Efficiently Controllable Graphs
Name
PhysRevLett.118.260501.pdf
Size
117.71 KB
Format
Adobe PDF
Checksum (MD5)
b677339cddf724e44cad69b39d850eeb
Author(s)
Gokler, Can
Thompson, Kevin
Lloyd, Seth
Shor, Peter Williston
Date Issued
June 2017
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Gokler, Can; Lloyd, Seth; Shor, Peter and Thompson, Kevin. "Efficiently Controllable Graphs." Physical Review Letters 118, 260501 (June 2017): 1-5 © 2017 American Physical Society
Version
Final published version
Abstract
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that, when a controllable quantum network is described by such a graph and the gaps in eigenfrequencies and in transition frequencies are bounded exponentially in the number of vertices, the network is efficiently controllable, in the sense that universal quantum computation can be performed using a control sequence polynomial in the size of the network while controlling a vanishingly small fraction of subsystems. We show that networks corresponding to finite-dimensional lattices are efficiently controllable and explore generalizations to percolation clusters and random graphs. We show that the classical computational complexity of estimating the ground state of Hamiltonians described by controllable graphs is polynomial in the number of subsystems or qubits.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevLett.118.260501
