation.
Abstract: We present a quantum error correction code which protects a qubit of information against general one qubit errors. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state $|0〉$ to the encoded state. It can also be converted into a decoder by running it backward. The original state of the encoded qubit can then be restored by a simple unitary transformation.
1,078 citations
TL;DR: It is demonstrated that fault-tolerant universal computation is possible for any stabilizer code, including the five-quantum-bit code.
Abstract: In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a theory of fault-tolerant operations on stabilizer codes based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-quantum-bit code.
1,061 citations
TL;DR: A new version of the quantum threshold theorem is proved that applies to concatenation of a quantum code that corrects only one error, and this theorem is used to derive arigorous lower bound on the quantum accuracy threshold e0, the best lower bound that has been rigorously proven so far.
Abstract: We prove a new version of the quantum threshold theorem that applies to concatenationof a quantum code that corrects only one error, and we use this theorem to derive arigorous lower bound on the quantum accuracy" threshold e0. Our proof also appliesto concatenation of higher-distance codes, and to noise models that allow faults to becorrelated in space and in time. The proof uses new criteria for assessing the accuracy" offault-tolerant circuits, which are particularly conducive to the inductive analysis of recur-sire simulations. Our lower bound on the threshold, e0 ≥ 2.73 × 10-5 for an adversarialindependent stochastic noise model, is derived from a computer-assisted combinatorialanaly sis; it is the best lower bound that has been rigorously proven so far.
556 citations
TL;DR: The method presented is numerical and scales exponentially with the number of gates used in the approximation, and for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qu bit Steane code, it finds gate sequences sufficiently long and accurate to permit the Fault-Tolerant factoring of numbers thousands of bits long.
Abstract: We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates used in the approximation. However, for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qubit Steane code, we find gate sequences sufficiently long and accurate to permit the fault-tolerant factoring of numbers thousands of bits long. A general scaling law of how rapidly these fault-tolerant approximations converge to arbitrary single-qubit gates is also determined.
85 citations
TL;DR: In this article, a partially mechanized proof of the correctness of Steane's 7-qubit error-correcting code using the tool Quantomatic is given, which represents the largest and most complicated verification task yet carried out using Quomanatic.
Abstract: In this paper we give a partially mechanized proof of the correctness of Steane's 7-qubit error correcting code, using the tool Quantomatic. To the best of our knowledge, this represents the largest and most complicated verification task yet carried out using Quantomatic.
67 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 7 |
| 2019 | 5 |
| 2018 | 6 |
| 2017 | 9 |
| 2016 | 2 |