Related papers: Quantum error correction on infinite-dimensional H…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Graph states have been used to construct quantum error correction codes for independent errors. Hypergraph states generalize graph states, and symmetric hypergraph states have been shown to allow for the correction of correlated errors. In…
The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…
To perform reliable quantum computation, quantum error correction is indispensable. In certain cases, continuous covariance symmetry of the physical system can make exact error correction impossible. In this work we study the approximate…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Z\'emor, and all families of toric codes on $m$-dimensional hypercubic lattices. Similar to the latter,…
A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous…
This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable…
We present a new geometric perspective on quantum error correction based on spectral triples in noncommutative geometry. In this approach, quantum error correcting codes are reformulated as low energy spectral projections of Dirac type…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop…