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

Quantum computation is an emerging field that harnesses quantum mechanical phenomena through the manipulation of qubits to execute operations. The way in which a qubit is manipulated, using quantum algorithms or step-by-step commands, 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. The original quantum permutation algorithm uses a quantum Fourier transform and its universe to implement the algorithm.  Instead, it has been previously shown by Yalcinkaya and Gedik (2017) this algorithm can be optimized by minimizing the number of required quantum gates when implemented by substituting the quantum Fourier transform (QFT) and its inverse with simpler transformations. We are interested in extending this simpler implementation with higher qubit counts using cloud-accessible near-term mid-scale quantum processors through IBM Quantum Experience.  Using up to 5 qubits, we will construct circuits in Qiskit Qasm simulator and a series of NISQ hardware with various qubit mappings.  For each permutation, we built circuits that achieved 8192 times, while averaging each distribution over 5 samples by the processor, with a runtime of 1 minute or less. We found that with increasing qubit number the optimized QPA shows marked improvement over previous studies utilizing QFTs and further we present the resulting speed and accuracy required to run the algorithm on higher qubits. We hope to investigate ways to apply pulse-level control to this algorithm in the future to further demonstrate the quantum advantage using currently available NISQ hardware.