Quantum Communication with Time-Bin Encoded Microwave Photons

Heralding techniques are useful in quantum communication to circumvent losses without resorting to error-correction schemes or quantum repeaters. Such techniques are realized, for example, by monitoring for photon loss at the receiving end of the quantum channel while not disturbing the transmitted quantum state. We describe and experimentally benchmark a scheme that incorporates error detection in a direct quantum channel connecting two transmon qubits using traveling microwave photons. This is achieved by encoding the quantum information as a time-bin superposition of a single photon, which simultaneously realizes high communication rates and high fidelities. The presented scheme is straightforward to implement in circuit quantum electrodynamics and is fully microwave controlled, making it an interesting candidate for future modular quantum-computing architectures.

Figure 1

A schematic representation of the pulse sequence implementing the time-bin encoding process at (a) the sender and (b) the receiver. In the level diagrams, the gray vertical lines represent Hamiltonian matrix elements due to microwave drive between transmon levels, while the diagonal ones show the transmon-resonator coupling. (a) The qubit state is initially stored as a superposition of $|g0⟩$ (blue dot) and $|e0⟩$ (red dot). The first two pulses map this state to a superposition of $|e0⟩$ and $|f0⟩$ and the third pulse transfers $|f0⟩$ into $|g0⟩$ while emitting a photon in time bin $a$ (see the red symbol for the photon in mode $a$). Then, after $|e0⟩$ is swapped to $|f0⟩$, the last pulse again transfers $|f0⟩$ into $|g0⟩$ and emits a photon in time bin $b$. (b) Reversing the protocol, we reabsorb the photon, mapping the time-bin superposition back onto a superposition of transmon states. (c) A simplified schematic of the circuit quantum-electrodynamics (QED) setup. At each of the nodes, a transmon (orange) is capacitively coupled to two Purcell-filtered resonators, which are used for readout (gray) and remote quantum communication (yellow). The directional quantum channel consists of a semirigid coaxial cable intersected by an isolator, modified from Ref. [21].

Figure 2

(a) The pulse scheme used to characterize the time-bin encoding protocol for transferring qubit states between two distant nodes using quantum-process tomography (QPT). ${}^{\zeta }{R}_{ij}^{\varphi }$ labels a Gaussian derivative-removal-by-adiabatic-gate (DRAG) microwave pulse [54, 55] for the transition between states $i$ and $j$ (specifically, the transmon transitions $|g⟩\leftrightarrow |e⟩$ and $|e⟩\leftrightarrow |f⟩$ and the transmon-resonator transition $|f0⟩\leftrightarrow |g1⟩$) of angle $\varphi =\{\pi /2,\pi \}$ around the rotation axis $\zeta =\{x,y\}$. If no axis is specified, the pulses induce rotations around the $x$ axis. (b) The real part of the qutrit density matrix ${\rho }_{\mathrm{cor}}$ for the input state $|-⟩=(|g⟩-|e⟩)/\sqrt{2}$ after the state-transfer protocol, reconstructed correcting for measurement errors. The magnitude of each imaginary element of the density matrix is $<0.017$. (c) The projection of ${\rho }_{\mathrm{cor}}$ (b) onto the $ge$ subspace ${\rho }_{\mathrm{cor}}^{\mathrm{pr}}$ performed numerically, which we use to reconstruct the process matrix ${\chi }_{\mathrm{cor}}^{\mathrm{pr}}$ [absolute value shown in (d)]. The colored bars show the measurement results and the gray wire frames the ideal density or process matrix, respectively. The results of numerical master-equation simulations are depicted as red wire frames.

Figure 3

(a) The pulse scheme for generating remote entanglement between nodes A and B (see text for details). (b) The real part of the two-qutrit density matrix ${\rho }_{\mathrm{cor}}$, reconstructed after execution of the time-bin remote-entanglement protocol using measurement-error correction. The colored bars indicate the measurement results, the ideal expectation values for the Bell state $|{\psi }^{+}⟩=(|g_A,e_B⟩+|e_A,g_B⟩)/\sqrt{2}$ are shown as gray wire frames, and the results of a master-equation simulation are shown as red wire frames. The magnitude of the imaginary part of each element of the density matrix is $<0.024$. (c) The numerical projection of the ${\rho }_{\mathrm{cor}}$ onto the $ge$ subspace to obtain the two-qubit density matrix ${\rho }_{\mathrm{cor}}^{\mathrm{pr}}$, which is in excellent agreement with our MES (trace distance of $0.028$).

Figure 4

(a) The pulse scheme for generating remote entanglement between nodes A and B. The probability that a quantum jump from $|f⟩\to |e⟩$ or $|e⟩\to |g⟩$ of the qutrit at node A (b) or node B (c) is detected during the time-bin remote-entanglement protocol. The data are based on 2000 stochastic trajectories of a numerical master-equation simulation (see Appendix pp1 for details).

Figure 5

A false-color micrograph of a sample of the same design as used for node A. The circuit elements are color coded as in Fig. 1. The inset shows a scanning electron micrograph of the asymmetric superconducting quantum-interference device (SQUID) with a ratio of 5:1 between the areas of the Josephson junctions used in the transmon (modified from Ref. [21]).