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The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
The XZZX code is a variant of the surface code tailored to address biased noise in realistic quantum devices. We propose a simulated annealing (SA) decoder for the XZZX code. Our SA decoder is amenable to parallelization because its MCMC…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
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.…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
Measurement-based quantum computing is an alternative paradigm to the circuit-based model. This approach can be advantageous in certain scenarios, such as when read-out is fast and accurate, but two-qubit gates realized via inter-particle…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
One hurdle to performing reliable quantum computations is overcoming noise. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers.…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
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…
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore…
We develop error-tolerant quantum state discrimination(QSD) strategies that maintain reliable performance under moderate noise. Two complementary approaches are proposed: CrossQSD, which generalizes unambiguous discrimination with tunable…
We investigate the fidelity of the measurement-based quantum computation (MBQC) when it is coupled with boson environment, by measuring cluster state fidelity and gate fidelity. Two different schemes of cluster state preparation are…
Magic state distillation is a resource intensive subroutine that consumes noisy input states to produce high-fidelity resource states that are used to perform logical operations in practical quantum-computing architectures. The resource…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
Self-correcting quantum memories demonstrate robust properties that can be exploited to improve active quantum error-correction protocols. Here we propose a cellular automaton decoder for a variation of the color code where the bases of the…