  There is no unique way to encode a quantum algorithm into a quantum circuit.
With limited qubit counts, connectivities, and coherence times, circuit
optimization is essential to make the best use of near-term quantum devices. We
introduce two separate ideas for circuit optimization and combine them in a
multi-tiered quantum circuit optimization protocol called AQCEL. The first
ingredient is a technique to recognize repeated patterns of quantum gates,
opening up the possibility of future hardware co-optimization. The second
ingredient is an approach to reduce circuit complexity by identifying zero- or
low-amplitude computational basis states and redundant gates. As a
demonstration, AQCEL is deployed on an iterative and efficient quantum
algorithm designed to model final state radiation in high energy physics. For
this algorithm, our optimization scheme brings a significant reduction in the
gate count without losing any accuracy compared to the original circuit.
Additionally, we have investigated whether this can be demonstrated on a
quantum computer using polynomial resources. Our technique is generic and can
be useful for a wide variety of quantum algorithms.
