Quantum Computing in Discrete- and Continuous-Variable Architectures
This defense presents a theoretical framework for hybrid discrete-variable (DV) and continuous-variable (CV) quantum systems, focusing on quantum control, state preparation, and error correction. Hybrid CV-DV architectures leverage the stability of oscillators and the fast gate speeds of qubits, offering a promising path for scalable quantum computation. A key contribution of this work is non-abelian quantum signal processing (NA-QSP), a generalization of QSP where control parameters are non-commuting operators, such as position and momentum. We introduce Gaussian-Controlled-Rotation (GCR), the first non-abelian composite pulse sequence, enabling precise CV control via DV ancillae with improved gate fidelity and robustness. With the help of GCR, we address high-fidelity, deterministic state preparation of squeezed, cat, and Gottesman-Kitaev-Preskill (GKP) states, bypassing the need for numerical optimizers. Further, we explore high-fidelity universal control of error-corrected qubits encoded in oscillators, including logical readout and pieceable gate teleportation. Our results demonstrate that logical operations on GKP qubits can achieve high fidelity using GCR, even in the presence of certain ancillary errors. Extending GCR to multi-mode systems enables efficient entangling gates and error-corrected two-qubit rotations, with broader applicability to qudits and arbitrary qubit lattices. This work establishes NA-QSP as a foundation for hybrid CV-DV quantum control, state preparation, and GKP-based error correction, paving the way for scalable fault-tolerant quantum computing.
Thesis Committee: Steven Girvin (advisor), Shruti Puri, Michel Devoret, Robert Schoelkopf, and Liang Jiang (external)