相关论文: A Theory of Quantum Error-Correcting Codes
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…
I give an overview of the basic concepts behind quantum error correction and quantum fault tolerance. This includes the quantum error correction conditions, stabilizer codes, CSS codes, transversal gates, fault-tolerant error correction,…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
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…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…
The existence of quantum error correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum information theory. However, standard error correction refers to abstract quantum…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
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…
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Universal fault-tolerant quantum computation requires overcoming the Eastin--Knill theorem on quantum error correction (QEC) codes that protect information from noise. This is often accomplished through strategies like magic state…
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…