We develop a multi-valued logic for quantum computing for use in multi-level
quantum systems, and discuss the practical advantages of this approach for
scaling up a quantum computer. Generalizing the methods of binary quantum
logic, we establish that arbitrary unitary operations on any number of d-level
systems (d > 2) can be decomposed into logic gates that operate on only two
systems at a time. We show that such multi-valued logic gates are
experimentally feasible in the context of the linear ion trap scheme for
quantum computing. By using d levels in each ion in this scheme, we reduce the
number of ions needed for a computation by a factor of log d.Comment: Revised version; 8 pages, 3 figures; to appear in Physical Review
