Relaxation is a common way for dealing with combinatorial optimization problems. Quantum random-access optimization (QRAO) is a quantum-relaxation-based optimizer that uses fewer qubits than the number of bits in the original problem by encoding multiple variables per qubit using quantum random-access code (QRAC). Reducing the number of qubits will alleviate physical noise (typically, decoherence), and […]
Relaxation is a common way for dealing with combinatorial optimization problems.
To perform reliable information processing in quantum computers, quantum error correction (QEC) codes are essential for the detection and correction of errors in the qubits. Among QEC codes, topological QEC codes are designed to interact between the neighboring qubits, which is a promising property for easing the implementation requirements. In addition, the locality to the […]
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 […]
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 […]
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 […]
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 […]