Related papers: Belief propagation as a partial decoder
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
Real-time decoding is a key ingredient in future fault-tolerant quantum systems, yet many decoders are too slow to run in real time. Prior work has shown that parallel window decoding schemes can scalably meet throughput requirements in the…
We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random $k$-XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a…
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major…
In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the…
Quantum error correction is necessary to protect logical quantum states and operations. However, no meaningful data protection can be made when the syndrome extraction is erroneous due to faulty measurement gates. Quantum data-syndrome (DS)…
The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a…
In decoding linear block codes, it was shown that noticeable reliability gains can be achieved by introducing learnable parameters to the Belief Propagation (BP) decoder. Despite the success of these methods, there are two key open…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
The behavior of real quantum hardware differs strongly from the simple error models typically used when simulating quantum error correction. Error processes are far more complex than simple depolarizing noise applied to single gates, and…
We present an efficient quantum algorithm for a structured state discrimination problem we call the subspace decoding task. Building on this, we show that the algorithm enables efficient and optimal decoding of certain families of…
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
In this paper, we propose a novel message-passing decoding approach that leverages the degeneracy of quantum low-density parity-check codes to enhance decoding performance, eliminating the need for serial scheduling or post-processing. Our…
Finite alphabet iterative decoders (FAID) with multilevel messages that can surpass BP in the error floor region for LDPC codes on the BSC were previously proposed. In this paper, we propose decimation-enhanced decoders. The technique of…
Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
Fast quantum data transmission faces several shortcomings such as the indistinguishability of some partly overlapping signals, the channel noises, and so on. Based on the encoded quantum data transmission protocol, an unconventional scheme…