On April 17, Shraddha Singh succcessfully defended the thesis, “Quantum Computing in Discrete- and Continuous-Variable Architectures” (advisors: Steven Girvin and Shruti Puri).
Singh’s dissertation sits firmly within the topic of quantum error correction — the ability to ensure fidelity in calculations when dealing with highly finnicky quantum data. Many proposed quantum computing systems rely upon bits of quantum information called qubits, which are prone to error; Singh’s work combines the utility of qubits with the stability and power of oscillators, towards the goal of building quantum computers resilient to errors.
Singh explained, “My thesis is an early step in the process to see if we can harness a hybrid approach to quantum systems,” Singh said, adding that she is proud her work will be part of an outreach efforts such as QWAY.”
Singh contined, ““I like to think about the possible applications for the work we do in quantum research. It motivates us to do our best to build these new machines.”
She has joined IBM in Yorktown Heights, NY, as a research scientist. Her job will be focused on building the theory of quantum error correction for superconducting circuits (the platform for quantum computing explored by IBM).
Thesis Abstract: 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.