5 research outputs found
Constructing all qutrit controlled Clifford+T gates in Clifford+T
For a number of useful quantum circuits, qudit constructions have been found
which reduce resource requirements compared to the best known or best possible
qubit construction. However, many of the necessary qutrit gates in these
constructions have never been explicitly and efficiently constructed in a
fault-tolerant manner. We show how to exactly and unitarily construct any
qutrit multiple-controlled Clifford+T unitary using just Clifford+T gates and
without using ancillae. The T-count to do so is polynomial in the number of
controls , scaling as . With our results we can construct
ancilla-free Clifford+T implementations of multiple-controlled T gates as well
as all versions of the qutrit multiple-controlled Toffoli, while the analogous
results for qubits are impossible. As an application of our results, we provide
a procedure to implement any ternary classical reversible function on trits
as an ancilla-free qutrit unitary using T gates.Comment: 14 page