Efficient Ancilla-Free Multi-Qudit Clifford Gate Decomposition in Arbitrary Finite Dimension
Jacob Farinholt · arXiv (Cornell University) · 2013
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 show that any Clifford transformation between two stabilizers can be constructed using a number of basis gates that grows linearly with the number of qudits and less than quadratically with the dimension of the Hilbert space, while an arbitrary Clifford operator can be decomposed using a number of basis gates that grows quadratically with the number of qudits and less than quadratically with the dimension.