Linear and Logarithmic Time Compositions of Quantum Many-Body Operators

F. Motzoi, M. P. Kaicher, and F. K. Wilhelm
Phys. Rev. Lett. 119, 160503 – Published 18 October 2017
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Abstract

We develop a generalized framework for constructing many-body-interaction operations either in linear time or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given for Pauli strings, many-control Toffoli gates, number- and parity-conserving interactions, unitary coupled cluster operations, and sparse matrix generators. We provide a linear time protocol that works by creating a superposition of exponentially many different possible operator strings and then uses dynamical decoupling methodology to undo all the unwanted terms. A logarithmic time protocol overcomes the speed limit of the first by using ancilla registers to condition evolution to the support of the desired many-body interaction before using parallel chaining operations to expand the string length. The two techniques improve substantially on current strategies (reductions in time and space ranging from linear to exponential), are applicable to different physical interaction mechanisms such as cnot, XX, and XX+YY, and generalize to a wide range of many-body operators.

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  • Received 1 May 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.160503

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

F. Motzoi1, M. P. Kaicher2, and F. K. Wilhelm2

  • 1Department of Physics and Astronomy, Aarhus University, 8000 Aarhus, Denmark
  • 2Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany

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Issue

Vol. 119, Iss. 16 — 20 October 2017

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