Nonreciprocal quantum information processing with superconducting diodes in circuit quantum electrodynamics

Abstract

Introducing new components and functionalities into quantum devices is critical in advancing state-of-the-art hardware. Here, we propose superconducting diodes (SDs) as a coherent nonreciprocal element in circuit quantum electrodynamics (cQED) architectures. In particular, we use an asymmetric SQUID as an SD controlled with a flux bias. We spectroscopically characterize SD and show that flux bias acts cooperatively with the nonlinear diode response to induce direction-dependent resonance shifts in the transmission spectrum. We use the SD as an elementary component to realize coherent nonreciprocal qubit-qubit coupling. With a minimal two qubit system, we demonstrate a nonreciprocal half-iSWAP gate with tunable Bell-state generation, thereby showcasing the potential of intrinsic nonreciprocity as a tool in coherent control in quantum technologies. Our work enables high-fidelity signal routing and entanglement generation in all-to-all connected microwave quantum networks, where nonreciprocity is embedded at the device level.

Figures (5)

• Figure 1: Superconducting diode (SD) and nonreciprocal qubit-qubit coupling: (a) Circuit of two qubits inductively coupled to a SD. Here, the SD is formed by an asymmetric SQUID (shown in blue) which is biased by external flux, $\Phi_0$. The supercurrent is allowed along the direction of forward bias (shown as bound Cooper pairs), and is blocked along the direction of reverse bias (shown as broken Cooper pairs). (b) Schematic of nonreciprocal coupling due to SD. The broken time reversal ($\mathcal{T}$)-symmetry necessary to induce a diode response generically makes the coupling between qubits to be complex, $J_{12} = Je^{i\phi_{12}}$ with non-local phase $\phi_{12}=\varphi$ is determined by nonreciprocal response by asymmetric mode propagation in SD.
• Figure 2: Spectroscopic characterization of superconducting diode on a two-port network: (a) Transmission spectrum at fixed off-resonant pump frequency $\omega_p /\omega_r= 0.99$, normalized by resonator frequency $\omega_r = 5$ GHz, shows scattering matrix $S(\omega)$ with respect to probe frequency $\omega_{pr}/\omega_r$ for $\delta\omega = 0$. (b) Transmission spectrum with $\delta\omega = 50$ MHz showing clear asymmetric shift between $S_{21}$ and $S_{12}$. (c) Nonreciprocity ratio, $R(\omega)$, for same parameters as in panel (b). For all simulations the following parameter were used $\omega_p / \omega_r = 0.99$, Kerr nonlinearity $\Lambda/\omega_r = 10^{-7}$, two photon loss $\kappa/\omega_r = 10^{-4}$. (d) Third-order Josephson nonlinearity, $c_3/\Delta$ with , for the asymmetric SQUID versus flux $\Phi_b$, and transmission, $\tau_1$ ($\tau_2 = 0.8$).
• Figure 3: Coherent control of population dynamics via effective qubit-qubit coupling through SD and dynamic evolution of concurrence in two qubit system. (a-d) The population dynamics of qubits $n_1(t),n_2(t)$ at $\varphi \in [-\pi/2,0,\pi/2]$ (green, red and blue lines). Panels a,b show $n_1(t),n_2(t)$, respectively with $n_1(t=0),n_2(t=0)=1$, and the system initialization is reversed in panels c,d. (e,f) Concurrence $C_{01}$ and $C_{10}$ plotted against $J t$ for different $\varphi \in [-\pi/2, 0, \pi/2]$. For $\varphi= 0$ (red) the concurrence $C_{01}$ and $C_{10}$ are identical. For $\varphi = \pm \pi/2$ (blue for $C_{01}$ and green for $C_{10}$), we observe that the concurrence grows close to 1.0 signaling maximal entanglement at time scale of half-iSWAP facilitated by SD nonreciprocity. (g) Heatmap for entanglement transfer contrast, $\Delta C(t)$ at $t=\pi/4J$ as a function of $\varphi$ and $\Gamma$. $\Delta C(t=\pi/4J)$ is maximum at $\Gamma/J = 2$ and $\varphi = \pm\pi/2$, and significant nonreciprocity sustains throughout the phase space. (h) $\Delta C(t)$ in variation with $Jt$ and $\varphi$ showing maximum entanglement contrast at $\varphi = \pm \pi/2$ at the scale of time of half-iSWAP. All plots were made with following parameters $\gamma_{1} = 0$, $J=1$, $\Gamma = 0.5$, unless mentioned otherwise.
• Figure 4: Bell state tomographic representation of density matrices of the qubit pairs via linear reconstruction after half-iSWAP ($t = \pi/4J$) applied to qubits. The system is initialized to $\Psi(t=0) = |01\rangle$ for all panels. (a-d) $\textbf{Re}[\rho]$ and $\textbf{Im}[\rho]$ without account of decays, $\gamma_1,\Gamma = 0$ for $\varphi \in [\pi/2,-\pi/2, \pi/4, -\pi/4]$ reproducing Bell state derived in Eq. (\ref{['eq:bell-state-diode']}). Blue colors represent positive values while red represent negative values. Tunable Bell-states are formed with non-trivial phase captured in $\textbf{Im}[\rho]\neq 0$. (e-f) Tomographic reconstruction of density matrix with collective cross decay, $\Gamma/J = 1$ at $\varphi = \pm \pi/2$. The Bell state generation is nonreciprocal determined by cooperative action of diode nonreciprocity and decay. For $\varphi = \pi/2$, $|\Psi_-\rangle$ is generated with nearly $80\%$ fideltiy and for $\varphi = -\pi/2$ no Bell state is formed as fidelity remains below 50% (nearly 30%). This demonstrates the diodes ability to generate and distribute entanglement directionally between the qubit systems.
• Figure S1: Asymmetric SQUID with different CPRs $I_1 (\phi)$ and $I_2 (\phi)$ in the two JJs.