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Digital-analog quantum computing (DAQC) offers a promising approach toaddressing the challenges of building a practical quantum computer. Byefficiently allocating resources between digital and analog quantum circuits,DAQC paves the way for achieving optimal performance. We propose an algorithmdesigned to enhance the performance of quantum annealing. This method employs aquantum gate to estimate the goodness of the final annealing state and find theground state of combinatorial optimization problems. We explore two strategiesfor integrating the quantum annealing circuit into the DAQC framework: (1) forstate preparation, and (2) for embedding within the quantum gate. While theformer strategy does not yield performance improvements, we discover that thelatter enhances performance within a specific range of annealing time.Algorithms demonstrating enhanced performance utilize the imaginary part of theinner product of two states from different quantum annealing settings. Thismeasure reflects not only the energy of the classical cost function but alsothe trajectory of the quantum dynamics. This study provides an example of howprocessing quantum data using a quantum circuit can outperform classical dataprocessing, which discards quantum information.

Enhancing Quantum Annealing in Digital-Analog Quantum Computing