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Is there a quantum processor with physically implemented Toffoli gate?

Quantum Computing Asked on April 20, 2021

Recently, I came across the article Realization of efficient quantum gates with a superconducting qubit-qutrit circuit where its authors proposed a physical implementation of three qubits quantum gates with two physical qubits and one physical qutrit controlled by microwave pulses.

As a result, they were able to implement physically CCZ gate which when accompanied by two Hadamards implements Toffoli gate.

They also proposed configuration implementing Fredking gate, another three qubits gate which together with Hadamard gate form universal set.

Finally, they showed that their design can be used for implementation of $CC-U$ gate, where
$$
U=
begin{pmatrix}
cos(theta) & mathrm{e}^{ivarphi}sin(theta)
mathrm{e}^{-ivarphi}sin(theta) & -cos(theta)
end{pmatrix},
$$

which is more or less similar to $U3$ gate on IBM Q (to be precise $U(theta, varphi) = U3(2theta,-varphi,pi+varphi)$).

As it seems that this proposal is able to cut lenght of circuit, particularly in case of Toffoli gates (implemented by physical CC-Z gate and two Hadamards only) and therefore enables us to implement more complex cirucits, I am curious if such design is being implemented or at least considered by companies like IBM or Google for their next generation of quantum processors. I highly appreciate any links.

2 Answers

Although I can't find an online resource currently, I'm pretty certain that people in QuTech (Tim Taminiau and his group, specifically) are trying to physically implement a Toffoli gate in their NV-center systems. It's definitely on-going research though.

Both Google and IBM use transmons as their systems - entangling gates are implemented here using physical 'coupling' resonance cavities - as far as I known, it would in principle be possible to connect multiple (i.e. $3$) qubits, so that one would get a coupled Hamiltonian between $3$ qubits simultaneously. I, however, am not knowledgeable enough to judge the feasibility of this.

Correct answer by JSdJ on April 20, 2021

Not quite what you're asking, but...

With something like the IBM processors, if you have the right permissions, you can get "pulse level" control of the system. This means you can directly manipulate the Hamiltonian. In principle, this can give you multi-qubit gates directly, if only you can design your pulses correctly.

Answered by DaftWullie on April 20, 2021

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