Control synthesis for continuously-parameterized families of quantum gates can enable critical advantages for mid-sized quantum computing applications in advance of fault-tolerance. We combine quantum optimal control with physics-informed machine learning to efficiently synthesize control surfaces that interpolate among continuously-parameterized gate families. Using optimal control as an active learning strategy to guide pretraining, we bootstrap a physics-informed neural network to achieve rapid convergence to nonlinear control surfaces sufficient for our desired gates. We find our approach is critical for enabling an expressiveness beyond linear interpolation, which is important in cases of hard quantum control. We show in simulation that by adapting our pretraining to use a few reference pulse calibrations, we can apply transfer learning to quickly calibrate our learned control surfaces when devices fluctuate over time. We demonstrate synthesis for one and two qubit gates with one or two parameters, focusing on gate families for variational quantum algorithm (VQA) ansatz. By avoiding the inefficient decomposition of VQA ansatz into basis gate sets, continuous gate families are a potential method to improve the noise robustness of VQAs in the near term. Our framework shows how accessible optimal control tools can be combined with simple machine learning to enable practitioners to achieve 3x speedups for their algorithms by going beyond the standard gate sets.
Control synthesis for continuously-parameterized families of quantum gates can enable critical advantages for mid-sized quantum computing applications in advance of fault-tolerance. We combine quantum optimal control with physics-informed machine learning to efficiently synthesize control surfaces that interpolate among continuously-parameterized gate families. Using optimal control as an active learning strategy to guide pretraining, we bootstrap a physics-informed neural network to achieve rapid convergence to nonlinear control surfaces sufficient for our desired gates. We find our approach is critical for enabling an expressiveness beyond linear interpolation, which is important in cases of hard quantum control. We show in simulation that by adapting our pretraining to use a few reference pulse calibrations, we can apply transfer learning to quickly calibrate our learned control surfaces when devices fluctuate over time. We demonstrate synthesis for one and two qubit gates with one or two parameters, focusing on gate families for variational quantum algorithm (VQA) ansatz. By avoiding the inefficient decomposition of VQA ansatz into basis gate sets, continuous gate families are a potential method to improve the noise robustness of VQAs in the near term. Our framework shows how accessible optimal control tools can be combined with simple machine learning to enable practitioners to achieve 3x speedups for their algorithms by going beyond the standard gate sets.
Control synthesis for continuously-parameterized families of quantum gates can enable critical advantages for mid-sized quantum computing applications in advance of fault-tolerance. We combine quantum optimal control with physics-informed machine learning to efficiently synthesize control surfaces that interpolate among continuously-parameterized gate families. Using optimal control as an active learning strategy to guide pretraining, we bootstrap a physics-informed neural network to achieve rapid convergence to nonlinear control surfaces sufficient for our desired gates. We find our approach is critical for enabling an expressiveness beyond linear interpolation, which is important in cases of hard quantum control. We show in simulation that by adapting our pretraining to use a few reference pulse calibrations, we can apply transfer learning to quickly calibrate our learned control surfaces when devices fluctuate over time. We demonstrate synthesis for one and two qubit gates with one or two parameters, focusing on gate families for variational quantum algorithm (VQA) ansatz. By avoiding the inefficient decomposition of VQA ansatz into basis gate sets, continuous gate families are a potential method to improve the noise robustness of VQAs in the near term. Our framework shows how accessible optimal control tools can be combined with simple machine learning to enable practitioners to achieve 3x speedups for their algorithms by going beyond the standard gate sets.
We present a general method to quickly generate high-fidelity control pulses for any continuously-parameterized set of quantum gates after calibrating a small number of reference pulses. We find that interpolating between optimized control pulses for different quantum operations does not immediately yield a high-fidelity intermediate operation. To solve this problem, we propose a method to optimize control pulses specifically to provide good interpolations. We pick several reference operations in the gate family of interest and optimize pulses that implement these operations, then iteratively re-optimize the pulses to guide their shapes to be similar for operations that are closely related. Once this set of reference pulses is calibrated, we can use a straightforward linear interpolation method to instantly obtain high-fidelity pulses for arbitrary gates in the continuous operation space. We demonstrate this procedure on the three-parameter Cartan decomposition of two-qubit gates to obtain control pulses for any arbitrary two-qubit gate (up to single-qubit operations) with consistently high fidelity. Compared to previous neural network approaches, the method is 7.7x more computationally efficient to calibrate the pulse space for the set of all single-qubit gates. Our technique generalizes to any number of gate parameters and could easily be used with advanced pulse optimization algorithms to allow for better translation from simulation to experiment.
