Transmon-qubit readout using an in situ bifurcation amplification in the mesoscopic regime

R. Dassonneville, T. Ramos, V. Milchakov, C. Mori, L. Planat, F. Foroughi, C. Naud, W. Hasch-Guichard, J.J. García-Ripoll, N. Roch, and O. Buisson

Phys. Rev. Applied 20, 044050 – Published 19 October 2023

Abstract

We demonstrate a transmon-qubit readout based on the nonlinear response to a drive of polaritonic meters in situ coupled to the qubit. Inside a three-dimensional readout cavity, we place a transmon molecule consisting of a transmon qubit and an ancilla mode interacting via nonperturbative cross-Kerr-coupling. The cavity couples strongly only to the ancilla mode, leading to hybridized lower and upper polaritonic meters. Both polaritons are anharmonic and dissipative, as they inherit a self-Kerr nonlinearity $U$ from the ancilla and effective decay $κ$ from the open cavity. Via the ancilla, the polariton meters also inherit the nonperturbative cross-Kerr-coupling to the qubit. This results in a high qubit-dependent displacement $2 χ > κ, U$ that can be read out via the cavity without causing Purcell decay. Moreover, the polariton meters, being nonlinear resonators, present bistability, and bifurcation behavior when the probing power increases. In this work, we focus on the bifurcation at low power in the few-photon regime, called the mesoscopic regime, which is accessible when the self-Kerr and decay rates of the polariton meter are similar, $U \sim κ$ . Capitalizing on a latching mechanism by bifurcation, the readout is sensitive to transmon-qubit relaxation error only in the first tens of nanoseconds. We thus report a single-shot fidelity of 98.6% while having an integration time of 500 ns and no requirement for an external quantum-limited amplifier.

Received 31 July 2023
Accepted 26 September 2023

DOI:https://doi.org/10.1103/PhysRevApplied.20.044050

Physics Subject Headings (PhySH)

Kerr effect Optoelectronics Polaritons Quantum information with solid state qubits

Low-temperature superconductors Optical microcavities Superconducting qubits

Microwave techniques

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

R. Dassonneville ^1,2,*, T. Ramos ³, V. Milchakov¹, C. Mori¹, L. Planat¹, F. Foroughi ¹, C. Naud¹, W. Hasch-Guichard¹, J.J. García-Ripoll ³, N. Roch ¹, and O. Buisson ¹

¹Université Grenoble-Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
²Aix Marseille Université, CNRS, IM2NP, Marseille, France
³Institute of Fundamental Physics, IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain

