The optimization of robust quantum control is often tailored to specific tasks and suffers from inefficiencies due to the complexity of cost functions. Our recent findings indicate a highly effective methodology for the engineering of quantum gates by initiating the process with a robust control configuration of any arbitrary gate. We first introduce the Quantum Control Robustness Landscape (QCRL), a conceptual framework that maps control parameters to noise susceptibility. This framework facilitates a systematic investigation of equally robust controls for diverse quantum operations. By navigating through the level sets of the QCRL, our Robustness-Invariant Pulse Variation (RIPV) algorithm allows for the variation of control pulses while preserving robustness. Numerical simulations demonstrate that our single- and two-qubit gates exceed the quantum error correction threshold even with substantial noise. This methodology opens up a new paradigm for quantum gate engineering capable of effectively suppressing generic noise.
The optimization of robust quantum control is often tailored to specific tasks and suffers from inefficiencies due to the complexity of cost functions. Our recent findings indicate a highly effective methodology for the engineering of quantum gates by initiating the process with a robust control configuration of any arbitrary gate. We first introduce the Quantum Control Robustness Landscape (QCRL), a conceptual framework that maps control parameters to noise susceptibility. This framework facilitates a systematic investigation of equally robust controls for diverse quantum operations. By navigating through the level sets of the QCRL, our Robustness-Invariant Pulse Variation (RIPV) algorithm allows for the variation of control pulses while preserving robustness. Numerical simulations demonstrate that our single- and two-qubit gates exceed the quantum error correction threshold even with substantial noise. This methodology opens up a new paradigm for quantum gate engineering capable of effectively suppressing generic noise.
Robust quantum control is critical for developing quantum technologies, especially within the noisy intermediatescale quantum (NISQ) era. We introduce the Quantum Control Robustness Landscape (QCRL), a novel framework that maps control parameters to their robustness against noise. This framework offers an efficient mechanism for identifying resilient control solutions. In contrast to the traditional Quantum Control Landscape, which concentrates on optimizing fidelity for specific quantum gates, the QCRL provides a comprehensive perspective on gate engineering by facilitating the navigation of level sets. This capability enables the identification of equally robust control solutions for a universal family of quantum gates, thereby streamlining the process of achieving resilient quantum operations. By exploring these level sets, QCRL serves as a potent tool for both comprehending control schemes and optimizing robust quantum gates with continuous parameters.
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.
The performance of quantum processors in the noisy intermediate-scale quantum (NISQ) era is severely constrained by environmental noise and other uncertainties. While the recently proposed quantum control robustness landscape (QCRL) offers a powerful framework for generating robust control pulses for parametric gate families, its application has been practically restricted to quasi-static noise. To address the spectrally complex, time-varying noise prevalent in reality, we propose filter function-enhanced QCRL (FF-QCRL), which integrates filter function formalism into the QCRL framework. The resulting FF-QCRL algorithm minimizes a generalized robustness metric that faithfully encodes the impact of stochastic processes, enabling robust pulse-family generation for parametric gates under realistic time-varying noise. Numerical validation in a representative single-qubit setting confirms the effectiveness of the proposed method.
Reliable quantum information technologies depend on precise actuation and techniques to mitigate the effects of un-desired disturbances such as environmental noise and imperfect calibration. In this work, we present a general framework based in geometric optimal control theory to synthesize smooth control pulses for implementing arbitrary noise-robust quantum gates. The methodology applies to generic unitary quantum dynamics with any number of qubits or energy levels, any number of control fields, and any number of disturbances, extending existing dynamical decoupling approaches that are only applicable for limited gate sets or small systems affected by one or two disturbances. The noise-suppressing controls are computed via indirect trajectory optimization based on Pontryagin's maximum principle, eliminating the need to make heuristic structural assumptions on parameterized pulse envelopes.
This work develops measures for quantifying the effects of field noise upon targeted unitary transformations. Robustness to noise is assessed in the framework of the quantum control landscape, which is the mapping from the control to the unitary transformation performance measure (quantum gate fidelity). Within that framework, a geometric interpretation of stochastic noise effects naturally arises, where more robust optimal controls are associated with regions of small overlap between landscape curvature and the noise correlation function. Numerical simulations of this overlap in the context of quantum information processing reveal distinct noise spectral regimes that better support robust control solutions. This perspective shows the dual importance of both noise statistics and the control form for robustness, thereby opening up new avenues of investigation on how to mitigate noise effects in quantum systems.
Dynamically corrected gates were recently introduced [K. Khodjasteh and L. Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence and pure dephasing on qubits. The effectiveness of dynamically corrected gates in an illustrative non-Markovian spin-bath setting is investigated numerically, confirming the expected fidelity performance in a wide parameter range. Robustness against a class of systematic control errors is automatically incorporated in the perturbative error regime.