Related papers: Nonadditive quantum error-correcting code
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…
Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where C_1 and C_2 are classical codes, is used to obtain codes for up to 16 information qubits…
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…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
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…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
In this work we prove that the 5-qubit quantum error correcting code does not fix qubit independent errors, even assuming that the correction circuit does not introduce new errors. We say that a quantum code does not fix a quantum computing…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
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…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…
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…
We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad.…
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
Quantum error correction is a crucial tool for mitigating hardware errors in quantum computers by encoding logical information into multiple physical qubits. However, no single error-correcting code allows for an intrinsically…