Related papers: A Universal Operator Theoretic Framework for Quant…
Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent…
Medium-scale quantum devices that integrate about hundreds of physical qubits are likely to be developed in the near future. However, such devices will lack the resources for realizing quantum fault tolerance. Therefore, the main challenge…
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
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 investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes, including additive and nonadditive codes, based on the codeword stabilized framework on subsystems. The codeword stabilized…
We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact…
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by…
A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information.…
We present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors, by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit…
Quantum error correcting codes are designed to pinpoint exactly when and where errors occur in quantum circuits. This feature is the foundation of their primary task: to support fault-tolerant quantum computation. However, this feature…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…
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…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…