Reducing the Depth of Quantum Circuits Using Additional Circuit Lines

The synthesis of Boolean functions, as they are found in many quantum algorithms, is usually conducted in two steps. First, the function is realized in terms of a reversible circuit followed by a mapping into a corresponding quantum realization. During this process, the number of lines and the quantum costs of the resulting circuits have mainly been considered as optimization objectives thus far. However, beyond that also the depth of a quantum circuit is vital. Although first synthesis approaches that consider depth have recently been introduced, the majority of design methods did not consider this metric.

In this paper, we introduce an optimization approach aiming for the reduction of depth in the process of mapping a reversible circuit into a quantum circuit. For this purpose, we present an improved (local) mapping of single gates as well as a (global) optimization scheme considering the whole circuit. In both cases, we incorporate the idea of exploiting additional circuit lines which are used in order to split a chain of serial gates. Our optimization techniques enable a concurrent application of gates which significantly reduces the depth of the circuit. Experiments show that reductions of approx. 40% on average can be achieved when following this scheme.