Related papers: Linear Logic and Quantum Error Correcting Codes
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
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…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
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 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…
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We describe a linear quantum optical circuit capable of demonstrating a simple quantum error correction code in a four photon experiment.
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…