Related papers: Optimal Circuit-Level Decoding for Surface Codes
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study…
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…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
The overheads of classical decoding for quantum error correction on superconducting quantum systems grow rapidly with the number of logical qubits and their correction code distance. Decoding at room temperature is bottle-necked by…
We study exact decoding for the toric code and for planar and rotated surface codes under the standard independent \(X/Z\) noise model, focusing on Separate Minimum Weight (SMW) decoding and Separate Most Likely Coset (SMLC) decoding. For…
Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
The surface code, with a simple modification, exhibits ultra-high error correction thresholds when the noise is biased towards dephasing. Here, we identify features of the surface code responsible for these ultra-high thresholds. We provide…
Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the…
Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the…
Quantum error correction (QEC) is essential for fault-tolerant quantum computation. Often in QEC errors are assumed to be independent and identically distributed and can be discretised to a random Pauli error during the execution of a…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing…
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…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
We study the performance of distance-three surface code layouts under realistic multi-parameter noise models. We first calculate their thresholds under depolarizing noise. We then compare a Pauli-twirl approximation of amplitude and phase…
Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of…