Related papers: Spacetime Spins: Statistical mechanics for error c…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
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.
A quantum error correcting code protects encoded logical information against errors. Transversal gates are a naturally fault-tolerant way to manipulate logical qubits but cannot be universal themselves. Protocols such as magic state…
Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$…
By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. Furthermore, we introduce a new class of codes which we have called weak…
We study measurement-induced symmetry-protected topological (SPT) order in a wide class of quantum random circuit models by combining calculations within the stabilizer formalism with tensor network simulations. We construct a family of…
Stabilizer-based simulation of quantum error-correcting codes typically relies on the Pauli-twirling approximation (PTA) to render non-Clifford noise classically tractable, but PTA can distort the behavior of physically relevant channels…
Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one…
We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
Measurements can detect errors in a decohered quantum memory allowing active error correction to increase the memory time. Previous understanding of this mechanism has focused on evaluating the performance of error correction algorithms…
An important measure of utility for a quantum code is the identification of which logical operations can be implemented fault-tolerantly on its codespace. We introduce a framework which leverages the automorphism groups of associated…
Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms. We improve on this method by studying stabiliser decompositions of ZX…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
We introduce a framework called spacetime concatenation for fault-tolerant compilation of syndrome extraction circuits of stabilizer codes. Spacetime concatenation enables efficient compilation of syndrome extraction circuits into dynamical…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…