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Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
We construct a new family of permutationally invariant codes that correct $t$ Pauli errors for any $t\ge 1$. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
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…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin codes that correspond to permutation-invariant multiqubit…
The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer.…
Quantum convolutional coding is a technique for encoding a stream of quantum information before transmitting it over a noisy quantum channel. Two important goals in the design of quantum convolutional encoders are to minimize the memory…
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…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
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…
We present a quantum error correcting code that is invariant under the conditional time evolution between spontaneous emissions and which can correct for one general error. The code presented here generalizes previous error correction codes…
We develop an intrinsic enumerator framework for quantum error correction in unitary representations of symmetry groups. An intrinsic quantum code is a subspace of a representation $V$ of a group $G$, and errors are organized by the…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
Recently, there has been increasing interest in designing schemes for quantum computations that are robust against errors. Although considerable research has been devoted to developing quantum error correction schemes, much less attention…
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…