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The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
Designs and methods for nested lattice codes using Construction D' lattices for coding and convolutional code lattices for shaping are described. Two encoding methods and a decoding algorithm for Construction D' coding lattices that can be…
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…
Modern platforms for potential qubit candidates, such as trapped ions or neutral atoms, allow long range connectivity between distant physical qubits through shuttling. This opens up an avenue for transversal logical CNOT gates between…
The work identifies the first lattice decoding solution that achieves, in the general outage-limited MIMO setting and in the high-rate and high-SNR limit, both a vanishing gap to the error-performance of the (DMT optimal) exact solution of…
In this paper, we propose a novel three-time-slot transmission scheme combined with an efficient embedded linear channel equalization (ELCE) technique for the Physical layer Network Coding (PNC). Our transmission scheme, we achieve about…
Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer…
We introduce a framework which allows to systematically and arbitrarily scale the code distance of local fermion-to-qubit encodings in one and two dimensions without growing the weights of stabilizers. This is achieved by embedding…
Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computations if the error rate is below a threshold value.…
A powerful feature of stabiliser error correcting codes is the fact that stabiliser measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code…
We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting…
Quantum error correction (QEC) plays a crucial role in correcting noise and paving the way for fault-tolerant quantum computing. This field has seen significant advancements, with new quantum error correction codes emerging regularly to…
The surface code is one of the most popular quantum error correction codes. It comes with efficient decoders, such as the Minimum Weight Perfect Matching (MWPM) decoder and the Union-Find (UF) decoder, allowing for fast quantum error…
High-resolution 3D medical image generation remains challenging because fully volumetric models are computationally expensive, while efficient 2D slice generators often fail to preserve anatomical consistency across the third dimension. We…
Layered manufacturing inherently suffers from staircase defects along surfaces that are gently slopped with respect to the build direction. Reducing the slice thickness improves the situation but never resolves it completely as flat layers…
We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical $T$ gate or a logical non-Pauli measurement that prepares a magic $|T\rangle$ state. The…
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…
Recent literature including our past work provide analysis and solutions for using (i) erasure coding, (ii) parallelism, or (iii) variable slicing/chunking (i.e., dividing an object of a specific size into a variable number of smaller…
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…
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…