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DOI: 10.4230/LIPIcs.TQC.2013.294
Optimal Quantum Circuits for Nearest-Neighbor Architectures

Authors: David J. Rosenbaum

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

Abstract
We show that the depth of quantum circuits in the realistic architecture where a classical controller determines which local interactions to apply on the kD grid Z^k where k >= 2 is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed. This allows minimum-depth circuits (up to a constant factor) for the nearest-neighbor architecture to be obtained from minimum-depth circuits in the standard abstract model. Our work therefore justifies the standard assumption that interactions can be performed between arbitrary pairs of qubits. In particular, our results imply that Shor's algorithm, controlled operations and fanouts can be implemented in constant depth, polynomial size and polynomial width in this architecture. We also present optimal non-adaptive quantum circuits for controlled operations and fanouts on a kD grid. These circuits have depth Theta(sqrt[k](n)), size Theta(n) and width Theta(n). Our lower bound also applies to a more general class of operations.
Cite as

David J. Rosenbaum. Optimal Quantum Circuits for Nearest-Neighbor Architectures. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 294-307, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{rosenbaum:LIPIcs.TQC.2013.294,
  author =	{Rosenbaum, David J.},
  title =	{{Optimal Quantum Circuits for Nearest-Neighbor Architectures}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{294--307},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.294},
  URN =		{urn:nbn:de:0030-drops-43290},
  doi =		{10.4230/LIPIcs.TQC.2013.294},
  annote =	{Keywords: 2D, Nearest Neighbor, Quantum Architecture, Quantum Complexity, Quantum Computation}
}
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