Related papers: Abelian multi-cycle codes for single-shot error co…
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require…
We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the…
Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated…
In our recent paper entitled "Quantum Quasi-Cyclic Low-Density Parity-Check codes" [ICIC 2009. LNCS 5754], it was claimed that some new quantum codes can be constructed via the CSS encoding/decoding approach with various lengths and rates.…
Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is…
Quantum error correction is critical to the design and manufacture of scalable quantum computing systems. Recently, there has been growing interest in quantum low-density parity-check codes as a resource-efficient alternative to surface…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…
Vast numbers of qubits will be needed for large-scale quantum computing due to the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to…
For any positive integer $g \ge 2$, we derive general condition for the existence of a $2g$-cycle in the Tanner graph of two-dimensional ($2$-D) classical quasi-cyclic (QC) low-density parity-check (LDPC) codes. Depending on whether $p$ is…
Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and…
We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3% for the {4,5}-hyperbolic surface code in a phenomenological noise model (as compared to…
Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for…
Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the…
We explicitly construct a class of holographic quantum error correction codes with non-trivial centers in the code subalgebra. Specifically, we use the Bacon-Shor codes and perfect tensors to construct a gauge code (or a stabilizer code…