Related papers: Single Quantum Deletion Error-Correcting Codes
Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
I provide an introduction to quantum computers, describing how they might be realized using language accessible to a solid state physicist. A listing of the minimal requirements for creating a quantum computer is given. I also discuss…
We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic…
Quantum computing offers significant speedups, but the large number of physical qubits required for quantum error correction introduces engineering challenges for a monolithic architecture. One solution is to distribute the logical quantum…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
In this article, we present the unbalanced quantum error correcting codes(one-party-QECC), a novel idea for correcting unbalanced quantum errors. In some quantum communication tasks using entangled pairs, the error distributions between two…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…
We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite…
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to…
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…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric $n$-vertices colourable graph and a group of operations (colouring rules) on the graph: find the minimum sequence…
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 devise a scheme that protects quantum coherent states of light from probabilistic losses, thus achieving the first continuous-variable quantum erasure-correcting code. If the occurrence of erasures can be probed, then the decoder…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…