Related papers: Degenerate Viterbi decoding
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
Syndrome decoding is an integral but computationally demanding step in the implementation of quantum error correction for fault-tolerant quantum computing. Here, we report the development and benchmarking of Artificial Neural Network (ANN)…
Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
In this paper, we propose a Riemannian steepest descent method for solving a blind deconvolution problem. We prove that the proposed algorithm with an appropriate initialization will recover the exact solution with high probability when the…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
In this paper, we analyze the quantum counting under the decoherence, which can find the number of solutions satisfying a given oracle. We investigate probability distributions related to the first order term of the error rate on the…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
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…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
We introduce a sliding window decoder based on belief propagation (BP) with guided decimation for the purposes of decoding quantum low-density parity-check codes in the presence of circuit-level noise. Windowed decoding keeps the decoding…
We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model.
The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…
Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…