  There is no unique way to encode a quantum algorithm into a quantum circuit.
With limited qubit counts, connectivity, and coherence times, a quantum circuit
optimization is essential to make the best use of near-term quantum devices. We
introduce a new circuit optimizer called AQCEL, which aims to remove redundant
controlled operations from controlled gates, depending on initial states of the
circuit. Especially, the AQCEL can remove unnecessary qubit controls from
multi-controlled gates in polynomial computational resources, even when all the
relevant qubits are entangled, by identifying zero-amplitude computational
basis states using a quantum computer. As a benchmark, the AQCEL is deployed on
a quantum algorithm designed to model final state radiation in high energy
physics. For this benchmark, we have demonstrated that the AQCEL-optimized
circuit can produce equivalent final states with much smaller number of gates.
Moreover, when deploying AQCEL with a noisy intermediate scale quantum
computer, it efficiently produces a quantum circuit that approximates the
original circuit with high fidelity by truncating low-amplitude computational
basis states below certain thresholds. Our technique is useful for a wide
variety of quantum algorithms, opening up new possibilities to further simplify
quantum circuits to be more effective for real devices.
