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A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding…
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.
Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…
If entanglement is available, the error-correcting ability of quantum codes can be increased. We show how to optimize the minimum distance of an entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding ebits to a…
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…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed…
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
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 this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which…
We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by…
Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…