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Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for…
The concept of the smoothing parameter plays a crucial role in both lattice-based and code-based cryptography, primarily due to its effectiveness in achieving nearly uniform distributions through the addition of noise. Recent research by…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…
We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements and three auxiliary qubits per plaquette. This realization gains substantial…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
In this paper we do a detailed numerical investigation of the fault-tolerant threshold for optical cluster-state quantum computation. Our noise model allows both photon loss and depolarizing noise, as a general proxy for all types of local…
Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
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…
Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of…
Quantum computers have the potential to change the way we solve computational problems. Due to the noisy nature of qubits, the need arises to correct physical errors occurring during computation. The surface code is a promising candidate…
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…
Accurate noise estimation is essential for fault-tolerant quantum computing, as decoding performance depends critically on the fidelity of the circuit-level noise parameters. In this work, we introduce a differentiable Maximum Likelihood…
We propose a new decoder for "matchable'' qLDPC codes that uses a Markov Chain Monte Carlo algorithm - called the worm algorithm - to approximately compute the probabilities of logical error classes given a syndrome. The algorithm hence…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We study a comprehensive list of quantum codes as candidates of codes to be used at the bottom, physical, level in a fault-tolerant code architecture. Using the Aliferis-Gottesman-Preskill (AGP) ex-Rec method we calculate the…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our…