Enhancing qubit readout fidelity with two-mode squeezing of the coherent measurement signal

Abstract

The ability to perform high-fidelity quantum nondemolition qubit readout is pivotal for the realization of large and powerful quantum computers. Such readout of superconducting qubits is generally enabled by amplifying the weak dispersive measurement signals using phase-preserving quantum-limited Josephson amplifiers with sufficient gain to dilute the contribution of the added noise by the output chain. Here, we further enhance the qubit readout fidelity by (1) simultaneously measuring the two-mode squeezed states of the amplified readout signals at the signal and idler frequencies of the nondegenerate amplifier and (2) coherently combining them at the classical processing stage following a relative rotation that maximizes the signal to noise ratio of the qubit-encoded readout quadrature. Such readout scheme exhibits enhancement in the readout fidelity for all practical values of amplifier gain and noise added by the output chain and is fully compatible with frequency multiplexed setups used in large quantum processors.

Figures (5)

• Figure 1: Harnessing two-mode squeezing of amplified qubit readout signals.a Illustration of a dispersive qubit readout signal amplified by a nondegenerate quantum-limited amplifier (e.g., JM) connected to two output lines. Antisqueeezing in the $I$ ($Q$) quadrature carrying (lacking) the qubit state information can be obtained in scenario b (c) by coherently combining the simultaneous $IQ$ measurements referred back to the output ports $a$ and $b$ of the JM and rotated by a relative phase of $\pi$ ($0$). Using the processing protocol of b (c) we get an enhancement (reduction) in the qubit readout fidelity in comparison to the standard readout with phase-preserving quantum-limited amplification (represented by the measurement result depicted in the upper arm of a). In this illustration, we use low $G=2$, $G_{\rm{sys}}=4$, and $N_{\rm{sys}}=1$ to keep the size of the 2D scatter at the output of the HEMTs relatively small so that the main features of the readout method are not obscured. We also use $\theta=54^{\circ}$.
• Figure 2: Qubit readout fidelity measured using mode a, b and the combined mode ab of the JM for different gains. The following applies to the various gains listed on the left side of the figure. a (b) Readout measurement shots in the $IQ$ plane taken with mode a (b) corresponding to initialization of the qubit in the $g$ and $e$ states. c (d) Histograms of the data in a (b) taken along quadrature $I$. e The readout fidelity of the combined mode ab versus the relative rotation angle $\phi$. f (g) same as a (b) obtained for the combined mode ab with $\phi=\pi$ ($\phi=0$). h (i) same as c (d) corresponding to the data in f (g). g The extracted average photon number of the combined mode for states $g$ and $e$ versus $\phi$. The solid curves in the various histogram plots correspond to double Gaussian fits. All measurements are taken at a fixed $\bar{n}_{\rm{in}}=90$.
• Figure 3: The average photon number at the JM output, $R$, and $F$ versus $\bar{n}_{\rm{in}}$. The following applies to the various gains listed on the left side of the figure. a The data represent measured average photon numbers at the JM output for mode $a$ ($\bar{n}_a$) and $b$ ($\bar{n}_b$) corresponding to the qubit $g$ (blue and cyan) and $e$ states (red and magenta). The solid and dashed black lines are fits based on Eqs. (\ref{['n_a_bar_text']}) and (\ref{['n_b_bar_text']}). b is similar to a. The data represent the fictitious average photon number at the JM output for the combined mode $ab$ corresponding to $\phi=0$ ($\bar{n}_{ab,0}$) and $\phi=\pi$ ($\bar{n}_{ab,\pi}$). The dashed and solid black lines are fits based on Eqs. (\ref{['n_ab_bar_pi_r_text']}) and (\ref{['n_ab_bar_zero_r_text']}). c The power SNR ($R$) versus $\bar{I}^2_{\rm{in}}$. The circles, squares, and diamonds correspond to $R$ measured for mode $a$, the combined mode $ab$ that maximizes $R$, and minimizes it, respectively. The green and black solid lines and the black dashed line are theory fits based on Eqs. (\ref{['R_a_uniform_r_text']}), (\ref{['R_ab_max_text']}), and (\ref{['R_ab_min_text']}), respectively. d Assignment fidelity versus $\bar{n}_{\rm{in}}$ measured with mode $a$ (green circles), mode $b$ (blue stars), combined mode $ab$ that maximizes $R$ (black squares), and minimizes it (black diamonds). The green and black solid curves and the black dashed curve are theory fits obtained by substituting the results of Eqs. (\ref{['R_a_uniform_r_text']}), (\ref{['R_ab_max_text']}), and (\ref{['R_ab_min_text']}) in Eq. (\ref{['F_vs_R']}), respectively.
• Figure 4: Calculated dependence of $R$ and $F$ on JM gain $G$ and added noise by the output chains $N_{\rm{sys}}$.a$R$ obtained for mode $a$ (Eq. (\ref{['R_a_uniform_r_text']})). b maximum $R$ obtained for the combined mode $ab$ (Eq. (\ref{['R_ab_max2_text']})). c Calculated ratio $R_{ab}/R_a$ of the metrics in panels b and a. d$F$ obtained for mode $a$ (using Eqs. (\ref{['R_a_uniform_r_text']}) and (\ref{['F_vs_R']})). e maximum $F$ obtained for the combined mode $ab$ (using Eqs. (\ref{['R_ab_max2_text']}) and (\ref{['F_vs_R']})). c Calculated difference, i.e., $F_{ab}-F_a$, of the fidelities in panels e and d. In panels a, b, d, e, $\bar{I}^2_{\rm{in}}=5$ is used. All calculations are done for equal added noise by the output chains, i.e., $N_{\rm{sys}} \equiv N_{\rm{sys},a}=N_{\rm{sys},b}$.
• Figure 5: Calculated fidelity versus $N_{\rm{sys}}$ for fixed gains.a and b show cross sections of the calculated $F_a$ (black), $F_{ab}$ (blue), and $\Delta F=F_{ab}-F_{a}$ versus $N_{\rm{sys}}$ of Fig. \ref{['RandFvsGandN']}, taken at fixed JM gains of $10$ dB (a) and $20$ dB (b).