Related papers: Error Threshold for Color Codes and Random 3-Body …
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
A quantum error correction code is assessed over its ability to correct errors in noisy quantum circuits. This task requires extensive simulations of faulty quantum circuits, which are often made tractable by considering stochastic Pauli…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…
Color codes are a leading class of topological quantum error-correcting codes with modest error thresholds and structural compatibility with two-dimensional architectures, which make them well-suited for fault-tolerant quantum computing…
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…
Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the…
Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by…
The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We…
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
We estimate the resource requirements for the quantum simulation of the ground state energy of the one dimensional quantum transverse Ising model (TIM), based on the surface code implementation of a fault tolerant quantum computer. The…
It is known that noisy topological quantum codes are related to random bond Ising models where the order-disorder phase transition in the classical model is mapped to the error threshold of the corresponding topological code. On the other…
We calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme and Milburn [Nature 409, pp. 46--52 (2001)] under an error model where photon detectors have efficiency <100% but all other components --…
The threshold theorem promises a path to fault-tolerant quantum computation, provided the physical error rate is below a critical threshold. While transversal gates efficiently implement logical operations, they propagate errors and can…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…