Related papers: Color code off-the-hook: avoiding hook errors with…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent…
Future quantum architectures are expected to be modular, with quantum processors connecting multiple quantum processing units (QPUs) via photonic interconnects. In topological quantum error correction, such as color codes, this creates seam…
Modular quantum computing architectures require error correction schemes that remain effective in the presence of noisy inter-processor operations. As such, minimizing the number of such operations on logical circuits partitioned across…
Surface codes based on stabilizer circuits may pave the way for large scale fault-tolerant quantum computation. The surface code uses only single- and two-qubit gates and the error threshold falls close to 1% for a large range of errors.…
Stabilizer channels are stabilizer circuits that implement logical operations while mapping from an input stabilizer code to an output stabilizer code. They are widely used to implement fault tolerant error correction and logical operations…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables…
Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some…
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric $n$-vertices colourable graph and a group of operations (colouring rules) on the graph: find the minimum sequence…
We propose modifying topological quantum error correcting codes by incorporating space-time defects, termed ``time vortices,'' to reduce the number of physical qubits required to achieve a desired logical error rate. A time vortex is…
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
Quantum error correcting code can diagnose potential errors and correct them based on measured outcomes by leveraging syndrome measurement. However, mid-circuit measurement has been technically challenging for early fault-tolerant quantum…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…
We improve the planar honeycomb code by describing boundaries that need no additional physical connectivity, and by optimizing the shape of the qubit patch. We then benchmark the code using Monte Carlo sampling to estimate logical error…
We consider distance colourings in graphs of maximum degree at most $d$ and how excluding one fixed cycle length $\ell$ affects the number of colours required as $d\to\infty$. For vertex-colouring and $t\ge 1$, if any two distinct vertices…
Probabilistic error cancellation (PEC) is unbiased but suffers exponential sampling overhead set by noise-weighted circuit volume, whereas quantum error-detecting codes (QEDCs) remove many physical faults by stabilizer post-selection but…