Qudit-Basis Universal Quantum Computation Using X[superscript (2)]
Name
PhysRevLett.120.160502.pdf
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278.29 KB
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Checksum (MD5)
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Author(s)
Niu, Yuezhen
Chuang, Isaac
Shapiro, Jeffrey H
Date Issued
April 2018
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Niu, Murphy Yuezhen et al. "Qudit-Basis Universal Quantum Computation Using X[superscript (2)]." Physical Review Letters 120, 16 (April 2018): 160502 © 2018 American Physical Society
Version
Final published version
Abstract
We prove that universal quantum computation can be realized—using only linear optics and χ[superscript (2)] (three-wave mixing) interactions—in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ[superscript (2)] Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ[superscript (2)] interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection or subtraction, a technique enabled by χ[superscript (2)] interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool, in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.120.160502
