How to implement the square root of SWAP gate?

How to implement the square root of SWAP gate?

Implementing controlled- U gates using CNOTs is a standard construction, which can be found in a range of places, see e.g. https://arxiv.org/abs/quant-ph/9503016. Depending how you do this step, you might have to fix the “global” phase of the 1st qubit (given the 2nd is | 1 ⟩ ).

How to make a S W A P using square root of CNOT?

To make a S W A P, we can instead use a square root of cnot conjugated by oppositely oriented cnots. To verify that this is indeed a S W A P, you can simply square it and verify that it ends up in the way we expect (using the fact that cnots square to identity).

What does Proposition 3 say about square root construction?

Proposition 3 (Book III): If in a circle a straight line through the center bisect a straight line not through thecenter, it also cuts it at right angles; and if it cut it at right angles it also bisects it. Štefan Porubský: Square and Square Root Construction by Compass and Straightedge.

Is the swap gate a two qubit operation?

The SWAP gate is two-qubit operation. Expressed in basis states, the SWAP gate swaps the state of the two qubits involved in the operation:

Is there a swap gate for qudits in CNOT?

The gate generalizes the CNOT implementation of the SWAP gate for qubits and keeps its most important properties, like symmetry and simplicity. We only use three copies of the same controlled qudit gate.

Can a quantum circuit be simulated using CNOT gates?

Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations. Both CNOT and S W A P are universal two-qubit gates and can be transformed into each other. The questions are not identical, and are likely to attract different audiences.

Is the S W A P and CNOT gate the same?

Both CNOT and S W A P are universal two-qubit gates and can be transformed into each other. The questions are not identical, and are likely to attract different audiences. -DaftWullie Can the difference be regarded as applied vs theoretic?