Towards Practical Fault-Tolerant Quantum Computing

Quantum computers hold the promise of solving classically intractable problems. However, quantum systems are intrinsically faulty due to the environment-induced noise and decoher- ence. As such, fault-tolerant quantum computers, which can run a quantum computation successfully even if the physical operations are faulty, are needed for solving utility-scale problems. Building such a fault-tolerant quantum computer requires a fault-tolerant scheme, which replaces target quantum circuits with new circuits that involve extra qubits and more gates but are robust against all physical faults with the help of quantum error correction. The state-of-the-art fault-tolerant scheme, which we refer to as the baseline scheme, encodes qubits into planar surface-code patches and performs encoded logical operations via code deformations and lattice surgeries. However, its large space-time overhead, which requires millions of physical qubits and takes days for large computations, poses a formidable chal- lenge for scaling quantum computing to practical levels. In this thesis, we introduce new fault-tolerant schemes by leveraging new hardware and coding features not previously con- sidered by the baseline scheme. Specifically, we present new schemes for bosonic systems that feature an infinite-dimensional Hilbert space, design noise-tailored topological codes, and in- vestigate low-overhead schemes on hardware with long-range connectivity using the recently developed quantum low-density-parity-check codes. Our results demonstrate that by incor- porating these hardware-specific schemes and employing improved quantum codes, we can drastically reduce the overhead barrier towards practical fault-tolerant quantum computing.