  Quantum computation offers the potential to solve fundamental yet otherwise
intractable problems across a range of active fields of research. Recently,
universal quantum-logic gate sets - the building blocks for a quantum computer
- have been demonstrated in several physical architectures. A serious obstacle
to a full-scale implementation is the sheer number of these gates required to
implement even small quantum algorithms. Here we present and demonstrate a
general technique that harnesses higher dimensions of quantum systems to
significantly reduce this number, allowing the construction of key quantum
circuits with existing technology. We are thereby able to present the first
implementation of two key quantum circuits: the three-qubit Toffoli and the
two-qubit controlled-unitary. The gates are realised in a linear optical
architecture, which would otherwise be absolutely infeasible with current
technology.
