Millimeter Wave Readout of a Superconducting Qubit

Abstract

Millimeter waves are emerging as an enabling technology for connecting and enhancing different quantum platforms such as Rydberg atoms, optomechanics, and superconducting qubits. In this work, we focus on the interaction between millimeter wave photons and conventional transmon qubits, specifically for qubit readout. We study a circuit quantum electrodynamic (cQED) system consisting of a millimeter-wave cavity at $ω_r = 2π\times 34.7$ GHz and a transmon qubit at $ω_q = 2π\times 3.1$ GHz coupled at rate $g = 2π\times 1.3$ GHz. With such a large detuning between cavity and qubit, $ω_r/ω_q > 10$, we are able to suppress drive induced unwanted state transitions, enabling strong drives for qubit readout. We measure no resonant state transitions up to $1,000$ drive photons and readout the qubit state with more than $100$ photons to achieve a measurement fidelity greater than 99% without the aid of a quantum limited amplifier.

Figures (14)

• Figure 1: Circuit QED system with the transmon operating in the microwave frequency range and the readout resonator in the millimeter wave frequency range. (a) Transmon qubit coupled to electric field of millimeter wave frequency 3D cavity mode. The amplitude and direction of the simulated electric field are indicated by the size and orientation of the displayed arrows. (b) Optical micrograph of the transmon qubit used in this work. (c) The readout mode is implemented as the fundamental mode of a 3D cavity machined out of 6061 Al. The transmon is fabricated on a sapphire substrate with Al paddles and a Josephson junction (supplemental section \ref{['supp:fab']}). (d) The readout mode and transmon are capacitively coupled at rate $g = 2\pi \times 1.3G Hz$.
• Figure 2: Floquet simulation of a charge driven transmon for varying drive frequency $\omega_d$ and normalized strength $\xi^2$ averaged over possible values of gate charge. The transmon's deviation from its ideal displaced state is shown for initial states $\left|0\right\rangle$ and $\left|1\right\rangle$ (upper and lower panels respectively) over the range of typically chosen readout frequencies and extending in to the millimeter wave range. The deviation is characterized by the parameter $\Theta_i$ indicating hybridization of the initial state with higher energy states of the transmon. We observe large hybridization and potential for state transition over much of the drive frequency and strength space of conventional qubit readout. With the readout drive at millimeter wave frequencies (above $30G Hz$), the simulations predict drive induced resonant state transitions are highly suppressed (See supplemental section \ref{['supp:floquet']} for more details).
• Figure 3: Experimental data probing drive induced transitions of the transmon. We probe the effect of a drive near the readout frequency with varying strength on the transmon qubit state. The transmon is prepared in either (a) $\left|0\right\rangle$ or (b) $\left|1\right\rangle$ 20,000 times. We track the state of the transmon after applying a variable strength drive with photon number $\bar{n}_d$ and measure the probability of transitioning from the initial state to various final states. With the transmon initialized in the $\left\{ \left|0\right\rangle, \left|1\right\rangle \right\}$ subspace, we find no observable resonant state transitions. At drive photon numbers $\bar{n}_d \gtrsim 1,000$, we observe the onset of the quantum to classical regime. The transmon state is distributed over many levels as seen by the rise in the probability of transition to the $\{\left|n\right\rangle\}_{n\geq4}$ manifold while initialized in either $\left|0\right\rangle$ or $\left|1\right\rangle$.
• Figure 4: Experimental data of reading out qubit state with increasing photon number. We prepare the qubit state in $\left|0\right\rangle$ and $\left|1\right\rangle$ 50,000 times and readout for a fixed time of $\tau_r = 780n s$. As we increase the number of readout photons we observe an improvement in the measurement fidelity, (a) $\bar{n}_r = 1, \mathcal{F}_{\left|0\right\rangle} =\mathcal{F}_{\left|1\right\rangle} = 0.535$, (b) $\bar{n}_r = 10, \mathcal{F}_{\left|0\right\rangle} =\mathcal{F}_{\left|1\right\rangle} = 0.790$, (c) $\bar{n}_r = 109, \mathcal{F}_{\left|0\right\rangle} =\mathcal{F}_{\left|1\right\rangle} = 0.992$.
• Figure S1: Readout resonator response when the transmon is initialized in $\left\{ \left|0\right\rangle, \left|1\right\rangle, \left|2\right\rangle, \left|3\right\rangle \right\}$. The readout resonator is shifted by the cross-Kerr shift $\chi_n$ when the transmon is prepared in state $\left|n\right\rangle$. The arrow indicates the frequency used for multi state readout shown in Figure \ref{['fig:multistate_readout']}.