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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…
In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. These systems can be realized in large-scale quantum networks or condensed onto a single chip with closely situated nodes.…
The behavior of real quantum hardware differs strongly from the simple error models typically used when simulating quantum error correction. Error processes are far more complex than simple depolarizing noise applied to single gates, and…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
Quantum error correcting (QEC) codes protect quantum information from decoherence, as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general,…
Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select…
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…
High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major…
We present a comprehensive and self-contained simplified review of the quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%,…
Large-scale quantum computers rely on quantum error correction to protect the fragile quantum information. Among the possible candidates of quantum computing devices, silicon-based spin qubits hold a great promise due to their compatibility…
Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors,…
The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of…
Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…