Fluxon Readout of a Superconducting Qubit

An experiment demonstrating a link between classical single-flux quantum digital logic and a superconducting quantum circuit is reported. We implement coupling between a moving Josephson vortex (fluxon) and a flux qubit by reading out of a state of the flux qubit through a frequency shift of the fluxon oscillations in an annular Josephson junction. The energy spectrum of the flux qubit is measured using this technique. The implemented hybrid scheme opens an opportunity to readout quantum states of superconducting qubits with the classical fluxon logic circuits.

Figure 1

An annular Josephson junction coupled to a flux qubit. The junction is homogeneously biased by an external current source $I_b$. The flux qubit is controlled by a dc control line current $I_{\text{CL}}$ and a microwave signal $I_{\text{ac}}$ at the frequency of ${\nu }_e$. The purple lines schematically show the flow of the electrical currents. The fluxon equilibrium oscillation frequency ${\nu }_0$ is shifted by an amount $\delta \nu$ due to fluxon scattering on the current dipole produced by a flux qubit. Microwave radiation from the fluxon is picked up by a capacitively coupled microstrip antenna and later fed to a cryogenic amplifier (not shown).

Figure 2

(a) The theoretical persistent current $I_p$ of the ground state of the flux qubit versus magnetic frustration (black line) calculated for our flux qubit parameters. The red line shows the expected fluxon frequency shift in kHz for $\gamma =0.4$ and $\mu =0.05$. (b) The experimentally measured modulation of the fluxon oscillation frequency due to the coupling to the flux qubit. Black dots show the measured mean frequency of fluxon oscillations. Every point consists of 100 averages; bias is $\gamma =0.39$. The red line shows the corresponding fit.

Figure 3

(a) The theoretically expected persistent current $I_p$ for the ground state of the flux qubit versus magnetic flux (black line). The spikes indicate the presumed transitions to the first excited state at flux bias points corresponding to $E_{12}=14\mathrm{GHz}$ flux qubit energy splitting. The green line shows the expected persistent current $I_p$ for the first excited state. (b) Modulation of the fluxon’s oscillation frequency due to the coupling to the qubit, measured in the power domain. Measured power $P$ relates to the power at the fixed frequency offset $+50\mathrm{kHz}$ from the fluxon mean oscillation frequency ${\nu }_f$. Every point consists of 10 averages with video filter bandwidth of 10 Hz. The red line depicts the corresponding theory fit.

Figure 4

Fluxon response on the microwave excitation applied to the flux qubit. Color scale corresponds to the detected power. Measured power $P$ relates to the power at the fixed frequency offset $+50\mathrm{kHz}$ from the fluxon mean oscillation frequency ${\nu }_f$. Every point consists of 10 averages with video filter bandwidth of 1 Hz. The flux qubit spectrum can be clearly seen as the red-yellow curved trace. The black dashed line depicts the corresponding fit of the flux qubit.