Sign- and Magnitude-Tunable Coupler for Superconducting Flux Qubits

We experimentally confirm the functionality of a coupling element for flux-based superconducting qubits, with a coupling strength $J$ whose sign and magnitude can be tuned in situ. To measure the effective $J$, the ground state of a coupled two-qubit system has been mapped as a function of the local magnetic fields applied to each qubit. The state of the system is determined by directly reading out the individual qubits while tunneling is suppressed. These measurements demonstrate that $J$ can be tuned from antiferromagnetic through zero to ferromagnetic.

Figure 1

(a) Device schematic: SQUID loops $i$, mutual inductances $M^{ij}$, flux bias lines $f_x^i$, current bias lines $i_i$ and voltage taps $v_i$ as indicated (see text). (b) Photograph of device. (c) Energetics of the coupled qubit system. Qubits are represented as bistable potentials with pseudospins as indicated. Local biases ${ϵ}^i$ are applied to each qubit. The lowest lying qubit states are separated by $E=\sqrt{({ϵ}^i{)}^2+({\Delta }^i{)}^2}$. The coupler is represented as a monostable potential that mediates the interaction $J$.

Figure 2

Bias sequence. CJJ biases $f_x^d$, $f_x^e$ are raised to $\frac{1}{2}$, held for $60\mu \mathrm{s}$, and then returned to zero over $20\mu \mathrm{s}$. Readout dc SQUID flux bias $f_x^{f,g}$ is held at zero during qubit evolution and raised to its operating point during the current bias ramps on $i_f$, $i_g$. Control lines $f_x^a$, $f_x^b$, and $f_x^c$ are held constant throughout this procedure.

Figure 3

Measured probabilities for each of the four possible flux states for small ${\Delta }_q$, at coupler flux bias $f_x^b=-0.03$.

Figure 4

Ground state stability diagrams: (a) AFM coupling, (b) zero coupling, and (c) FM coupling. The calibrated degeneracy lines for the individual qubits and extreme values of coupled flux are indicated by solid and dashed lines, respectively.

Figure 5

Coupling strength (in units of coupled flux) versus $f_x^b$ as obtained from ground state mapping and from $d{M}^{qb}{I}_p^q/d{\Phi }_x^b$ scaled by $M^{qb}{I}_p^q$ with $I_p^q=0.5\pm 0.1\mu \mathrm{A}$ [see Eq. (1)].