Variational quantum algorithms (VQAs) are the leading algorithm for achieving quantum advantage using near-term quantum computers. VQAs use parameterized quantum circuits for inference, and the variational parameters in quantum circuits can be trained using a classical optimizer. The parameters are trained to guide how the quantum bits evolve and make the final measurements closely match the ground truth. However, this way of learning from raw data makes it difficult to capture the underlying dynamic information in the data, especially for time series data. To address this limitation, we proposed continuous variational quantum algorithms (CVQAs) for time series in this paper. CVQAs use quantum variational circuits to parameterize the dynamics of time series, thus they can learn the dynamic information behind the data. After the dynamics are trained, the prediction results will be obtained by a differential equation solver working on the dynamics. Since we aim to model the dynamics of data instead of the data itself, the quantum circuit in our approach will need fewer qubits and variational gates. To evaluate our proposed approach, we compare our model with baseline models on several weather time series. Experimental results prove that our approach has better or equivalent results but with fewer qubits and variational gates compared to baseline models.
We introduce an approach to improve the accuracy and reduce the sample complexity of near term quantum-classical algorithms. We construct a simpler initial parameterized quantum state, or ansatz, based on the past causal cone of each observable, generally yielding fewer qubits and gates. We implement this protocol on a trapped ion quantum computer and demonstrate improvement in accuracy and time-to-solution at an arbitrary point in the variational search space. We report a
∼27% improvement in the accuracy of the calculation of the deuteron binding energy and
∼40% improvement in the accuracy of the quantum approximate optimization of the MAXCUT problem applied to the dragon graph
T3,2. When the time-to-solution is prioritized over accuracy, the former requires
∼71% fewer measurements and the latter requires
∼78% fewer measurements.
We introduce SantaQlaus, a resource-efficient optimization algorithm tailored for variational quantum algorithms (VQAs), including applications in the variational quantum eigensolver (VQE) and quantum machine learning (QML). Classical optimization strategies for VQAs are often hindered by the complex landscapes of local minima and saddle points. Although some existing quantum-aware optimizers adaptively adjust the number of measurement shots, their primary focus is on maximizing gain per iteration rather than strategically utilizing quantum shot-noise (QSN) to address these challenges. Inspired by the classical Stochastic AnNealing Thermostats with Adaptive momentum (Santa) algorithm, SantaQlaus explicitly leverages inherent QSN for optimization. The algorithm dynamically adjusts the number of quantum measurement shots in an annealing framework: fewer shots are allocated during the early, high-temperature stages for efficient resource utilization and landscape exploration, while more shots are employed later for enhanced precision. Numerical simulations on VQE and QML demonstrate that SantaQlaus outperforms existing optimizers, particularly in mitigating the risks of converging to poor local optima, all while maintaining shot efficiency. This paves the way for efficient and robust training of quantum variational models.