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arXiv:1409.8178

Accounting for Classical Hardware in the Control of Quantum Devices

Ian Hincks, Christopher Granade, Troy W. Borneman, David G. Cory

Published Sep 29, 2014• 14 citations
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Abstract

High fidelity coherent control of quantum systems is critical to building quantum devices and quantum computers. We provide a general optimal control framework for designing control sequences that account for hardware control distortions while maintaining robustness to environmental noise. We demonstrate the utility of our algorithm by presenting examples of robust quantum gates optimized in the presence of nonlinear distortions. We show that nonlinear classical controllers do not necessarily incur additional computational cost to pulse optimization, enabling more powerful quantum devices.

DOI
10.48550/arxiv.1409.8178

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High fidelity coherent control of quantum systems is critical to building quantum devices and quantum computers. We provide a general optimal control framework for designing control sequences that account for hardware control distortions while maintaining robustness to environmental noise. We demonstrate the utility of our algorithm by presenting examples of robust quantum gates optimized in the presence of nonlinear distortions. We show that nonlinear classical controllers do not necessarily incur additional computational cost to pulse optimization, enabling more powerful quantum devices.
High-quality control is a fundamental requirement for quantum computation, but practically it is often hampered by the presence of various types of noises, which can be static or time dependent. In many realistic scenarios, multiple noise sources coexist, and their resulting noise effects need to be corrected to a sufficient order, posing significant challenges for the design of effective robust control methods. Here, we explore the method of robust quantum optimal control to generally tackle the problem of resisting multiple noises from a complicated noise environment. Specifically, we confine our analysis to classical stochastic noises that can be described by classical noise models. This method employs a gradient-based multiobjective optimization algorithm to maximize the control figure of merit, and meanwhile to minimize the perturbative effects of the noises that are allowed for. To verify its effectiveness, we apply this method to a number of examples, including robust entangling gate in a trapped-ion system and robust controlled-ZZZ gate in superconducting qubits, under commonly encountered static and time-dependent noises. Our simulation results reveal that robust optimal control can find smooth, robust pulses that can simultaneously resist several noises and thus achieve high-fidelity gates. Therefore, we expect that this method will find wide applications on current noisy quantum computing devices.
The ability to engineer high-fidelity gates on quantum processors in the presence of systematic errors remains the primary barrier to achieving quantum advantage. Quantum optimal control methods have proven effective in experimentally realizing high-fidelity gates, but they require exquisite calibration to be performant. We apply robust trajectory optimization techniques to suppress gate errors arising from system parameter uncertainty. We propose a derivative-based approach that maintains computational efficiency by using forward-mode differentiation. Additionally, the effect of depolarization on a gate is typically modeled by integrating the Lindblad master equation, which is computationally expensive. We employ a computationally efficient model and utilize time-optimal control to achieve high-fidelity gates in the presence of depolarization. We apply these techniques to a fluxonium qubit and suppress simulated gate errors due to parameter uncertainty below ${10}^{\ensuremath{-}7}$ for static parameter deviations of the order of 1%.
Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
The effective use of current Noisy Intermediate-Scale Quantum (NISQ) devices is often limited by the noise which is caused by interaction with the environment and affects the fidelity of quantum gates. In transmon qubit systems, the quantum gate fidelity can be improved by applying control pulses that can minimize the effects of the environmental noise. In this work, we employ physics-guided quantum optimal control strategies to design optimal pulses driving quantum gates on superconducting qubit systems. We test our results by conducting experiments on the IBM quantum hardware using their OpenPulse API. We compare the performance of our pulse-optimized quantum gates against the default quantum gates and show that the optimized pulses improve the fidelity of the quantum gates, in particular the single-qubit gates. We discuss the challenges we encountered in our work and point to possible future improvements.
Autocorrelated noise appears in many solid-state qubit systems and hence needs to be taken into account when developing gate operations for quantum information processing. However, explicitly simulating this kind of noise is often less efficient than approximate methods. Here, we focus on the filter function formalism, which allows the computation of gate fidelities in the presence of autocorrelated classical noise. Hence, this formalism can be combined with optimal control algorithms to design control pulses, which optimally implement quantum gates. To enable the use of gradient-based algorithms with fast convergence, we present analytically derived filter function gradients with respect to control pulse amplitudes, and analyze the computational complexity of our results. When comparing pulse optimization using our derivatives to a gradient-free approach, we find that the gradient-based method is roughly 2 orders of magnitude faster for our test cases. We also provide a modular computational implementation compatible with quantum optimal control packages.