In this work, we first consider standard quantum control problems for superconducting transmon qubits. Such quantum systems have been studied extensively both from an analytical and a numerical perspective [MSG&al11; TMW16]. Analytical pulses usually show dependencies from system parameters that are not easily found in numerical solutions. Therefore, our approach is then to employ neural networks to learn the functional dependence of optimal quantum control solutions from system parameters. We show that we can optimize such solutions analytically for single and two-qubit gates using either very few parameter samples or large numbers of pulse frequencies for large parameter ranges. Afterward, we move to a higher level of optimization. We consider variational gates in trapped-ion quantum computers [MMN&al16]. In this setting, we employ a hybrid scheme that uses both reinforcement learning and continuous optimization to optimize both circuit structure and variational angles concurrently [BDS&al18; SEL&al22]. We show that our reinforcement learning algorithm assisted by a continuous optimizer can construct effective solutions to the gate synthesis problem that matches and surpasses standard circuit compilers. Next, we consider variational optimization of non-linear maps [HCS&al23] acting on quantum states such as entanglement purification protocols. An entanglement purification protocol acts as a highly non-linear map, but it still outputs a faithful representation of a quantum system. Optimizing it for a specific family of states requires reducing the number of operations needed to retrieve the original state. This optimization has the potential to make purification protocols easier to implement on a quantum device. In fact, the exponential scaling of the purification protocol with the number of states [DB07] implies that such protocols may not be applied directly without careful engineering. We also show that the performance of standard purification protocols for arbitrary two-qubit input states leads to poor output values of the concurrence. Our optimized protocols prove instead able to increase the value of the concurrence above the maximum limit of traditional analytical protocols. We also show how the twirling operation becomes an obstacle to the performance of the protocol itself when considering random two-qubit states, although it is a useful tool in the design of entanglement purification protocols. Finally, we study parameter sampling in quantum circuits, focusing in particular on the LCU methods. Such problems are particularly interesting for meta-variational settings [CKA21] where we compute the average over observables evaluated at different points in the parameter space. They are also relevant for optimal quantum control algorithms because the computation of the fidelity with respect to a target operation is the basis of most optimal quantum control routines. In conclusion, we analyze several optimization problems that are relevant for quantum science and technology. We show that machine learning-assisted solutions can be applied successfully to engineer optimal quantum control pulses and compilation strategies based on variational angles. Also in the context of entanglement purification, we show how our optimized protocols can surpass current strategies for multiparametric families of states.
Pulse-level compilation can reduce the depth and calibration overhead associated with decomposing continuously parameterized quantum operations into fixed gate libraries, but conventional optimal control requires a new optimization for each target and can be sensitive to hardware uncertainty. We introduce a physics-informed neural compilation framework that learns a reusable map from continuously parameterized single-qubit gate targets directly to experimentally admissible control waveforms. The compiler is trained end-to-end through differentiable quantum dynamics without precomputed optimal-pulse labels, and its robustness is improved by first diagnosing physically relevant failure modes and then applying tail-risk-aware fine-tuning. On a three-qubit liquid-state nuclear magnetic resonance (NMR) model, the learned compiler generalizes across Haar-distributed single-qubit targets with mean nominal fidelity above 0.99 and generates new pulses in submillisecond inference time. Matched benchmarks reveal complementary advantages: robust gradient ascent pulse engineering (GRAPE) achieves the highest per-target fidelity, whereas the trained neural compiler amortizes the optimization cost across the target family, enabling substantially faster online pulse generation. Risk-aware training substantially broadens tolerance to radio-frequency (RF)-amplitude errors, including perturbations beyond the training range. Experiments on a three-spin NMR processor reproduce the predicted broadening of the RF-tolerance response, although the absolute experimental correlations are lower than the simulated values. These results establish a general workflow combining amortized machine learning, physical sensitivity diagnosis, risk-aware control, optimal-control benchmarking, and hardware testing, providing a route toward fast and robust pulse-level compilation for repeatedly varying quantum operations.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their usefulness in predicting such pulses. Our PINN is a feedforward neural network that utilizes an unsupervised learning approach, whose loss function includes terms that enforce the equations that govern the evolution of a quantum system, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We use a sinusoidal activation function and adopt variance-type weight initialization, tailored to our activation function. By analyzing the model's performance with important machine learning metrics, we demonstrate that the choice of our architecture is well-suited for this type of problem. We ensure that our network avoids the vanishing and exploding gradients with our relevant choices. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness.