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  • Letter
  • Open Access

Implementing a fast unbounded quantum fanout gate using power-law interactions

Andrew Y. Guo1,2,*, Abhinav Deshpande1,2, Su-Kuan Chu1,2, Zachary Eldredge1,2, Przemyslaw Bienias1,2, Dhruv Devulapalli1,2, Yuan Su1,3,4, Andrew M. Childs1,3,4, and Alexey V. Gorshkov1,2

  • 1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 2Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 3Department of Computer Science, University of Maryland, College Park, Maryland 20742, USA
  • 4Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742, USA

  • *guoa@umd.edu
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Phys. Rev. Research 4, L042016 – Published 27 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042016

Abstract

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm to be performed on a D-dimensional lattice of qubits in time that scales (poly)logarithmically in the number of qubits, using interactions with α≤2D. As a corollary, we show that power-law systems with α≤2D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a technique to give a general lower bound—linear in the size of the system—on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than was possible with previously available techniques.

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Phys. Rev. Research 4, L042016– Published 27 October, 2022
  • Received 12 June 2022
  • Accepted 12 October 2022
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