Related papers: Quantum Codes from Twisted Unitary $t$-groups
Error operator bases for systems of any dimension are defined and natural generalizations of the bit/sign flip error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
Quantum information platforms made great progress in the control of many-body entanglement and the implementation of quantum error correction, but it remains a challenge to realize both in the same setup. Here, we propose a mixture of two…
We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…
Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem…
We show how to construct a large class of quantum error correcting codes, known as CSS codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger…
Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise…
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…
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…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
The realistic coherent errors could induce very different behaviors compared with their stochastic counterparts in the quantum error correction (QEC) and fault tolerant quantum computation. Their impacts are believed to be very subtle, more…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on…
The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network. The tensors correspond to tetrahedra in a triangulation of the manifold, with values determined by a fixed spherical category. For…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit…