Related papers: Cylindrical and M\"obius Quantum Codes for Asymmet…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…
Surface codes are quantum error correcting codes normally defined on 2D arrays of qubits. In this paper, we introduce a surface code design based on the fact that the severity of bit flip and phase flip errors in the physical quantum…
Quantum Surface codes are a kind of quantum topological stabilizer codes whose stabilizers and qubits are geometrically related. Due to their special structures, surface codes have great potential to lead people to large-scale quantum…
Calderbank-Shor-Steane (CSS) quantum error-correcting codes are based on pairs of classical codes which are mutually dual containing. Explicit constructions of such codes for large blocklengths and with good error correcting properties are…
Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$…
We introduce surface ZZZY codes, a novel family of quantum error-correcting codes designed for asymmetric channels. Derived from standard surface codes through tailored modification of generators, ZZZY codes can be decoded by the minimum…
In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary…
The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT…
Surface codes are versatile quantum error-correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used Pauli $X$ or Pauli $Z$ operators in a square structure, these…
Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
Quantum error correction suppresses noise in quantum systems to allow for high-precision computations. In this work, we introduce Multivariate Bicycle (MB) Quantum Low-Density Parity-Check (QLDPC) codes, via an extension of the framework…
We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…
Topological quantum codes are favored because they allow qubit layouts that are suitable for practical implementation. An $N$-qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
We investigate the performance of two quantum error-correcting codes, the surface code and the Bacon-Shor code, for implementation with spin qubits in silicon. In each case, we construct a logical qubit using a planar array of quantum dots,…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…