Related papers: Quantum Codes from Toric Surfaces
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…
Toric codes are error-correcting codes that are derived from toric varieties, which hold a unique correspondence to integral convex polytopes. In this paper, we focus on integral convex polytopes $P \subseteq \mathbb{R}^2$ and the toric…
In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. These systems can be realized in large-scale quantum networks or condensed onto a single chip with closely situated nodes.…
The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the…
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
Fault-tolerant quantum computation using quantum error-correcting codes requires fault-tolerant constructions of nontransversal gates. Shor proposed a fault-tolerant construction of a nontransversal gate, i.e., the Toffoli gate for a family…
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 states can quickly decohere through interaction with the environment. Quantum error correction is a method for preserving coherence through active feedback. Quantum error correction encodes the quantum information into a logical…
We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a $[\![10,1,2]\!]$ code that is the smallest known stabilizer code…
A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements, while maintaining low circuit depth, to minimizing the circuit…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…
CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank-Shor-Steane quantum code, defined over a q-ary…
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…
We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…
A description of complete normal varieties with lower dimensional torus action has been given by Altmann, Hausen, and Suess, generalizing the theory of toric varieties. Considering the case where the acting torus T has codimension one, we…
Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper,…