Related papers: Ultrahigh threshold nonstabilizer nonlinear quantu…
Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
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…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
The Pauli stabilizer formalism is perhaps the most thoroughly studied means of procuring quantum error-correcting codes, whereby the code is obtained through commutative Pauli operators and ``stabilized'' by them. In this work we will show…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
A central challenge in quantum error correction is identifying powerful quantum codes tailored to specific hardware and determining their error thresholds above which quantum information is unprotected. This problem is hard because we…
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…
The physical symmetries of a system play a central role in quantum error correction. In this work we encode a qubit in a collection of systems with angular-momentum symmetry (spins), extending the tools developed in Phys. Rev. Lett. 127,…
Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
Hybrid codes simultaneously encode both quantum and classical information, allowing for the transmission of both across a quantum channel. We construct a family of nonbinary error-detecting hybrid stabilizer codes that can detect one error…
Mapping an error syndrome to the error operator is the core of quantum decoding network and is also the key step of recovery. The definitions of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix were presented, and…
We investigate a scheme of fault-tolerant quantum computation based on the cluster model. Logical qubits are encoded by a suitable code such as the Steane's 7-qubit code. Cluster states of logical qubits are prepared by post-selection…