Remote Entanglement via Adiabatic Passage Using a Tunably Dissipative Quantum Communication System

Effective quantum communication between remote quantum nodes requires high fidelity quantum state transfer and remote entanglement generation. Recent experiments have demonstrated that microwave photons, as well as phonons, can be used to couple superconducting qubits, with a fidelity limited primarily by loss in the communication channel [P. Kurpiers et al., Nature (London) 558, 264 (2018); C. J. Axline et al., Nat. Phys. 14, 705 (2018); P. Campagne-Ibarcq et al., Phys. Rev. Lett. 120, 200501 (2018); N. Leung et al., npj Quantum Inf. 5, 18 (2019); Y. P. Zhong et al., Nat. Phys. 15, 741 (2019); A. Bienfait et al., Science 364, 368 (2019)]. Adiabatic protocols can overcome channel loss by transferring quantum states without populating the lossy communication channel. Here, we present a unique superconducting quantum communication system, comprising two superconducting qubits connected by a 0.73 m-long communication channel. Significantly, we can introduce large tunable loss to the channel, allowing exploration of different entanglement protocols in the presence of dissipation. When set for minimum loss in the channel, we demonstrate an adiabatic quantum state transfer protocol that achieves 99% transfer efficiency as well as the deterministic generation of entangled Bell states with a fidelity of 96%, all without populating the intervening communication channel, and competitive with a qubit-resonant mode-qubit relay method. We also explore the performance of the adiabatic protocol in the presence of significant channel loss, and show that the adiabatic protocol protects against loss in the channel, achieving higher state transfer and entanglement fidelities than the relay method.

Figure 1

Experimental device. (a) Optical micrograph of the device (left), with magnified views of one qubit and its associated tunable coupler (right top), and one variable loss coupler (right bottom). (b) A simplified circuit schematic, with two superconducting qubits ($Q_1$ and $Q_2$, blue), coupled by tunable couplers ($G_1$ and $G_2$, purple) to a 0.73 m-long superconducting transmission line (orange). The transmission line is interrupted near $Q_1$ by a tunable switch. The switch comprises two tunable couplers $D_1$ (red) and $D_2$ (teal), with $D_1$ connected to an external $50\mathrm{\Omega }$ load to ground (dashed box), while $D_2$ connects to the remainder of the transmission line. Complete circuit diagram and parameters are provided in [17].

Figure 2

Variable loss transmission channel. (a) Vacuum Rabi swaps between qubit $Q_1$ and four sequential resonant transmission line modes. The coupling is set to $|g_1|/2\pi =5.0\pm 0.1\mathrm{MHz}\ll {\omega }_{\mathrm{FSR}}/2\pi$. (b) Measurement of the energy lifetime $T_{1r}$ of one resonant mode in the transmission line, at 5.351 GHz, with equivalent quality factors $Q$ shown on right; inset shows pulse sequence. A $\pi$ pulse to qubit $Q_1$ puts it in the excited state, and this excitation is swapped into the resonant mode for a time $t$, after which it is recovered and the qubit $P_e$ measured. The corresponding lifetime is measured as a function of transmission line loss, controlled during the lifetime measurement using coupler $D_1$. With $D_1$ turned off, we find the intrinsic lifetime $T_{1r}=3410\pm 40\mathrm{ns}$ (orange); with maximum loss, we find $T_{1r}=28.7\pm 0.2\mathrm{ns}$ (blue). The standard deviation of each data point is smaller than the points. Dashed lines are results calculated with a circuit model; see [17].

Figure 3

Quantum state transfer and remote entanglement using the adiabatic protocol. (a) Adiabatic state transfer between qubits $Q_1$ and $Q_2$, measured with intrinsic loss in the transmission line. Blue (orange) circles represent excited state populations of $Q_1$ ($Q_2$) measured simultaneously at time $t$. Left inset: Control pulse sequence. The couplers are set so that coupling $g_2$ starts at its maximum with $g_1$ set to zero. Dissipation in the resonant channel mode is controlled using $D_1$, here, set to zero coupling. Right inset: Quantum process tomography, yielding a process fidelity ${\mathcal{F}}_p=0.96\pm 0.01$. (b) Adiabatic remote entanglement. Right inset shows control pulse sequence: With $Q_1$ initially prepared in $|e⟩$, $G_1$ and $G_2$ are controlled using the adiabatic protocol to share half of $Q_1$’s excitation with $Q_2$, resulting in a Bell singlet state $|{\psi }^{-}⟩=(|eg⟩-|ge⟩)/\sqrt{2}$. Blue (orange) circles represent excited state populations of $Q_1$ ($Q_2$) measured simultaneously at time $t$. Left inset: Reconstructed density matrix of the final Bell state, yielding a state fidelity ${\mathcal{F}}_s=0.964\pm 0.007$ and concurrence $\mathcal{C}=0.95\pm 0.01$. In all panels, dashed lines are from master equation simulations accounting for channel dissipation and qubit imperfections (see [17]).

Figure 4

Quantum communication in the presence of channel loss, using both the relay method and adiabatic protocol. (a) Measured transfer efficiency $\eta$ (left) and process fidelity ${\mathcal{F}}_p$ (right) for the adiabatic protocol (red) and the relay method (blue), for different resonant channel mode lifetimes $T_{1r}$, with equivalent quality factors $Q$ shown on top. (b) Measured Bell state fidelity ${\mathcal{F}}_s$ (left) and concurrence $\mathcal{C}$ (right) for adiabatic protocol (red) and relay method (blue). In all panels, error bars are 1 standard deviation; red and blue dashed lines are from simulations including all sources of loss, and black dashed lines are from a master equation simulation for the adiabatic protocol with no $Q_1$ spurious coupling loss (see [17]).