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A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses…
There is a bijection between odd prime dimensional qudit pure stabilizer states modulo invertible scalars and affine Lagrangian subspaces of finite dimensional symplectic $\mathbb{F}_p$-vector spaces. In the language of the stabilizer…
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
Qubit loss is a major source of error in quantum computation, as it invalidates the algebraic structure of the standard stabilizer formalism for quantum error-correcting codes. On the one hand, it complicates decoding; on the other hand, it…
The dynamical-algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
In quantum information and computation research, symbolic methods have been widely used for human specification and reasoning about quantum states and operations. At the same time, they are essential for ensuring the scalability and…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous…