Optimization and experimental realization of the quantum permutation algorithm

Abstract

The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales quadratically with $n$ due to the quantum Fourier transforms included. We show here for the $n$-qubit case that the algorithm can be simplified so that it requires only $O(n)$ quantum gates, which theoretically reduces the complexity of the implementation. In order to test our results experimentally, we utilize IBM's $5$-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the $2$-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the $3$-qubit case with a considerable success probability by taking the advantage of our simplified scheme.

9 pages, 8 figures, Sec. 3B revised

References in corpus (18)

• Quantum Mechanics helps in searching for a needle in a haystack
• Charge insensitive qubit design derived from the Cooper pair box
• Building logical qubits in a superconducting quantum computing system
• A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
• Quantum Data Fitting
• Experimental Comparison of Two Quantum Computing Architectures
• Demonstration of weight-four parity measurements in the surface code architecture
• Performing Quantum Computing Experiments in the Cloud
• Experimental test of Mermin inequalities on a 5-qubit quantum computer
• Computational speed-up in a single qudit NMR quantum information processor
• Computational speed-up with a single qudit
• Entropic uncertainty and measurement reversibility
• Quantum phase space measurement and entanglement validation made easy
• Experimental realization of nondestructive discrimination of Bell states using a five-qubit quantum computer
• Leggett-Garg test of superconducting qubit addressing the clumsiness loophole
• Determining the parity of a permutation using an experimental NMR qutrit
• Linear optical demonstration of quantum speed-up with a single qudit
• Demonstration of quantum permutation algorithm with a single photon ququart

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