Robust control of quantum processors using space curves

Abstract

Quantum computers can significantly speed up the solution of certain classical tasks and even provide solutions to problems that are classically intractable. However, achieving this requires a fault-tolerant architecture with components and quantum operations (gates) whose physical error rates are below a specific threshold. Advanced quantum control methods can suppress environmental noise and implement below-threshold gates, but there are infinitely many ways to do so. These methods can rely entirely on analytical solutions or combine them with numerical optimization, where pulse properties are treated as optimization goals. Analytical constraints are always met exactly, but numerically optimized goals may only be satisfied approximately, leading to tradeoffs. Therefore, a modular analytical framework is needed that fixes some objectives in advance while optimizing only a selected subset. In this dissertation, I employ Space Curve Quantum Control (SCQC), a method that generates noise-resistant quantum gates using differential geometry. In SCQC, a space curve's global geometric properties dictate the gate's noise-robustness, while the controls that realize it are extracted from its local quantities. The first part of the dissertation is devoted to extending SCQC for arbitrary and simultaneous noise suppression, with experimentally-friendly pulses. I first derive the geometric conditions and curve examples for suppressing two separate noise types simultaneously. Then, I extend SCQC by deriving the adjoint representation equations of the associated quantum evolution. This allows one to describe the entire control design in terms of space curve elements and propose a systematic control design approach called the Bézier Ansatz for Robust Quantum (BARQ) control method. BARQ can encode the target gate upfront and allow optimization only for noise-robustness properties. This approach solves the usually unavoidable tradeoff between gate fidelity and noise-sensitivity and is capable of producing control pulses with experimentally-friendly features. The second part of the dissertation applies BARQ in two leading qubit modalities. I first describe my participation in experiments on IBM's superconducting devices, where doubly-robust BARQ pulses demonstrate at least one order-of-magnitude error reduction in the presence of engineered noise. The second platform is a four-qubit trapped-ion register hosted in the Quantum Scientific Computing Open User Testbed (QSCOUT) ecosystem. I show that utilizing BARQ pulses can reduce gate errors up to two times and effectively combat motion-induced decoherence.