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The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
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…
The toric code is a canonical example of a topological error-correcting code. Two logical qubits stored within the toric code are robust against local decoherence, ensuring that these qubits can be faithfully retrieved as long as the error…
Steane code is one of the most widely studied quantum error-correction codes, which is a natural choice for fault-tolerant quantum computation (FTQC). However, the original Steane code is not fault-tolerant because the CNOT gates in an…
With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have…
Entangled quantum probes can achieve Heisenberg-limited measurement precision, but this advantage is typically destroyed by noise. We address this issue by introducing a framework that we call encoded quantum signal processing, which…
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely…
A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical…
The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware. In this work, we identify a new type of structured noise motivated by neutral atom qubits,…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the…
We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…
We propose a simplified version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ. The new code belongs to the class of subsystem stabilizer codes. It…
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…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
We present a unified one-shot coding framework designed for the communication and compression of messages among multiple nodes across a general acyclic noisy network. Our setting can be seen as a one-shot version of the acyclic discrete…
The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack…