Proposal for realizing a multiqubit tunable phase gate of one qubit simultaneously controlling $n$ target qubits using cavity QED

We propose a way to realize a multiqubit tunable phase gate of one qubit simultaneously controlling $n$ target qubits with atoms in cavity QED. In this proposal, classical pulses interact with atoms outside a cavity only, thus the experimental challenge of applying a pulse to an intracavity single atom without affecting other atoms in the same cavity is avoided. Because of employing a first-order large detuning, the gate can be performed fast when compared with the use of a second-order large detuning. Furthermore, the gate operation time is independent of the number of qubits. This proposal is quite general and can be applied to various superconducting qubits coupled to a resonator, nitrogen-vacancy centers coupled to a microsphere cavity, or quantum dots in cavity QED.

Figure 1

(a) Schematic circuit of a multiqubit cp gate with qubit 1 (on top) simultaneously controlling $n$ target qubits ($2,3,...,n+1$). (b) The circuit for a phase gate with many control qubits ($2,3,...,n+1$) acting on one target (qubit 1).

Figure 2

(a) Atom-cavity off-resonant interaction. (b) Atom-pulse off-resonant interaction.

Figure 3

Proposed setup for the gate realization with the control atom (the red dot), the $n$ identical target atoms (the dark dots), and a cavity. For simplicity, only five atoms are drawn here. Each atom can be trapped and loaded into or out of the cavity by a one-dimensional translating optical lattice trap [11, 12].

Figure 4

Fidelity versus $\theta$. Lines from top to bottom correspond to $n=1$, $n=2,...,$ and $n=15$, respectively. Here, $n$ is the number of target atoms ($2,3,...,n+1$).

Figure 5

Fidelity versus $b$. Here, $b={\Delta }_c/g=\Delta /{\Omega }_2.$