Incoherent Qubit Control Using the Quantum Zeno Effect

The quantum Zeno effect is the suppression of Hamiltonian evolution by repeated observation, which pins the system to an eigenstate of the measurement observable. Using measurement alone, control of the state can be achieved if the observable is slowly varied, so that the state tracks the now time-dependent eigenstate. We demonstrate this using a circuit-QED readout technique that couples to a dynamically controllable observable of a qubit. Continuous monitoring of the measurement record allows us to detect an escape from the eigenstate, thus serving as a built-in form of error detection. We show this by postselecting on realizations with high fidelity with respect to the target state. Our dynamical measurement operator technique offers a new tool for numerous forms of quantum feedback protocols, including adaptive measurements and rapid state purification.

Figure 1

(a),(b) Schematic of the main components in the experimental setup. (a) A transmon qubit in a 3D aluminum cavity. A weakly coupled port is used to simultaneously input three microwave tones; a Rabi drive at ${\omega }_q$ is used to create an effective low frequency qubit at ${\omega }_{q-\mathrm{eff}}/2\pi ={\mathrm{\Omega }}_R/2\pi =40\mathrm{MHz}$ (orange), while two sideband tones resonantly couple the effective qubit to the cavity (green). (b) The output signal is amplified with a JPA and demodulated at room temperature with an IQ mixer. The signal and JPA phase are aligned along the $Q$ quadrature. The red and blue ellipses illustrate the distribution of results for each of the two possible detector outputs, with respect to the measurement operator. (c) Illustration of the $XY$ plane in the Bloch sphere of the effective qubit. The green arrow denotes axis of the time-dependent measurement operator ${\sigma }_{\delta (t)}$.

Figure 2

(a) Average state behavior of a qubit being dragged at varying rotation speeds $v$. Dots are tomography results in the $XY$ plane of the Bloch sphere after the fixed time indicated in the legend and for rotation speeds from 0.01 to 0.18 MHz in steps of 0.01 MHz. Lines are theory plots with the experimental parameters given in the main text. (b) Two example selected trajectories for a dragging rate of $v=0.05\mathrm{MHz}$ and a duration of $5\mu \mathrm{s}$: one illustrating successful dragging of the qubit state, whose state remains pure, while the other undergoes a jump and continues to get dragged along the opposite pole. Colors in the figure correspond to time evolution. The colored lines outside the Bloch sphere indicate the time axis going from blue for $t=0\mu \mathrm{s}$ to red for $t=5\mu \mathrm{s}$; these illustrate the position of the measurement axis as function of time. The same colors correspond to the time evolution of the two trajectories shown.

Figure 3

(a) Ensemble histograms of the qubit state as function of time, showing the $XY$ plane of the Bloch sphere, for two example velocities of 0.02 and 0.04 MHz, with ${\mathrm{\Gamma }}_D/2\pi =0.13\mathrm{MHz}$. The state is initialized at $|y=+1⟩$. The measurement axis is represented by white lines, while the theoretically calculated natural jump axis is indicated by red lines. The white arrow indicates the direction of rotation. The ensemble average as a function of time in the frame of the jump axis is shown perpendicular to the jump axis (b) and along the jump axis (c). Data are generated by averaging the trajectories as a function of time for the dragging velocities in the Zeno regime ${\mathrm{\Gamma }}_D\ge 2|\mathrm{\Omega }|$. Black dashed lines show theoretical results using the experimental parameters given in the main body.

Figure 4

Fidelity as function of postselection threshold. Postselection is performed with respect to the average voltage of the detector signal. Each trace corresponds to a fixed dragging rate and shows fidelity with respect to the eigenstate of the measurement operator after rotating for $4\mu \mathrm{s}$. The $X$ axis is the normalized postselection threshold, normalized such that $\pm 1$ corresponds to the average values of the signal for the $\pm 1$ eigenstates of the measurement operator.