quantum gates is uncountable, whereas the number of finite sequences from a finite set is countable. To solve this problem, we only require that any quantum operation can be approximated by a sequence of gates from this finite set. Moreover, for unitaries on a constant number of qubits, the Solovay–Kitaev theorem guarantees that this can be done efficiently. Some universal quantum gate sets include: The rotation operators , , , the phase shift gate and CNOT are commonly used to form a universal quantum gate set. The Clifford set {CNOT, H, S} + T gate. The Clifford set alone is not a universal quantum gate set, as it can be efficiently simulated classically according to the Gottesman–Knill theorem. The Toffoli gate + Hadamard gate. The Toffoli gate alone forms a set of universal gates for reversible boolean algebraic logic circuits which encompasses all classical computation. Deutsch gate A single-gate set of universal quantum gates can also be formulated using the parametrized three-qubit Deutsch gate , named after physicist David Deutsch. It is a general case of CC-U or controlled-controlled-Unitary gate, and is defined as Unfortunately, a working Deutsch gate has remained out of reach, due to lack of a protocol. There are some proposals to realize a Deutsch gate with dipole-dipole interaction in neutral atoms. A universal logic gate for reversible classical computing, the Toffoli gate, is reducible to the Deutsch gate, , thus showing that all reversible classical logic operations can be performed on a universal quantum computer. There also exist single two-qubit gates sufficient for universality. In 1996, Adriano Barenco showed that the Deutsch gate can be decomposed using only a single two-qubit gate (Barenco gate), but it is hard to realize experimentally. This feature is exclusive to quantum circuits, as there is no classical two bit gate that is both reversible and universal. Universal two-qubit gates could be implemented to improve classical reversible circuits in fast low power microprocessors. Circuit composition Serially wired gates Assume that we have two gates A and B, that both act on qubits. When B is put after A in a series circuit, then the effect of the two gates can be described as a single gate C. Where is matrix multiplication. The resulting gate C will have the same dimensions as A and B. The order in which the gates would appear in a circuit diagram is reversed when multiplying them