Related papers: Optimal Error Correcting Code For Ternary Quantum …
Large-scale quantum computers rely on quantum error correction to protect the fragile quantum information. Among the possible candidates of quantum computing devices, silicon-based spin qubits hold a great promise due to their compatibility…
For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode $k$ qudits into…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
We propose a new scheme for quantum error correction using robust continuous variable probe modes, rather than fragile ancilla qubits, to detect errors without destroying data qubits. The use of such probe modes reduces the required number…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. The quantum register is a multi charge-qubit system in a semiconductor environment, where the main sources of noise are phase…
In this paper, we provise an implementation of five, seven and nine-qubits error correcting codes on a classical computer using the quantum simulator Feynman program. We also compare the three codes by computing the fidelity when double…
In classical case there is simplest method of error correction with using three equal bits instead of one. In the paper is shown, how the scheme fails for quantum error correction with complex vector spaces of usual quantum mechanics, but…
Most quantum error correcting codes are predicated on the assumption that there exists a reservoir of qubits in the state $\ket{0}$, which can be used as ancilla qubits to prepare multi-qubit logical states. In this report, we examine the…
We propose an error correction coding algorithm for continuous quantum variables. We use this algorithm to construct a highly efficient 5-wavepacket code which can correct arbitrary single wavepacket errors. We show that this class of…
We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the…
Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses…
We investigate the performance of a three qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of dephasing errors but only in situations where…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…