Quantum Nondemolition Measurement of a Superconducting Qubit in the Weakly Projective Regime

Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong backaction. We show that the backaction of a dc-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum nondemolition character, with a QND fidelity of 75%.

Figure 1

(a) Scanning electron microscopy picture of the flux qubit and the dc SQUID. (b) Optical picture of the readout circuit. (c) Schematic of the readout circuit including a dc SQUID shunted with a resistor $R=125\Omega$ and a capacitor $C=1\mathrm{pF}$, and a HEMT cryogenic amplifier allowing a very fast detection of the qubit state.

Figure 2

(a) Current pulse for the qubit readout. (b) Output voltage. Dots correspond to real time signal, while the solid lines are average of 16 traces corresponding to the state $S$ or $D$. (c) Histogram of the output voltage. (d) Energy spectrum of the flux qubit. The color scale indicates the switching probability of the detector. (e) Rabi oscillation for a measurement repetition rate of 10 kHz or 1 MHz with an identical manipulation and readout sequence at a qubit frequency of $E/h=13\mathrm{GHz}$. The three dashed lines represent $P(g)$, $P(e)$, and $P_m$.

Figure 3

(a) Qubit operation and readout sequence including two Rabi oscillations of angles ${\theta }_A$ and ${\theta }_B$, and two readout pulses $A$ and $B$. The qubit operation frequency is set at $E/h=13\mathrm{GHz}$. (b) Switching probabilities $P_A$, $P_B$ in readout $A$ and $B$ as a function of the delay between the two measurements. $P_B^{\mathrm{free}}$ is the free qubit relaxation decay measured with readout $B$ without applying the readout pulse $A$. (c) $P_A$, $P_B$ as a function of the duration of the first Rabi pulse $T_{RA}$. $P_B(\pi )$ and $P_B(0)$ are the results readout $B$ with or without a $\pi$ rotation between the two measurements. (d),(e),(f) Switching probabilities in the first readout $P_A$ and in second readout in the case that the first readout did not $P_B(S_A)$ or did switch $P_B(D_A)$ as a function of the durations $T_{RA}$ and $T_{RB}$ of both Rabi pulses.