Efficient Quantum Circuit Design with a Standard Cell Approach

We propose a new method for designing quantum circuits which utilizes standard cells similar to those found in classical circuit design. This method can be used prior to deciding to compile to either NISQ or lattice surgery circuits to obtain good resource estimates for a final compiled circuit. Our method relies on the regular structure found in many quantum circuits, and allows for estimation of the resources necessary for the circuit without using complex compilation methods. We demonstrate the effectiveness of our method by first designing standard cells for two Toffoli gate decompositions then using these standard cells to route a quantum multiplier on a 3D architecture with nearest neighbor connectivity. When comparing the SWAP depth and SWAP count of the final circuit with an equivalent circuit routed using automated routing tools available in cirq, we find that our method results in a shallower SWAP-depth (by at least 2.5x) and uses fewer SWAP gates.