Encoded universality from a single physical interaction

  • Authors:

  • J. Kempe;D. Bacon;D. P. DiVincenzo;K. B. Whaley

  • Affiliations:

  • Departments of Chemistry, University of California, Berkeley and Departments of Mathematics;Departments of Chemistry, University of California, Berkeley and Departments of Physics;IBM Research Division, T.J. Watson Research Center, Yorktown Heights, New York;Departments of Chemistry, University of California, Berkeley

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2001

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Abstract

We present a theoretical analysis of the paradigm of encoded universality, using a Lie algebraic analysis to derive specific conditions under which physical interactions can provide universality. We discuss the significance of the tensor product structure in the quantum circuit model and use this to define the conjoining of encoded qudits. The construction of encoded gates between conjoined qudits is discussed in detail. We illustrate the general procedures with several examples from exchange-only quantum computation. In particular, we extend our earlier results showing universality with the isotropic exchange interaction to the derivation of encoded universality with the anisotropic exchange interaction, i.e., to the XY model. In this case the minimal encoding for universality is into qutrits rather than into qubits as was the case for isotropic (Heisenberg) exchange. We also address issues of fault-tolerance, leakage and correction of encoded qudits.