Control Methods Gain Stability Against Hardware Errors with New Optimisation Technique

Quantum optimal control seeks to design control pulses resilient to unavoidable hardware imperfections and modelling errors. Andrew T. Kamen from the Pritzker School of Molecular Engineering at the University of Chicago, Samuel Fine from the Department of Computer Science at the same institution, and Bikrant Bhattacharyya from the California Institute of Technology, working with Frederic T. Chong from the Department of Computer Science at the University of Chicago and Andy J. Goldschmidt from the Johns Hopkins Applied Physics Laboratory, present a systematic comparison of common robustness metrics. Their research highlights numerical discrepancies between established methods, adjoint end-point and toggling-frame approaches, for approximating first-order susceptibility. Significantly, the team introduces a crucial discretization to the toggling-frame estimator, demonstrably enhancing its accuracy, and uniquely frames robustness as a primary objective within a constrained optimal control scheme. This novel approach allows for the simultaneous optimisation of control, fidelity, and robustness, offering a pathway to more precise and physically informed control pulse design for both single- and two-qubit systems. Scientists are developing more resilient quantum controls to combat hardware imperfections, as quantum gates are sensitive to errors from hardware drift and miscalibration. Researchers treat robustness as a primary objective within the quantum control design process, optimising control pulses to minimise susceptibility to errors and shield quantum information from environmental noise. A key innovation involves a systematic comparison of adjoint end-point and toggling-frame approaches for quantifying error susceptibility, revealing previously unrecognised numerical discrepancies between them. Demonstrations using single- and two-qubit examples under realistic hardware constraints showcase the analytic advantages of this new methodology. By positioning robustness as a first-class objective within direct, constrained optimal control, the team created a framework capable of balancing performance, complexity, and hardware limitations. A framework of direct, constrained trajectory optimisation underpins this work, allowing systematic investigation of robust quantum control design. Direct optimisation efficiently accommodates nonlinear constraints on states and controls, crucial for managing fidelity thresholds and control bandwidth limitations in real-world quantum systems. Although theoretically equivalent, the study reveals numerical differences between adjoint end-point and toggling-frame approaches, highlighting the need for careful technique selection. Initial analysis revealed significant discrepancies between the two numerical approximations for first-order susceptibility, demonstrating that the toggling-frame estimator contains discretization error. Specifically, the toggling metric exhibited quantization error, minimising the inaccurate metric instead of the actual susceptibility, while the adjoint objective closely followed the upsampled objective when Q exceeded 0.01. Correcting this discretization error through a perturbative expansion, increasing the order parameter ‘j’ caused the toggling objective to converge towards the accurate, upsampled integral, with higher orders proving necessary for larger time steps. Optimisation of an iSWAP gate, exp[iπ/4 (X1X2 + Y1Y2)], under realistic constraints yielded notable results when fidelity was constrained to 0.9999. Figure 6 illustrates this, showing the universal objective failed to achieve comparable robustness, while Figure 7 details the susceptibility of each error operator, revealing significant improvements with the adjoint method for the dominant error mechanisms. Simulations involving single- and two-qubit gates demonstrate the benefits of physics-informed robust controls over universally-robust solutions, quantifying the advantage of tailoring control designs to specific hardware characteristics. Scientists building quantum computers perpetually battle imprecision, as even tiny variations in hardware can rapidly degrade performance. Correcting this error allows for a more accurate prediction of a control pulse’s robustness, providing researchers with a more reliable tool for quantum control. By framing robustness as an integral part of the optimisation process, the team has created a more powerful and versatile framework, building a foundation for scalable quantum systems where maintaining fidelity in the face of noise is paramount. While computationally intensive and scaling to larger numbers of qubits will present challenges, this work represents a crucial step towards bridging the gap between theoretical quantum control and the reality of building practical quantum machines. 👉 More information 🗞 Comparing and correcting robustness metrics for quantum optimal control 🧠 ArXiv: https://arxiv.org/abs/2602.10349 Tags: Rohail T. As a quantum scientist exploring the frontiers of physics and technology. My work focuses on uncovering how quantum mechanics, computing, and emerging technologies are transforming our understanding of reality. I share research-driven insights that make complex ideas in quantum science clear, engaging, and relevant to the modern world. 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