Hybrid quantum classical optimization using near-term quantum technology is an emerging direction for exploring quantum advantage in high-dimensional systems. However, precise characterization of all experimental parameters is often impractical and challenging. A viable approach is to use algorithms that rely entirely on black-box inference rather than analytical gradients. Here, we combine randomized perturbation gradient estimation with adaptive momentum gradient updates and propose AdamSPSA and AdamRSGF algorithms. We prove the asymptotic convergence of the proposed algorithms in a convex setting and benchmark them against other gradient-based black-box optimization algorithms on nonconvex quantum optimal control tasks. Our results indicate that these algorithms accelerate the optimization rate, lower the optimization loss, and efficiently tune up high-fidelity Hann-window single-qubit gates from trivial initial conditions with up to 80 variables for a transmon qubit.
Hybrid quantum classical optimization using near-term quantum technology is an emerging direction for exploring quantum advantage in high-dimensional systems. However, precise characterization of all experimental parameters is often impractical and challenging. A viable approach is to use algorithms that rely entirely on black-box inference rather than analytical gradients. Here, we combine randomized perturbation gradient estimation with adaptive momentum gradient updates and propose AdamSPSA and AdamRSGF algorithms. We prove the asymptotic convergence of the proposed algorithms in a convex setting and benchmark them against other gradient-based black-box optimization algorithms on nonconvex quantum optimal control tasks. Our results indicate that these algorithms accelerate the optimization rate, lower the optimization loss, and efficiently tune up high-fidelity Hann-window single-qubit gates from trivial initial conditions with up to 80 variables for a transmon qubit.
Hybrid quantum-classical optimization using near-term quantum technology is an emerging direction for exploring quantum advantage in high-dimensional systems. However, precise characterization of all experimental parameters is often impractical and challenging. A viable approach is to use algorithms that rely only on black-box inference rather than analytical gradients. Here, we combine randomized perturbation gradient estimation with adaptive momentum gradient updates to create the AdamSPSA and AdamRSGF algorithms. We prove the asymptotic convergence of our algorithms in a convex setting, and we benchmark them against other gradient-based optimization algorithms on non-convex optimal control tasks. Our results show that these new algorithms accelerate the convergence rate, decrease the variance of loss trajectories, and efficiently tune up high-fidelity (above 99.9\%) Hann-window single-qubit gates from trivial initial conditions with twenty variables.
The efficient implementation of quantum computing is contingent upon high-fidelity quantum operations. Nevertheless, the fidelity of these operations is constrained by the precision of quantum system evolution control. The optimization of quantum control pulses is essential for improving the manipulation accuracy of superconducting qubits. Traditional optimization methods, including gradient descent and the gradient ascent pulse engineering algorithm, frequently encounter challenges such as slow convergence and susceptibility to local optima in pulse optimization problems. This study introduces an adaptive open-loop optimization algorithm based on the adaptive moment estimation (Adam) optimizer, capitalizing on the benefits of momentum and adaptive learning rate adjustments inherent in Adam. We conduct experimental analysis on the algorithm’s hyperparameters to achieve optimal solutions with a higher fidelity range at a faster convergence speed, effectively improving the fidelity and optimization efficiency of quantum gate operations. Through numerical simulations on the QuTiP platform, we validate the excellent performance of the Adam algorithm in quantum gate optimization. In optimizing the X and SWAP gates, its fidelity improved by 0.03% and 0.0016%, respectively, compared to the GRAPE algorithm. Compared to the CRAB method, the initial convergence speed of the Adam method increased fivefold, enabling it to achieve the target fidelity more rapidly. Future research will investigate closed-loop optimization strategies, utilizing feedback derived from the fidelity results of actual quantum computers to further augment quantum control performance
Optimal quantum control theory carries a huge promise for quantum technology. Its experimental application, however, is often hindered by imprecise knowledge of the input variables, the quantum system's parameters. We show how to overcome this by adaptive hybrid optimal control, using a protocol named Ad-HOC. This protocol combines open- and closed-loop optimal control by first performing a gradient search towards a near-optimal control pulse and then an experimental fidelity estimation with a gradient-free method. For typical settings in solid-state quantum information processing, adaptive hybrid optimal control enhances gate fidelities by an order of magnitude, making optimal control theory applicable and useful.
Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.
Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore the consequences of the prior observation that estimation of these quantities on quantum hardware results in a form of s t o c h a s t i c gradient descent optimization. We formalize this notion, which allows us to show that in many relevant cases, including VQE, QAOA and certain quantum classifiers, estimating expectation values with k measurement outcomes results in optimization algorithms whose convergence properties can be rigorously well understood, for any value of k . In fact, even using single measurement outcomes for the estimation of expectation values is sufficient. Moreover, in many settings the required gradients can be expressed as linear combinations of expectation values -- originating, e.g., from a sum over local terms of a Hamiltonian, a parameter shift rule, or a sum over data-set instances -- and we show that in these cases k -shot expectation value estimation can be combined with sampling over terms of the linear combination, to obtain ``doubly stochastic'' gradient descent optimizers. For all algorithms we prove convergence guarantees, providing a framework for the derivation of rigorous optimization results in the context of near-term quantum devices. Additionally, we explore numerically these methods on benchmark VQE, QAOA and quantum-enhanced machine learning tasks and show that treating the stochastic settings as hyper-parameters allows for state-of-the-art results with significantly fewer circuit executions and measurements.