Bidirectional Multiphoton Communication between Remote Superconducting Nodes

Quantum communication test beds provide a useful resource for experimentally investigating a variety of communication protocols. Here we demonstrate a superconducting circuit test bed with bidirectional multiphoton state transfer capability using time-domain shaped wave packets. The system we use to achieve this comprises two remote nodes, each including a tunable superconducting transmon qubit and a tunable microwave-frequency resonator, linked by a 2 m–long superconducting coplanar waveguide, which serves as a transmission line. We transfer both individual and superposition Fock states between the two remote nodes, and additionally show that this bidirectional state transfer can be done simultaneously, as well as being used to entangle elements in the two nodes.

Figure 1

Experimental layout. (a) Block diagram for the experiment, comprising two tunable qubits $Q1$, $Q2$ (green), capacitively coupled to two tunable resonators $R1$, $R2$ (orange), in turn coupled via two variable couplers $C1$, $C2$ (purple) to a 2 m–long waveguide (yellow). Circuit representations of these elements are shown in the dashed box. (b) Backside-illuminated optical photograph of fabricated device with false coloring, showing all components including the 2 m–long coplanar waveguide, as well as the printed circuit board to which the die is wirebonded for signal routing. A test pad for detecting shorts is directly above the midpoint of the waveguide. The test pad is physically disconnected prior to the experiment, removing the electrical connection to the waveguide. Test pads and trial Josephson junctions for measuring junction resistances are located to the top right of the waveguide. (c) Optical micrograph of device with false coloring corresponding to components shown in panel (a). The coplanar waveguide is patterned on the same die but is cropped from this image; see panel (b). Microwave XY lines are used to excite the qubits (i.e., for X and Y rotations), Z lines control the qubit frequency (yielding a Z rotation referenced to a system clock), D lines displace the resonators for Wigner tomography, F lines control the resonator frequency, G lines control the coupler, and Rd refers to the readout resonators. Subscripts indicate nodes 1 or 2.

Figure 2

(a) Standing waveguide modes seen by $R1$ at weak coupling. After a single excitation is swapped into $R1$, the coupling to the waveguide is turned on for time ${\tau }_r$, while the resonator is held at a constant frequency. (b) Ramsey-like experiment showing itinerant emission and recapture of a $|0⟩+|1⟩$ state in $R2$. The superposition state is swapped from $Q2$ to $R2$, emitted and recaptured from $R2$ with 20 ns rectangular pulses separated by delay ${\tau }_d$, while the resonator is held at a constant frequency, swapped back to $Q2$, and a $\pi /2$ pulse is applied to $Q2$ before measurement. $P_{e1}$ and $P_{e2}$ are the excitation probabilities of qubits $Q1$ and $Q2$, respectively, after the experimental pulse sequences. Detailed pulse sequences are given in Ref. [30].

Figure 3

Transfer of excited qubit states, from (a) qubit $Q1$ to qubit $Q2$ and from (b) $Q2$ to $Q1$. We excite the emitting qubit, swap the excitation to the adjacent resonator, transmit the excitation as a wave packet to the distant resonator by time-varying control of the couplers between the resonators and waveguide, then finally swap to the receiving qubit. Lines are a guide for the eye. (c) Simultaneous state swaps between the resonators. We initialize resonator $R1$ in a two-photon Fock state while initializing resonator $R2$ in a one-photon Fock state. These states are simultaneously released into the transmission line as itinerant wave packets that are then captured by the receiving resonators, and we use the associated qubit to analyze its associated resonator’s final state. The population of each resonator’s Fock states $|F_n⟩$, $n=0$, 1, 2 is shown as a function of time. Detailed pulse sequences are given in Ref. [30].

Figure 4

(a) Transfer of superposition Fock states. We prepare $|0⟩+|1⟩$ and $|0⟩+|2⟩$ states in resonator $R1$ and transfer these as itinerant wave packets to resonator $R2$. We use the corresponding qubits to reconstruct the Wigner tomograms in both resonators, as described in the main text. The lower graphs show NOON states $|n0⟩+|0n⟩$ with (b) $n=1$ and (c) $n=2$ itinerant transfers between the two tunable resonators. State preparation is described in the main text. Dotted lines indicate the ideal NOON states, while transparent colored bars are the reconstructed density matrices.