Gated Conditional Displacement Readout of Superconducting Qubits

We have realized a new interaction between superconducting qubits and a readout cavity that results in the displacement of a coherent state in the cavity, conditioned on the state of the qubit. This conditional state, when it reaches the cavity-following, phase-sensitive amplifier, matches its measured observable, namely, the in phase quadrature. In a setup where several qubits are coupled to the same readout resonator, we show it is possible to measure the state of a target qubit with minimal dephasing of the other qubits. Our results suggest novel directions for faster readout of superconducting qubits and implementations of bosonic quantum error-correcting codes.

Figure 1

(a) Principle of the experiment. A schematic superconducting two-level artificial atom (red) is placed where the field of a cavity (blue) is weak, for instance, close to a partially transmitting mirror, to be in the weak coupling regime. When the atom is driven at the frequency of the cavity, the electromagnetic field of the cavity is spontaneously displaced with a sense that depends on the state of the atom (dotted or solid line) and exits through the main aperture. (b) Multiqubit architecture. An arbitrary number of transmon chips are placed around the field of an aluminum postcavity (three chips in the current experiment). The target transmon (red) is driven through a filter mode (green), which is coupled to a microwave input coupler. The number of photons in the cavity is kept minimal using a cancellation port (see text). The field of the cavity is measured using the strongly coupled output port.

Figure 2

Conditional coherent states separation. (a) Phase-space representation of this separation under a rf pulse implementing our engineered interaction (gray solid line) and under a rf pulse driving the cavity directly (gray dashed line). In the former case, the field of the cavity is displaced along the $I$ quadrature with a sense that depends on the state of the transmon. The distance between the two possible steady states is noted ${\alpha }_m$. In the latter case, the cavity state would be displaced unconditionally along $Q$ and conditionally along $I$. The gray area indicates that, at small times, the two coherent states do not separate. (b) Log-log plot of the amplitude SNR as a function of time. The data are fitted with the theoretical SNR for a conditional displacement (solid line), adjusted in amplitude with the efficiency $\eta$, determined independently, and with a fit parameter corresponding to the coupling strength. The dashed line corresponds to the optimal dispersive readout with the same parameters and $\chi =\kappa$. The gray area corresponds to the delay shown in (a). (c) Demodulation envelope comprising a depletion section. The coupling strength varies from ${\zeta }_0$ for 750 ns (orange) to $-2{\zeta }_0$ for 120 ns (green). (d) Histogram of the demodulated signal. The axes are calibrated using the calibrated efficiency $\eta$ and the width $\sigma$ of the Gaussians along the $x$ axis. The squeezing is due to the amplifier being phase sensitive.

Figure 3

Quantum-nondemolition readout. (a) Results of successive single-shot measurements displaying six discrete jumps (black). The orange trace is a guide for the eye and is obtained with a latching filter applied to the data. The correlation between successive measurements indicates that the readout is nondestructive. (b) Histogram of the demodulated signal along the $I$ quadrature with postselecting the qubit in $|g⟩$ (diamonds) and in $|e⟩$ (crosses). The two distributions are fitted with Gaussians (light red, dashed and solid lines). When the qubit starts in $|g⟩$ (respectively, $|e⟩$) it mostly persists in $|g⟩$ (respectively, $|e⟩$). The gray dashed lines emphasize the number of jumps from $|g⟩$ (respectively, $|e⟩$) to $|e⟩$ (respectively, $|g⟩$).

Figure 4

Coherence of two unmeasured qubits coupled to a common when the target qubit is measured. (a) Sequence for a Ramsey experiment with fixed length. Between two qubit rotations of $\pi /2$ (where $\varphi$ indicates around what axis), either the measurement pulse (red) is applied or not. To mimic a decoupled quantum computation, $N$ echo pulses are inserted between the two $\pi /2$ pulses. (b) Ramsey fringes while performing one echo pulse. The triangles and solid lines are, respectively, the data and fit for the control experiment. The circles and dashed lines are the data and fit when the target qubit is measured. The two curves are phase shifted due to the Stark shift. The $y$ axis is normalized to the contrast of the control experiment. The experiment is performed on two different qubits (yellow and green) and the data are shown with opposite phases for clarity. (c) The evolution of the coherence for different numbers of echo pulses. The Ramsey contrasts are normalized by the amplitude of their respective control experiment.