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The quantum kernel method results clearly outperformed a classical SVM when analyzing low-resolution images with minimal feature selection on the quantum simulator, with inconsistent results when run on an actual quantum processor. We chose to use an existing quantum kernel method for classification. We applied dynamic decoupling error mitigation using the Mitiq package to the Quantum SVM kernel method, which, to our knowledge, has never been done for quantum kernel methods for image classification. We applied the quantum kernel method to classify real world image data from a manufacturing facility using a superconducting quantum computer. The manufacturing images were used to determine if a product was defective or was produced correctly through the manufacturing process. We also tested the Mitiq dynamical decoupling (DD) methodology to understand effectiveness in decreasing noise-related errors. We also found that the way classical data was encoded onto qubits in quantum states affected our results. All three quantum processing unit (QPU) runs of our angle encoded circuit returned different results, with one run having better than classical results, one run having equivalent to classical results, and a run with worse than classical results. The more complex instantaneous quantum polynomial (IQP) encoding approach showed better precision than classical SVM results when run on a QPU but had a worse recall and F1-score. We found that DD error mitigation did not improve the results of IQP encoded circuits runs and did not have an impact on angle encoded circuits runs on the QPU. In summary, we found that the angle encoded circuit performed the best of the quantum kernel encoding methods on real quantum hardware. In future research projects using quantum kernels to classify images, we recommend exploring other error mitigation techniques than Mitiq DD.

A new implementation of an adiabatically-trained ensemble model is derived that shows significant improvements over classical methods. In particular, empirical results of this new algorithm show that it offers not just higher performance, but also more stability with less classifiers, an attribute that is critically important in areas like explainability and speed-of-inference. In all, the empirical analysis displays that the algorithm can provide an increase in performance on unseen data by strengthening stability of the statistical model through further minimizing and balancing variance and bias, while decreasing the time to convergence over its predecessors.

One of the problems frequently mentioned as a candidate for quantum advantage is that of selecting a portfolio of financial assets to maximize returns while minimizing risk. In this paper we formulate several real-world constraints for use in a Quantum Annealer (QA), extending the scenarios in which the algorithm can be implemented. Specifically, we show how to add fundamental analysis to the portfolio optimization problem, adding in asset-specific and global constraints based on chosen balance sheet metrics. We also expand on previous work in improving the constraint to enforce investment bands in sectors and limiting the number of assets to invest in, creating a robust and flexible solution amenable to QA. Importantly, we analyze the current state-of-the-art algorithms for solving such a problem using D-Wave's Quantum Processor and compare the quality of the solutions obtained to commercially-available optimization software. We explore a variety of traditional and new constraints that make the problem computationally harder to solve and show that even with these additional constraints, classical algorithms outperform current hybrid solutions in the static portfolio optimization model.

Amplitude Estimation (AE) is a critical subroutine in many quantum algorithms, allowing for a quadratic speedup in various applications like those involving estimating statistics of various functions as in financial Monte Carlo simulations. Much work has gone into devising methods to efficiently estimate the amplitude of a quantum state without expensive operations like the Quantum Fourier Transform (QFT), which is especially prohibitive given the constraints of current NISQ devices. Newer methods have reduced the number of operations required on a quantum computer and are the most promising near-term implementations of the AE subroutine. While it remains to be seen the exact circuit requirements for a quantum advantage in applications relying on AE, it is necessary to continue to benchmark the algorithm's performance on current quantum computers and the circuit costs associated with such subroutines. Given these considerations, we expand on results from previous experiments in using Maximum Likelihood Estimation (MLE) to approximate the amplitude of a quantum state and provide empirical upper bounds on the current feasible circuit depths for AE on a superconducting quantum computer. Our results show that MLE using optimally-compiled circuits can currently outperform naive sampling for up to 3 Grover Iterations with a circuit depth of 131, which is higher than reported in other experimental results. This functional benchmark is one of many that will be continually monitored against current quantum hardware to measure the necessary progress towards quantum advantage.

Quantum algorithms can be used to perform unsupervised machine learning tasks like data clustering by mapping the distance between data points to a graph optimization problem (i.e. MAXCUT) and finding optimal solution through energy minimization using hybrid quantum classical methods. Taking advantage of the IBM runtime environment, we benchmark the performance of the "Warm-Start" (ws) variant of Quantum Approximate Optimization Algorithm (QAOA) versus the standard implementation of QAOA and the variational quantum eigensolver (VQE) for unstructured clustering problems using real world dataset with respect to accuracy and execution time. Our numerical results show a strong speedup in execution time for different optimization algorithms using the IBM Qiskit Runtime architecture and increased speedup in classification accuracy in ws-QAOA algorithm, Comment: arXiv admin note: substantial text overlap with arXiv:2108.13464

We demonstrate the simulation of a noncollinear molecule, e.g. H2O molecule using Variational Quantum Eigensolver (VQE) with high chemical accuracy. The 2D and 3D potential energy surface (PES) were reported. Taking advantage of the potential speedup in Qiskit runtime program, the optimal initial parameters for the variational quantum circuits were obtained after several consecutive iterations, thus resulting in accurate prediction of water's PES matching result obtained from exact diagonalization of the full Hamiltonian.

Quantum optimization algorithms can be used to recreate unsupervised learning clustering of data by mapping the problem to a graph optimization problem and finding the minimum energy for a MaxCut problem formulation. This research tests the "Warm Start" variant of Quantum Approximate Optimization Algorithm (QAOA) versus the standard implementation of QAOA for unstructured clustering problems. The performance for IBM's new Qiskit Runtime API for speeding up optimization algorithms is also tested in terms of speed up and relative performance compared to the standard implementation of optimization algorithms. Warm-start QAOA performs better than any other optimization algorithm, though standard QAOA runs the fastest. This research also used a non-convex optimizer to relax the quadratic program for the Warm-start QAOA.