  Digital-analog quantum computing (DAQC) offers a promising approach to
addressing the challenges of building a practical quantum computer. By
efficiently allocating resources between digital and analog quantum circuits,
DAQC paves the way for achieving optimal performance. We propose an algorithm
designed to enhance the performance of quantum annealing. This method employs a
quantum gate to estimate the goodness of the final annealing state and find the
ground state of combinatorial optimization problems. We explore two strategies
for integrating the quantum annealing circuit into the DAQC framework: (1) for
state preparation, and (2) for embedding within the quantum gate. While the
former strategy does not yield performance improvements, we discover that the
latter enhances performance within a specific range of annealing time.
Algorithms demonstrating enhanced performance utilize the imaginary part of the
inner product of two states from different quantum annealing settings. This
measure reflects not only the energy of the classical cost function but also
the trajectory of the quantum dynamics. This study provides an example of how
processing quantum data using a quantum circuit can outperform classical data
processing, which discards quantum information.
