Noise Robustness of Quantum Relaxation for Combinatorial Optimization
Relaxation is a common way for dealing with combinatorial optimization problems.
On the Logical Error Rate of Sparse Quantum Codes
The quantum paradigm presents a phenomenon known as degeneracy that can potentially improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse quantum codes and the logical error rate is not always correctly reported. In this article, we discuss previously existing methods […]
Neural-Network Decoders for Quantum Error Correction Using Surface Codes: A Space Exploration of the Hardware Cost-Performance Tradeoffs
Quantum error correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the classical electronic back-end. Decoders employing neural networks (NN) are well-suited for this task but their hardware implementation has […]
Log-Domain Decoding of Quantum LDPC Codes Over Binary Finite Fields
A quantum stabilizer code over GF(q) corresponds to a classical additive code over GF(q2) that is self-orthogonal with respect to a symplectic inner product. We study the decoding of quantum low-density parity-check (LDPC) codes over binary finite fields GF(q = 2l) by the sum-product algorithm, also known as belief propagation (BP). Conventionally, a message in a nonbinary BP for quantum codes […]
Decoding Quantum Error Correction Codes With Local Variation
In this article, we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local information is taken into account during the decoding process: the code distance associated with a given logical […]