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Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a…
Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a…
Quantum error correction (QEC) is often implemented on hardware that experiences biased noise, where dephasing errors occur more frequently than other errors. This has motivated many recent efforts to develop bias-tailored QEC codes, such…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
Quantum error correction is one of the fundamental building blocks of digital quantum computation. The Quantum Lego formalism has introduced a systematic way of constructing new stabilizer codes out of basic lego-like building blocks, which…
The overhead of quantum error correction (QEC) poses a major bottleneck for realizing fault-tolerant computation. To reduce this overhead, we exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into…
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…
In this paper we extend the work of Lisonek and Singh on construction X for quantum error-correcting codes to finite fields of order $p^2^ where p is prime. The results obtained are applied to the dual of Hermitian repeated root cyclic…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
Collective coherent noise poses challenges for fault-tolerant quantum error correction (FTQEC), as it falls outside the usual stochastic noise models. While constant excitation (CE) codes can naturally avoid coherent noise, a complete…
Encoding quantum information into a set of harmonic oscillators is considered a hardware efficient approach to mitigate noise for reliable quantum information processing. Various codes have been proposed to encode a qubit into an oscillator…
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Bosonic codes with rotational symmetry are currently one of the best performing quantum error correcting codes. Little is known about error propagation and code distance for these rotation codes in contrast with qubit codes and Bosonic…