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Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
To make practical quantum algorithms work, large-scale quantum processors protected by error-correcting codes are required to resist noise and ensure reliable computational outcomes. However, a major challenge arises from defects in…
We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of…
Quantum computation must be performed in a fault-tolerant manner to be realizable in practice. Recent progress has uncovered quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead. Existing schemes…
Existing real-time decoders for surface codes are limited to isolated logical qubits and do not support logical operations involving multiple logical qubits. We present DECONET, a first-of-its-kind decoding system that scales to thousands…
Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…
A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome…
With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical error in plausible hardware implementations of quantum error-correcting codes (QECC). In this work, we consider logical error rates…
A key challenge in fault-tolerant quantum computing is synthesising and optimising circuits in a noisy environment, as traditional techniques often fail to account for the effect of noise on circuits. In this work, we propose and…
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…
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
Hook errors are a major challenge in implementing logical operations with the surface code, because they can reduce the fault distance below the code distance. This motivates syndrome-extraction circuits that suppress hook-error effects for…
In the rotated surface code, hook errors (errors on auxiliary qubits midway through syndrome extraction that propagate to correlated two-qubit data errors) can reduce the circuit-level code distance by a factor of two if the extraction…
Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We…
With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an…
Quantum LDPC codes may provide a path to build low-overhead fault-tolerant quantum computers. However, as general LDPC codes lack geometric constraints, na\"ive layouts couple many distant qubits with crossing connections which could be…
In this paper, we introduce the gauge-fixed QLDPC surgery scheme, an improved logical measurement scheme based on the construction of Cohen et al. (Sci. Adv. 8, eabn1717). Our scheme leverages expansion properties of the Tanner graph to…
We present a set of efficiently implementable logical multi-qubit gates in concatenated quantum error correction codes using parity qubits. In particular, we show how fault-tolerant high-weight rotation gates of arbitrary angle can be…
The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled…