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Linear nearest neighbor optimization in quantum circuits: a multiobjective perspective

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Abstract

Several current implementations of quantum circuits rely on the linear nearest neighbor restriction, which only allows interaction between adjacent qubits. Most methods that address the process of converting a generic circuit to an equivalent circuit which satisfies this restriction, minimize the number of additional SWAP gates required by this process. Moreover, most methods which address this problem are designed for 1D circuits. Considering the new and promising proposals for 2D quantum circuits, what we propose is a new perspective on this problem, namely that it can be seen as a multiobjective optimization problem. To test our hypothesis, we developed a multiobjective evolutionary algorithm that solves this problem by considering two objectives: minimizing the size of the 2D grid where the circuit is placed, and minimizing the number of additional SWAP gates. Of the methods designed for 2D circuits, only one considers different grid sizes which are much larger than strictly necessary. Consequently, our algorithm makes considerations which other methods do not make, since it naturally finds the grid which requires fewer SWAP gates for the circuit conversion, whether it is one-dimensional or two-dimensional. Our experimental results indicate that allowing a larger grid size results in fewer additional SWAP gates in about 73% of the tested circuits. Additionally, the average improvement we found when using larger grid sizes is about 30%, while the best improvement over using the smallest possible grid is 63.8%.

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Acknowledgements

Special thanks to the Nara Institute of Science and Technology (NIST), specifically to Yasuhiko Nakashima, Hiroyuki Seki, Masaki Nakanishi, Shigueru Yamashita and Yuishi Hirata for motivating this work.

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Authors and Affiliations

  1. Catholic University of Asunción, Asunción, Paraguay

    Daniel Ruffinelli & Benjamín Barán

  2. National University of Asunción (UNA), San Lorenzo, Paraguay

    Benjamín Barán

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  1. Daniel Ruffinelli
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  2. Benjamín Barán
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Correspondence to Daniel Ruffinelli.

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Ruffinelli, D., Barán, B. Linear nearest neighbor optimization in quantum circuits: a multiobjective perspective. Quantum Inf Process 16, 220 (2017). https://doi.org/10.1007/s11128-017-1662-3

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