Encoded
universality from a single physical interaction
(pp33-55)
Julia Kempe, David Bacon, David P. DiVincenzo, and K. Brigitta Whaley
doi:
https://doi.org/10.26421/QIC1.s-6
Abstracts:
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.
Key words: quantum
cubits, tensor product structure |