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We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
Quantum computers have the possibility of a much reduced calculation load compared with classical computers in specific problems. Quantum error correction (QEC) is vital for handling qubits, which are vulnerable to external noise. In QEC,…
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…
Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding…
Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal…
We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…
Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the…
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error…
Noise robustness remains a critical challenge for deploying neural speech codecs in real-world acoustic scenarios where background noise is often inevitable. A key observation we make is that even slight input noise perturbations can cause…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can…
Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and…
Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are…
Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence…
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…
Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements, while maintaining low circuit depth, to minimizing the circuit…
The presence of noise in quantum computers hinders their effective operation. Even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. Testing and benchmarking noisy,…
In this paper we do a detailed numerical investigation of the fault-tolerant threshold for optical cluster-state quantum computation. Our noise model allows both photon loss and depolarizing noise, as a general proxy for all types of local…
The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical postprocessing. Therefore, it is desirable to measure only the information that is relevant for…