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Collective coherent noise poses challenges for fault-tolerant quantum error correction (FTQEC), as it falls outside the usual stochastic noise models. While constant excitation (CE) codes can naturally avoid coherent noise, a complete…
Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…
We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
Due to the low error tolerance of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing. Surface code (SC) associated with its decoding algorithm is one of the most promising quantum error…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient…
Spin qubits in quantum dots provide a promising platform for realizing large-scale quantum processors since they have a small characteristic size of a few tens of nanometers. One difficulty of controlling e.g., a few thousand qubits on a…
Quantum compilation is the problem of translating an input quantum circuit into the most efficient equivalent of itself, taking into account the characteristics of the device that will execute the computation. Compilation strategies are…
The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are…
Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane $[\![7,1,3]\!]$ code provide elegant theoretical…
Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…
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…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivity, and coherence times, a quantum circuit optimization is essential to make the best use of near-term quantum devices. We…
Current quantum processors are fragile, noisy and fairly limited in both quantity and quality with tens of qubits and physical error rates of around 10^-3. To realize practical quantum applications, however, error rates need to be below…
Fault-tolerance is the future of quantum computing, ensuring error-corrected quantum computation that can be used for practical applications. Resource requirements for fault-tolerant quantum computing (FTQC) are daunting, and hence,…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Real-time decoding of quantum error correction (QEC) is essential for enabling fault-tolerant quantum computation. A practical decoder must operate with high accuracy at low latency, while remaining robust to spatial and temporal variations…
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…