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How is the Toffoli gate used in quantum computing?
Universal reversible logic gate, applied in quantum computing. Circuit representation of Toffoli gate. In logic circuits, the Toffoli gate (also CCNOT gate), invented by Tommaso Toffoli, is a universal reversible logic gate, which means that any reversible circuit can be constructed from Toffoli gates.
How to implement the Toffoli gate in a circuit?
A implementation of Toffoli gate with above mentioned method is this: Note: Parameter θ is set to ± π 4. I tested the new gate “abilities” on input | 11 ⟩. Backend ibmqx2 was used, number of shots was set to 8,192. The circuit was designed to follow the backend physical implementation and hence to avoid qubits swaps after transpiling.
Can a reversible gate be implemented on a quantum computer?
Any reversible gate can be implemented on a quantum computer, and hence the Toffoli gate is also a quantum operator. However, the Toffoli gate can not be used for universal quantum computation, though it does mean that a quantum computer can implement all possible classical computations.
How are qubits moved in a quantum computer?
Sometimes we need to move information around in a quantum computer. For some qubit implementations, this could be done by physically moving them. Another option is simply to move the state between two qubits. This is done by the SWAP gate. The command above directly invokes this gate, but let’s see how we might make it using our standard gate set.
How many CNOT gates are needed for the Toffoli gate?
The application of many-body interaction could be used for direct operation of the gate in trapped ions, Rydberg atoms and superconducting circuit implementations. While the implementation of an n -qubit Toffoli with circuit model requires 2 n CNOT gates, the best known upper bound stands at 6 n -12 CNOT gates.
How are Toffoli gates used in designing arithmetic circuits?
If you use X, CNOT, SWAP, and Toffoli, it’s very natural to design arithmetic circuits, since these gates have a natural action on bits. If you wanted to design arithmetic circuits with a different gate set, it would probably be very difficult because the action of the gates would be very unintuitive.