^*remy.dassonneville@univ-amu.fr

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 20, Iss. 4 — October 2023

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Scheme of the setup. The cavity mode $\hat{c}$ of frequency $ω_{c}$ is strongly coupled to an anharmonic ancilla mode of frequency $ω_{a}$ and self-Kerr nonlinearity $U_{a}$ . The ancilla is also coupled to the qubit via a nonperturbative cross-Kerr-coupling of rate $g_{z z}$ . To perform readout, we send a coherent signal on the input of the cavity mode ${\hat{c}}_{in}$ and measure the transmitted cavity output field ${\hat{c}}_{out}$ . (b) Representation of the system in terms of cavity-ancilla polariton modes. Lower and upper polariton modes have distinct frequencies $ω_{l}$ and $ω_{u}$ , respectively, as well as different self-Kerr nonlinearities $U_{l}$ and $U_{u}$ inherited from the ancilla. Both polaritons are independently coupled to the qubit via cross-Kerr terms $χ_{l}$ and $χ_{u}$ , which allows us to use these polariton modes as direct meters of the qubit states. The readout can be extracted from the same output field $c_{out}$ due to the polariton leakage rates $κ_{l}$ and $κ_{u}$ . (c)–(e) Measurements (dots) and predictions (lines) for lower polariton $j = l$ (orange) and upper polariton $j = u$ (purple) as functions of the hybridization angle $θ$ of (c) the nonperturbative qubit-polariton cross-Kerr $χ_{j}$ , (d) the self-Kerr $U_{j j}$ and interpolariton cross-Kerr $U_{u l}$ (green), and (e) the polariton decay rates $κ_{j}$ . The predictions are calculated from the polariton model in Eqs. (2) and (3) using initial parameters $g_{z z}$ , $U_{a}$ , $κ_{c}$ , and $κ_{a}$ and plotted as black lines in panels (c)–(e), respectively. (f) Normalized self-Kerr polariton nonlinearity $U_{j j} / κ_{j}$ versus normalized qubit-polariton cross-Kerr-coupling $2 χ_{j} / κ_{j}$ for lower and upper polaritons. In panels (c)–(f), the working points in the present work and in Ref. [19] are marked by a purple and orange circles, respectively.
Reuse & Permissions
Figure 2
(a) Measured mean distance $D_{e g}^{\exp}$ between the two pointer states of the qubit as a function of drive frequency $ω_{d}$ and power $P_{in}$ . Horizontal dashed lines are guides to the eyes, indicating different regimes of the system. From bottom to top: linear, nonlinear with self-Kerr, higher-order nonlinearities, and strongly driven bare cavity regime. (b) Cross sections of $D_{e g}$ versus $ω_{d}$ normalized by their experimental maximum value at fixed drive powers indicated by the arrows. In green, experimental data; in red, theoretical model in the ancilla-cavity basis [Eq. (8)]; and in dashed purple, theoretical model in the polariton basis [Eq. (7)]. (c) Computed $D_{e g}^{th}$ using the model in Eq. (8). (d) Decomposition of upper polariton into cavity $p_{c}^{η}$ (green) and ancilla $p_{a}^{η}$ (brown) as a function of power $P_{in}$ when the qubit is in $η = g$ (solid lines) or $η = e$ (dashed lines). The proportions $p_{c}^{η}$ and $p_{a}^{η}$ are computed using model (8) and following the drive frequency-power line $ω_{d} (P_{in})$ indicated by the solid and dashed lines in panel (c), corresponding to the qubit states $η = g$ and $η = e$ , respectively.
Reuse & Permissions
Figure 3
Bistability region for the upper polariton mode. (a) Schematic of the hysteretic behavior. Left: Pulse sequence $Ω_{c} (t)$ for a ramp up and ramp down applied to the cavity. This induces a bifurcation up (and down) in $⟨ {\hat{c}}_{out} ⟩_{η}^{up}$ (and $⟨ {\hat{c}}_{out} ⟩_{η}^{down}$ ), at different points $B_{η}^{up}$ (and $B_{η}^{down}$ ). Right: Hysteretic signal $D_{η}^{u d}$ is reconstructed from the output signal during the ramp up and ramp down. (b),(c) Measurement of the bistability hysteretic signal $D_{η}^{u d}$ as a function of the input power $P_{in}$ and frequency $ω_{d} / 2 π$ when the qubit is prepared in (b) $η = g$ or in (c) $η = e$ . The color map corresponds to the experimental data and the contour lines correspond to the theory in Eq. (8).
Reuse & Permissions
Figure 4
Readout fidelity as a function of power and frequency. Superimposed are the computed bistability zones for the upper polariton as shown in Fig. 3. The point of maximum fidelity is indicated by a black star.
Reuse & Permissions
Figure 5
(a) Schematic of the experimental setup. Even though a JPA is present, it is not pumped in the current work and so does not bring amplification. As our reported readout does not require an external quantum-limited amplifier, the part framed with the dashed line can be removed in order to further optimize the output line and enhance the readout performance. (b) Picture of the two parts of the 3D oxygen-free high-conductivity (OFHC) copper cavity with the input-output pin connectors. The sample is placed at the center of the cavity. (c) Optical microscope and SEM pictures of the transmon molecule sample. The Josephson junctions are highlighted in red. The superconducting quantum interference device (SQUID) Josephson junctions implementing the coupling inductance $L_{a}$ are highlighted in green. (d) Lumped element circuit of the transmon molecule.
Reuse & Permissions

Physical Review Applied