Superconducting Qubit Storage and Entanglement with Nanomechanical Resonators

We propose a quantum computing architecture based on the integration of nanomechanical resonators with Josephson-junction phase qubits. The resonators are GHz-frequency, dilatational disk resonators, which couple to the junctions through a piezoelectric interaction. The system is analogous to a collection of tunable few-level atoms (the Josephson junctions) coupled to one or more electromagnetic cavities (the resonators). Our architecture combines desirable features of solid-state and optical approaches and may make quantum computing possible in a scalable, solid-state environment.

Figure 1

Left: equivalent-circuit model for a current-biased JJ. A capacitance $C$ and resistance $R$ in parallel with an ideal Josephson element with critical current $I_0$, all sharing a bias current $I_{\mathrm{b}}$. Right: potential in the cubic $s\to 1^{-}$ limit.

Figure 2

Two phase qubits coupled to a piezoelectric resonator.

Figure 3

Resonances measured in a 1.8 GHz AlN piezoelectric dilatational disk resonator, shown schematically on the left, from 300 down to 4.2 K. The resonance at 4.2 K has a quality factor of about 3500.

Figure 4

Qubit storage in nanomechanical resonator. (a) Thin descending and thick ascending solid curves are $|c_{10}{|}^2$ and $|c_{01}{|}^2$, respectively. The dotted curve is $s$, which has a trapezoidal shape. The dashed curve is the RWA prediction for $|c_{10}{|}^2$. (b) Qubit storage with arctangent bias-current profile. Other parameters are the same as (a), but the storage operation fails. (c) Qubit storage in larger resonator with $R=13.7\mu \mathrm{m}$; the other parameters are as in (a). Storage performs poorly.

Figure 5

Qubit transfer between two junctions. The solid curve is $|c_{100}{|}^2$, the dash-dotted curve is $|c_{001}{|}^2$, and the dashed curve is $|c_{010}{|}^2$. Thin, solid, and dotted curves show $s_1$ and $s_2$, respectively.

Figure 6

JJ entanglement. The dashed curve is the probability to be in the state (in the interaction representation) $(|100\rangle +|001\rangle )/\sqrt{2}$, and the thick solid curve is for $(|100\rangle -|010\rangle )/\sqrt{2}$. Thin, solid, and dotted curves are $s_1$ and $s_2$.