Browsing by Author "Lomonaco, Samuel J."
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Item Analyzing the Quantum Annealing Approach for Solving Linear Least Squares Problems(2018-09-27) Borle, Ajinkya; Lomonaco, Samuel J.With the advent of quantum computers, researchers are exploring if quantum mechanics can be leveraged to solve important problems in ways that may provide advantages not possible with conventional or classical methods. A previous work by O'Malley and Vesselinov in 2016 briefly explored using a quantum annealing machine for solving linear least squares problems for real numbers. They suggested that it is best suited for binary and sparse versions of the problem. In our work, we propose a more compact way to represent variables using two's and one's complement on a quantum annealer. We then do an in-depth theoretical analysis of this approach, showing the conditions for which this method may be able to outperform the traditional classical methods for solving general linear least squares problems. Finally, based on our analysis and observations, we discuss potentially promising areas of further research where quantum annealing can be especially beneficial.Item Quantum Approximate Optimization for Hard Problems in Linear AlgebraBorle, Ajinkya; Elfving, Vincent E.; Lomonaco, Samuel J.The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for Binary Linear Least Squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on the QISKIT simulator and an IBM Q 5 qubit machine. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our simulations show that Simulated Annealing can outperform QAOA for BLLS at a circuit depth of p≤3 for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on a cloud-based quantum computer