Related papers: Homological Quantum Error Correction with Torsion
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
We expand the class of holographic quantum error correcting codes by developing the notion of block perfect tensors, a wider class that includes previously defined perfect tensors. The relaxation of this constraint opens up a range of other…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Calderbank-Shor-Steane (CSS) quantum error-correcting codes are based on pairs of classical codes which are mutually dual containing. Explicit constructions of such codes for large blocklengths and with good error correcting properties are…
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and…
We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. The generalization yields new classes of quantum error correcting codes that have no finite-dimensional counterparts. The error correction…
Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
A major goal for fault-tolerant quantum computation (FTQC) is to reduce the overhead needed for error correction. One approach is to use block codes that encode multiple qubits, which can achieve significantly higher rates for the same code…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
The integration of quantum error correction codes and homomorphic encryption schemes is essential for achieving fault-tolerant secure cloud quantum computing. However, owing to the significant overheads associated with these schemes, their…
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…
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…
Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of…
Previous works (by Almiehri, Dong, Harlow, Pastakawski, Preskill, Yoshida and others) have established that quantum error correction plays an important role in understanding how the bulk degrees of freedom of an Anti-deSitter spacetime are…
This is the chapter \emph{Topological Codes} of the book \emph{Quantum Error Correction}, edited by Daniel A. Lidar and Todd A. Brun, Cambridge University Press, New York, 2013.…