Related papers: Non-local resources for error correction in quantu…
Error correcting codes use multi-qubit measurements to realize fault-tolerant quantum logic steps. In fact, the resources needed to scale-up fault-tolerant quantum computing hardware are largely set by this task. Tailoring next-generation…
Achieving high image quality is an important aspect in an increasing number of wireless multimedia applications. These applications require resource efficient error correction hardware to detect and correct errors introduced by the…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
Quantum low-density parity-check (QLDPC) codes are a leading approach to quantum error correction, yet conventional belief propagation (BP) decoders often perform poorly, primarily due to non-convergence exacerbated by stabilizer…
We propose and analyze a novel scheme based on LDPC codes for quantitative group testing. The key underlying idea is to augment the bipartite graph by introducing hidden non-binary variables to strengthen the message-passing decoder. This…
Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are…
We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
An information reconciliation method for continuous-variable quantum key distribution with Gaussian modulation that is based on non-binary low-density parity-check (LDPC) codes is presented. Sets of regular and irregular LDPC codes with…
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…
In this paper, we report an encoding and decoding method for irregular-quasic-cyclic low-density parity-check (IR-QC-LDPC) codes with multi rates. The algorithm is applicable to parity-check matrices which have dual-diagonal parity…
We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes, which is compatible with quantum computers with only nearest-neighbor interactions. The…
Quantum low-density parity check (QLDPC) codes can significantly reduce the overhead of quantum computing, provided the methods for performing logical operations do not require substantial space and time resources. A popular method for…
Quantum low-density parity-check codes are a promising approach to fault-tolerant quantum computation, offering potential advantages in rate and decoding efficiency. In this work, we introduce quantum Margulis codes, a new class of QLDPC…
Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…
Quantum low-density parity-check (QLDPC) codes offer a promising route to scalable fault-tolerant quantum computation, but their performance under iterative decoding is strongly influenced by short-cycle structure and other harmful…
Forward error correcting (FEC) codes are used in many communication standards with a wide range of re quirements. FEC codes should work close to capacity, achieve low error floors, and have low decoding complexity. In this paper, we propose…
Quantum low density parity check (QLDPC) codes are useful primitives for quantum information processing because they can be encoded and decoded efficiently. Besides, the error correcting capability of a few QLDPC codes exceeds the quantum…