Quantum Circuit Un-optimization as a Benchmark Task for Quantum Compilers

Compilation of large complex quantum circuits into simpler ones is an essential task to fully exploit the power of quantum computers. In this work, we consider an opposite task: "quantum circuit un-optimization (QCU)", which makes a circuit more redundant while preserving its functionality. With QCU, we can systematically generate many kinds of benchmark datasets for optimization. These un-optimized circuits can be useful for evaluating the performance of quantum compilers. We try a method of QCU, where we insert redundant identity gates each consisting of a unitary and its adjoint and swap them around the circuit. We examine how many depths the optimization module such as Qiskit and TKET can reduce from the un-optimized quantum circuits. We expect that QCU enables us to compare the performance of different quantum compilers and to improve them. Also, we can use QCU for defining a machine learning task whose aim is to classify quantum states generated by two classes of circuits, each of which is derived by applying QCU procedures to two distinct original circuits. This task is easy with quantum computers since we can just run the circuits and compute the inner products of the states, but it is not so easy on classical computers.