Quantum Rifling: Protecting a Qubit from Measurement Back Action

Quantum mechanics postulates that measuring the qubit’s wave function results in its collapse, with the recorded discrete outcome designating the particular eigenstate that the qubit collapsed into. We show that this picture breaks down when the qubit is strongly driven during measurement. More specifically, for a fast evolving qubit the measurement returns the time-averaged expectation value of the measurement operator, erasing information about the initial state of the qubit while completely suppressing the measurement backaction. We call this regime quantum rifling, as the fast spinning of the Bloch vector protects it from deflection into either of its eigenstates. We study this phenomenon with two superconducting qubits coupled to the same probe field and demonstrate that quantum rifling allows us to measure either one of the qubits on demand while protecting the state of the other from measurement backaction. Our results allow for the implementation of selective readout multiplexing of several qubits, contributing to the efficient scaling up of quantum processors for future quantum technologies.

Figure 1

Quantum rifling in a Stern-Gerlach setup. (a) Measurement of a spin initially prepared in a superposition state. The magnetic field measures the spin by deflecting its flight path in a direction dependent on the measured spin orientation. (b) Measurement during rifling. When the spin is strongly driven during measurement, the magnetic field cannot discriminate between spin states and the spin’s flight path is undisturbed. (c) Detection mechanism of the qubit state in our setup. The resonator experiences a qubit state-dependent shift in its resonance frequency by $\pm \chi$ relative to its bare frequency ${\omega }_r$ in the rotating frame. Thus after averaging the results of experiment (a), one would observe the red and blue resonator transmission curves. During quantum rifling, when the qubit’s state is driven resonantly with its transition energy, the resonator’s resonance shifts to ${\omega }_r$, leading to the dashed transmission curve following the averaging of the experiment presented in (b).

Figure 2

Resonator spectroscopy vs Rabi drive strength. (a) Continuous wave spectroscopy of the resonator transmission vs Rabi frequency. The resonator is probed by a mean photon number of $⟨n_{\text{photon}}⟩\approx 0.13$. The symbols below the plot show the qubit drive strength at which linecuts are shown in (c). (b) Steady-state numerical simulation of Eq. (2) extended to the three-level transmon model for the observable $|a⟩$ plotted as a function of $\delta {\omega }_r/2\pi$ and ${\mathrm{\Omega }}_R/2\pi$, assuming a steady-state drive and using experimental parameters quoted in the text. Dashed lines show the transitions in frequency between the $|0\pm ⟩$ and $|1\pm ⟩$ states.The arrows under the plot show the frequencies for the linecuts in (c). (c) Comparison of experimental data and numerical simulations presented in (a) and (b), as well as the analytical solution for a two-level qubit at three values of the Rabi drive strength. All data have been normalized such that the maximum amplitude without Rabi drive is 1.

Figure 3

Rabi decay rates vs Rabi frequency ${\mathrm{\Omega }}_R$ for different measurement strengths. (a) Example of a rifled Rabi measurement (${\mathrm{\Omega }}_R/2\pi =4.1\mathrm{MHz}$, $⟨n_{\text{photon}}⟩\approx 2.1$), with overlaying numerical fit of the equation shown in the inset. (b) Pulse protocol of the rifled Rabi measurement. The cavity pulse starts 10 ns after the qubit drive and stops 15 ns before its end. The actual readout pulse starts 5 ns after the qubit drive ends. (c) Measured and simulated rifled Rabi and standard Rabi decay rates. For a fixed probe power, the Rabi decay rate is measured for increasing Rabi drives, following the protocol presented in (b). The values for $⟨n_{\text{photon}}⟩$ are measured independently via the ac-Stark shit. For the simulations, the average number of photons is extracted by normalizing to the fitted curve for the lowest measurement strength, which is assumed to match the measurement.

Figure 4

Sequential measurement of two qubits coupled to the same resonator with and without rifling. (a) Gate protocol and measured single qubit density matrices. First, both qubits are brought to full superposition by applying a $R_y^{\pi /2}$ rotation. Then qubit 1 is rifled by applying a strong coherent Rabi drive for 1142 ns, while qubit 2 is read out via tomography pulses followed by a cavity readout pulse, which ends before the Rabi drive pulse on qubit 1. Lastly, qubit 2 is read out. (b) Same as (a), but qubit 1 is left idle for 1142 ns instead of rifling.