Related papers: A Theory of Fault-Tolerant Quantum Computation

In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…

To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from…

Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…

We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…

Exploring an efficient and scalable architecture of fault-tolerant quantum computing (FTQC) is vital for demonstrating useful quantum computing. Here, we propose and evaluate a scalable and practical architecture with a…

Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can…

Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses…

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…

Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and…

The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…

Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…

Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state…

Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum…

From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…

Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…

In the framework of quantum computational tensor network [D. Gross and J. Eisert, Phys. Rev. Lett. {\bf98}, 220503 (2007)], which is a general framework of measurement-based quantum computation, the resource many-body state is represented…

Recent advances in quantum error-correction (QEC) have shown that it is often beneficial to understand fault-tolerance as a dynamical process, a circuit with redundant measurements that help correct errors, rather than as a static code…

We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…

Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…

The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in…