Related papers: Ultrahigh threshold nonstabilizer nonlinear quantu…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
The possibility of using the two-fold topological degeneracy of spin-1/2 chiral spin liquid states on the torus to construct quantum error correcting codes is investigated. It is shown that codes constructed using these states on finite…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…
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…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit…
We study encodings that give the best known thresholds for the non-zero capacity of quantum channels, i.e., the upper bound for correctable noise, using an entropic approach to calculation of the threshold values. Our results show that…
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
Can robustness against experimental imperfections and noise be embedded into a quantum simulation? In this paper, we report on a special case in which this is possible. A spin chain can be engineered such that, in the absence of…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…