Related papers: Topological error correcting processes from fixed-…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Superconducting qubits, while promising for scalability and long coherence times, contain more than two energy levels, and therefore are susceptible to errors generated by the leakage of population outside of the computational subspace.…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
Motivated by the recent introduction of a $U(1)$-symmetric toric code model, we investigate symmetry-based deformations of topological order by systematically deconstructing the Gauss-law-enforcing star terms of the toric code (TC)…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…
Utility-scale quantum computers require quantum error correcting codes with large numbers of physical qubits to achieve sufficiently low logical error rates. The performance of quantum error correction (QEC) is generally predicted through…
We propose the X$^3$Z$^3$ Floquet code, a dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
We propose a scheme for detecting and correcting faults in any Clifford circuit. The scheme is based on the observation that the set of all possible outcome bit-strings of a Clifford circuit is a linear code, which we call the outcome code.…
Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for…
Decoding stabilizer codes such as the surface and toric codes involves evaluating free-energy differences in a disordered statistical mechanics model, in which the randomness comes from the observed pattern of error syndromes. We study the…
For fault-tolerant quantum memory defined by periodic Pauli measurements, called Floquet codes, we prove that every correctable, undetectable spacetime error occurring during the steady stage is a product of (i) measurement operators…
Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting…
This paper characterizes Goppa codes of certain maximal curves over finite fields defined by equations of the form $y^n = x^m + x$. We investigate Algebraic Geometric and quantum stabilizer codes associated with these maximal curves and…
Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases,…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
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…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…