Spin qubits have been successfully realized in electrostatically defined, lateral fewelectron quantum dot circuits [1][2][3][4]. Qubit readout typically involves spin to charge information conversion, followed by a charge measurement made using a nearby biased quantum point contact [1,5,6]. It is critical to understand the back-action disturbances resulting from such a measurement approach [7,8]. Previous studies have indicated that quantum point contact detectors emit phonons which are then absorbed by nearby qubits [9][10][11][12][13]. We report here the observation of a pronounced back-action effect in multiple dot circuits where the absorption of detector-generated phonons is strongly modified by a quantum interference effect, and show that the phenomenon is well described by a theory incorporating both the quantum point contact and coherent phonon absorption. Our combined experimental and theoretical results suggest strategies to suppress back-action during the qubit readout procedure.The back-action process considered in this paper involves deleterious inelastic tunneling events between two adjacent dots in a serial double or triple quantum dot (DQD, TQD). The energy difference ∆ between the initial and final electronic dot states is provided by the absorption of a non-equilibrium acoustic phonon, which itself is generated by the quantum point contact (QPC) detector [12]. Such an absorption process between adjacent dots is constrained by the energy conservation condition ∆ = | q|v ph (v ph is the sound velocity, q the phonon wavevector). More subtly, it is also sensitive to the difference in phase, ∆ϕ = d · q, of the associated phonon wave between the two dot positions, with d being the vector connecting the two dot centers [14,15].This q (and hence ∆) dependent phase difference controls the matrix element for phonon-absorption since it determines whether the electron-phonon couplings in each of the two individual dots add constructively or destructively (see Fig. 1) [16]. The result is an oscillatory probability for inelastic electron-transfer events involving phonon-absorption, with constructive interference occurring when ∆φ = (2n + 1)π (where n is an integer).Data showing a pronounced back-action effect are shown in Fig. 2a, which displays the stability diagram measured in charge detection for a few-electron DQD without a voltage drop between its left and right leads. The charge configuration of the quantum dot structures influences the conductance of a nearby QPC because of the capacitive coupling between the dots and the QPC.In order to serve as a charge detector it is necessary to drive a current through the detector QPC which, in turn, leads to the observed detector back-action. Multiple gates fabricated 85 nm above a high-mobility two-dimensional electron system (2DES) are used to define two dots and two QPCs (Fig. 2d). The differential transconductance dI QPC /dV L of the biased charge detectorDj p = FIG. 1: Interference in quantum dot-phonon interactions. a, The back-action charge fluctuations of...

We study theoretically transitions of a double quantum-dot qubit caused by nonequilibrium charge fluctuations in a nearby quantum point contact (QPC) used as a detector. We show that these transitions are related to the fundamental Heisenberg backaction associated with the measurement, and use the uncertainty principle to derive a lower bound on the transition rates. We also derive simple expressions for the transition rates for the usual model of a QPC as a mesoscopic conductor, with screening treated at the RPA level. Finally, numerical results are presented which demonstrate that the charge noise and shot noise backaction mechanisms can be distinguished in QPCs having nonadiabatic potentials. The enhanced sensitivity of the charge noise to the QPC potential is explained in terms of interference contributions similar to those which cause Friedel oscillations.