Demonstrating a Quantum Permutation Algorithm with Higher Qubit Near-term Intermediate Scale Quantum Processors

The Quantum Permutation Algorithm (QPA) determines the parity of a cyclic permutation in a single measurement. The original quantum permutation algorithm uses a quantum Fourier transform and its inverse to compute probabilities. This operator seems central to many quantum algorithms; however, Yalcinkaya and Gedik (2017) have shown that substituting simpler transforms for the quantum Fourier transform and its inverse can improve QPA performance. In this presentation, we consider the implementation of this modified QPA algorithm using NISQ machines and measure the impact of the quantum volume on our implementation. We construct circuits using qiskit and implement them on IBM's qasm simulator and a series of NISQ hardware with various qubit orderings. In particular, using both 5- and 7-qubit machines, we implement 2, 3, 4, and 5-qubit permutation circuits and execute each circuit 8192 times to collect statistics. We find that the optimized QPA shows improved performance over previous studies for 3-qubit circuits and higher. Further, we explicitly determine the required quantum volume to realize the QPA effectively for higher dimensional systems.