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Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Quantum Error Correction Codes (QECCs) are pivotal in advancing quantum computing by protecting quantum states against the adverse effects of noise and errors. With a variety of QECCs developed, including new developments and modifications…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
Quantum circuit testing is essential for detecting potential faults in realistic quantum devices, while the testing process itself also suffers from the inexactness and unreliability of quantum operations. This paper alleviates the issue by…
Quantum Error Correction (QEC) is one of the fundamental problems in quantum computer systems, which aims to detect and correct errors in the data qubits within quantum computers. Due to the presence of unreliable data qubits in existing…
We define QSE, a symbolic execution framework for quantum programs by integrating symbolic variables into quantum states and the outcomes of quantum measurements. The soundness of QSE is established through a theorem that ensures the…
Quantum error correction (QEC) is one of the crucial building blocks for developing quantum computers that have significant potential for reaching a quantum advantage in applications. Prominent candidates for QEC are stabilizer codes for…
Future quantum architectures are expected to be modular, with quantum processors connecting multiple quantum processing units (QPUs) via photonic interconnects. In topological quantum error correction, such as color codes, this creates seam…
Quantum Error Correction (QEC) decoding faces a fundamental accuracy-efficiency tradeoff. Classical methods like Minimum Weight Perfect Matching (MWPM) exhibit variable performance across noise models and suffer from polynomial complexity,…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
One of the most promising paths towards large scale fault tolerant quantum computation is the use of quantum error correcting stabilizer codes. Just like every other quantum circuit, these codes must be compiled to hardware in a way to…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…
Quantum computing is an emerging field recognized for the significant speedup it offers over classical computing through quantum algorithms. However, designing and implementing quantum algorithms pose challenges due to the complex nature of…
A central ingredient in fault-tolerant quantum algorithms is the initialization of a logical state for a given quantum error-correcting code from a set of noisy qubits. A scheme that has demonstrated promising results for small code…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
Quantum error correcting codes are designed to pinpoint exactly when and where errors occur in quantum circuits. This feature is the foundation of their primary task: to support fault-tolerant quantum computation. However, this feature…