Autonomous stabilization of remote entanglement in a cascaded quantum network

Abstract

Remote entanglement between widely separated qubits is a fundamental quantum phenomenon and a critical resource for quantum information applications. Generating entanglement between independent qubits separated by arbitrary, potentially large distances requires propagating quantum states, and is typically achieved using pulsed protocols combining distinct steps of local entanglement generation followed by distribution. This necessity raises an intriguing question: Can remote entanglement can be stabilized indefinitely, instead of only periodically regenerated and redistributed after decay? Here, we demonstrate that this is indeed possible, reporting autonomous stabilization of entanglement between two separate superconducting-qubit devices. Combining nonreciprocal waveguide coupling and local driving, we experimentally realize a symmetry-based coherent quantum-absorber scheme in a cascaded network. We quantify the degree of entanglement through quantum state tomography, finding that the protocol's entangling power is severely limited by imperfections that break the required symmetry. We show, however, that a modified protocol based on an alternate symmetry is far more robust, enabling us to achieve a concurrence approaching 0.5, a limit set only by local loss in the network. Our results enable on-demand delivery of high-fidelity entanglement in modular quantum processors and networks and pave the way for autonomously protecting distributed quantum information.

Figures (12)

• Figure 1: Setup for driven-dissipative remote entanglement stabilization. (a) Two qubits coupled to a unidirectional waveguide can be driven into an entangled steady state. Without loss, this coherent quantum-absorber system can exhibit an entangled dark state. (b, c) To demonstrate this idea, the two qubits are driven into the steady state at the same drive frequency, at a detuning $\varepsilon$ from their center frequency. Two-qubit quantum state tomography reveals the entanglement. (d) The experimental setup consists of two independent superconducting transmon qubit devices, connected by a low-loss coaxial cable link that is made unidirectional through a microwave circulator. Qubit state readout is performed through a dispersively coupled readout resonator that is not shown in this schematic (Appendix \ref{['app:setup']}).
• Figure 2: Network characterization. (a) The decay time of each qubit from the excited ($\ket{1}$) to the ground ($\ket{0}$) state is determined by the waveguide coupling, and measured in a conventional $T_1$ experiment. Symbols: experimental data. Solid lines: exponential fits, yielding $T_1$ times of 300 ns for qubit A (blue), and 130 ns for qubit B (orange). Dashed lines: for comparison, qubit relaxation measured prior to making the waveguide connection. (b) Simultaneously driven Rabi oscillations on both qubits. The qubits are $26.6$ MHz detuned from each other. The CQA model predicts entanglement stabilization at $\varepsilon=0$. (c) Measurement of transmission loss through coherent scattering. The magnitudes of the coherently scattered and subsequently emitted signals (data points) can be inferred from a numerical fit to the responses (solid black lines). Comparing the responses yields the efficiency of the unidirectional link.
• Figure 3: Steady-state entanglement with the CQA scheme. (a) Measured concurrence (markers) as a function of Rabi drive amplitude, with $\Omega_A = \Omega_B$ and $\varepsilon=0$. Solid line: Fit to a master equation simulation that includes all loss parameters as well as Stark shifts of the transmons (Appendix \ref{['app:analysis']}). (b) Measured concurrence as a function of drive duration for $\Omega/2\pi = 12\,\mathrm{MHz}$, indicated by the green arrow in (a). (c) Measured expectation values (solid bars) of all two-qubit correlators at $\Omega/2\pi = 12\,\mathrm{MHz}$. Black outlines: simulated expectation values.
• Figure 4: Improving concurrence with synthetic squeezing symmetry. (a) Simulated steady-state concurrence as a function of drive detuning $\varepsilon$ and drive strength $\Omega_A$ for different ratios $\Omega_B/\Omega_A$. (b) Measured steady-state concurrence (markers) as a function of drive strength $\Omega_A$ for parameters indicated by colored arrows in (a). Solid lines are fits to master equation simulations. Teal curve was shown in Fig. \ref{['fig:CQA']}a. (c) Two-qubit correlators for the state with the highest concurrence (maximum concurrence of the red curve in (a)). The measured state has $96\%$ fidelity with the simulated state. (d) Simulated maximum concurrence achievable in the present system as a function of the ratio of qubit-cable coupling strengths. The purple (green) lines show the maximum concurrence that can be stabilized using the CQA (synthetic TMS) symmetry. Dashed lines: optimal performance given the systems intrinsic loss rates (transmission loss, dephasing and intrinsic relaxation rates); solid lines: predicted performance in the absence of any loss. Black dashed lines: the experimental system investigated in this work; gray shading indicates uncertainty in the concurrence.
• Figure 5: Experimental Setup. (a) Most of the wiring diagram follows standard best practices krinner2019engineering. Noteworthy components: low-loss circulator: Quinstar Technology QCY-G0400801AUZ 4-8 GHz cryogenic circulator with $0.15$ dB typical insertion loss and $< 0.08$ dB insertion loss at $6$ GHz. Probe Line Low pass filters: 12 GHz (K$\&$L 5L250-10200). Output line: double-stage isolators (Low Noise Factory LNF-ISCIC4$\_$12A); HEMT amplifier (Low Noise Factory LNF-LNC4$\_$8C); room temperature low-noise amplifier (Low Noise Factory LNF-LNR4$\_$14C). Room temperature electronics: signal modulation and demodulation: Quantum Machines OPX+ and Quantum Machines Octave; VNA: Keysight P9374A. (b) The assembly of the experiment.