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Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity…
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…
This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of…
Reconciliation is a crucial procedure in post-processing of Quantum Key Distribution (QKD), which is used for correcting the error bits in sifted key strings. Although most studies about reconciliation of QKD focus on how to improve the…
Due to the high error rate of qubits, detecting and correcting errors is essential for achieving fault-tolerant quantum computing (FTQC). Quantum low-density parity-check (QLDPC) codes are one of the most promising quantum error correction…
In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…
We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…
Quantum error correction is essential for reliable quantum computation, where surface codes demonstrate high fault-tolerant thresholds and hardware efficiency. However, noise in single-shot measurements limits logical readout fidelity,…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…
In universal fault-tolerant quantum computing, implementing logical non-Clifford gates often demands substantial spacetime resources for many error-correcting codes, including the high-threshold surface code. A critical mission for…
Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
To make practical quantum algorithms work, large-scale quantum processors protected by error-correcting codes are required to resist noise and ensure reliable computational outcomes. However, a major challenge arises from defects in…
Fault-tolerant quantum computing will require accurate estimates of the resource overhead, but standard metrics such as gate fidelity and diamond distance have been shown to be poor predictors of logical performance. We present a scalable…
The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates.…
We present an efficient decoding algorithm for constant rate quantum hypergraph-product LDPC codes which provably corrects adversarial errors of weight $\Omega(\sqrt{n})$ for codes of length $n$. The algorithm runs in time linear in the…
A heavy focus for optical quantum computing is the introduction of error-correction, and the minimisation of resource requirements. We detail a complete encoding and manipulation scheme designed for linear optics quantum computing,…
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and…
We investigate iterative low-resolution message-passing algorithms for quasi-cyclic LDPC codes with horizontal and vertical layered schedules. Coarse quantization and layered scheduling are highly relevant for hardware implementations to…