With the advent of quantum annealers, many quantum computing algorithms are being developed. Solving linear systems is one of the important problems in science and engineering. Recently, a quadratic unconstrained binary optimization (QUBO) model that can implement a linear system in a quantum annealing device has been developed. The developed QUBO model has the advantage in that it can be used for the gate model by using the quantum approximate optimization algorithm. To verify the optimal QUBO model for a linear system, we derive several QUBO models with constrained coefficients for the linear system including the constrained method. We compare and discuss the results for each QUBO model on the D-Wave system.
Growing interest in quantum machine learning has resulted into very innovative algorithms and vigorous studies that demonstrate their power. These studies, although very useful, are often designed for fault-tolerant quantum computers that are far from reality of today's noise-prone quantum computers. While companies such as IBM have ushered in a new era of quantum computing by allowing public access to their quantum computers, quantum noise as well as decoherence are daunting obstacles that not only degrade the performance of quantum algorithms, but also make them infeasible for running on current-era quantum processors. We address the feasibility of a quantum machine learning algorithm on IBM quantum processors to shed light on their efficacy and weaknesses to design noise-aware algorithms that work around these limitations. We compare and discuss the results by implementing a quantum convolutional filter on a real quantum processor as well as a simulator.
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