Demonstrating a Quantum Permutation Algorithm with Higher Qubit (up to 16-qubit) Near-term Intermediate Scale Quantum Processors

Quantum computation is an emerging field that harnesses quantum mechanical phenomena through the manipulation of qubits. The way in which a qubit is manipulated is by quantum algorithms or step-by-step commands to change the state of the qubit and gives probabilities of a particular problem's outcome. One example of a quantum algorithm for a such system is the quantum permutation algorithm which determines the parity of a given cyclic permutation in a single measurement. Previously shown by Yalcinkaya and Gedik (2017) this algorithm can be optimized by minimizing the number of required quantum gates by replacing the quantum Fourier transform (QFT) and its inverse with simpler transformations. We are interested in expanding this to higher qubit numbers using cloud accessed near-term intermediate scale quantum processors through the IBM Quantum Experience. The goal of this work is to implement a modified quantum permutation algorithm using 16 qubits using Qiskit, IBM's qasm simulator and NISQ hardware with various qubit mappings. We found that increasing the qubit number shows improvement over previous studies utilizing QFTs. In the future, we plan to look at ways of applying pulse level control to this algorithm to further show quantum advantage using available NISQ hardware.