Monday, July 22, 2013

1307.5087 (Jacob Farinholt)

Efficient Ancilla-Free Multi-Qudit Clifford Gate Decomposition in
Arbitrary Finite Dimension

Jacob Farinholt
In many quantum computing algorithms, two things are generally assumed, namely, the existence of a constant, fresh supply of (near) perfectly prepared ancillas, as well as gates that efficiently implement the unitary operations. As ancillas are often difficult to prepare and tend to degrade with the quantum system, the first assumption is often unreasonable from a practical standpoint. While any universal set of quantum operations will most likely require the use of some ancillas, we provide a minimal set of ancilla-free gates that can be used to generate an important subset of unitary operations - the Clifford operations. This \emph{Clifford basis} consists of only 3 distinct gates, and exists in any finite dimension. Moreover, we provide a constructive algorithm to implement a Clifford transformation on any $n$-qudit stabilizer state, and show that the number of gates required to implement such a Clifford transformation grows linearly with the number of qudits, and less than quadratically with the dimension of the Hilbert space.
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