Multivalued logic gates for quantum computation - art. no. 052309

We develop a multivalued 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-le vel systems (d >2) can be decomposed into logic gates that operate an only two systems at a time. We show that such multivalued logic gates are experi mentally 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 numb er of ions needed for a computation by a factor of log(2) d.