Intracity Quantum Communication via Thermal Microwave Networks

Communication over proven-secure quantum channels is potentially one of the most wide-ranging applications of currently developed quantum technologies. It is generally envisioned that in future quantum networks, separated nodes containing stationary solid-state or atomic qubits are connected via the exchange of optical photons over large distances. In this work, we explore an intriguing alternative for quantum communication via all-microwave networks. To make this possible, we describe a general protocol for sending quantum states through thermal channels, even when the number of thermal photons in the channel is much larger than 1. The protocol can be implemented with state-of-the-art superconducting circuits and enables the transfer of quantum states over distances of about 100 m via microwave transmission lines cooled to only $T=4\mathrm{K}$. This opens up new possibilities for quantum communication within and across buildings and, consequently, for the implementation of intracity quantum networks based on microwave technology only.

Popular Summary

Communication over secure quantum channels is potentially one of the most wide-ranging applications of quantum technologies. The security stems from the encoding of information in fragile superpositions of individual photons, which are destroyed by any attempt to extract information from them. This fragility generally restricts quantum communication to the optical domain, where photons can travel over large distances without being absorbed or distorted. Also at optical frequencies, the detrimental effect of thermal radiation, which would overwhelm the weak quantum signal at microwave or radio frequencies, is negligible. We show that, surprisingly, this common point of view is not as restrictive as is usually assumed, and we describe a method for sending individual quantum states through thermal networks that could enable microwave-based quantum communication across buildings or even cities.

The key ingredient in our protocol is the addition of a high-quality microwave oscillator that connects a qubit (the quantum equivalent of a digital bit) to the communication channel. The oscillator is used to coherently cancel thermal noise, and it reduces residual imperfections with quantum error correction. Our protocol can be implemented with state-of-the-art superconducting circuits, which are currently one of the most advanced systems for quantum information processing but must be operated at millikelvin temperatures that are achievable only with expensive refrigerators. With our new method, quantum signals could be exchanged between two refrigerators located in different rooms, or even different buildings, by connecting them via microwave transmission lines cooled to a more convenient temperature of 4 K.

Even when realistic imperfections are taken into account, our method considerably extends the range of temperatures and frequencies over which quantum communication becomes possible. In the long run, this could open up completely new ways for distributing quantum information over medium and large distances using microwave technologies.

Figure 1

(a) Sketch of a thermal quantum network, where two nodes (for example, two superconducting qubits located inside separated dilution refrigerators) are connected via a unidirectional quantum communication channel at finite temperature $T_{\mathrm{ch}}$. (b) For the implementation of a noise-resilient transfer protocol, the qubit state is first mapped onto an intermediary oscillator. The oscillator is then coupled to the incoming and outgoing fields of the channel, $f_{\mathrm{in},\mathrm{i}}(t)$ and $f_{\mathrm{out},\mathrm{i}}(t)$, via a tunable decay rate ${\gamma }_i(t)$, which can be realized, for example, by a flux-tunable quantum interference device [45, 46, 47].

Figure 2

(a) Occupation number of qubits 1 and 2 ($L_i\equiv {\sigma }_i^{-}$) during the evolution generated by $H_{\mathrm{int}}$ in Eq. (3) and for a thermal occupation $N_{\mathrm{ch}}=2$ of the channel mode. (b) Comparison of the average fidelity $\overline{\mathcal{F}}$ for quantum states encoded locally in a two-level system (TLS) and a harmonic oscillator. (c) Average transfer fidelity for the case, where the dynamics of the local oscillators is restricted to the $N_{\mathrm{loc}}$ lowest number states.

Figure 3

(a) Example control pulses ${\gamma }_i(t)$ for implementing a perfect state transfer over long distances via a thermal quantum communication channel. Here, ${\gamma }_1(t)=\gamma e^{\gamma (t-t_{\mathrm{p}})}/(2-e^{\gamma (t-t_{\mathrm{p}})})$ for $t<t_{\mathrm{p}}/2$ and ${\gamma }_1(t)=\gamma$ for $t\ge t_{\mathrm{p}}/2$ [55]. The recapture pulse ${\gamma }_2(t)$ is chosen to be symmetric with respect to $t=t_{\mathrm{p}}/2$, and for all plots, a total pulse duration of $t_{\mathrm{p}}=20{\gamma }^{-1}$ has been assumed. (b) The resulting evolution of the populations of each intermediary oscillator for an initial state $|{\psi }_q⟩=|1⟩$. The green dashed line shows the average transfer fidelity for the same pulse sequence. (c) Expectation value of the photon number in the channel measured in between node 1 and node 2 with a detector of bandwidth $\mathrm{\Omega }/\gamma =4$. The individual curves show the results for $N_{\mathrm{ch}}=0$ and $|{\psi }_q⟩=|1⟩$ (green line), $N_{\mathrm{ch}}=5$ and $|{\psi }_q⟩=|1⟩$ (blue line), and $N_{\mathrm{ch}}=5$ and $|{\psi }_q⟩=|0⟩$ (red line).

Figure 4

(a) Channel losses are modeled by a series of beam splitters with reflectance $\mathrm{\Delta }R=\mathrm{\Delta }z/L_{\mathrm{ab}}$. For a homogeneous waveguide, the total loss can be taken into account by mixing the outgoing field of node 1 with a thermal field $h_{\mathrm{in}}$ on a beam splitter with reflectance ${ϵ}_{\mathrm{ch}}=1-e^{-L/L_{\mathrm{ab}}}$. (b) Illustration of the code words $|W_{\sigma }⟩$ used for correcting single-photon loss errors (left) and for correcting single-photon loss and single-photon absorption errors (right). (c) The average transfer fidelity is shown for a state transfer protocol without error correction (green solid line), for the case when single-photon losses are corrected (blue dotted line), and for the case when both single-photon loss and single-photon absorption errors are corrected (red dashed line).

Figure 5

(a) The coherent backscattering of fields by defects or imperfect connections is modeled by a pointlike scatterer with reflectance $|r_s{|}^2=1-|t_s{|}^2$, located at a distance $L_s$ from the first node. (b) Shape of the emitted wave packet (solid line) measured after the scatterer at the input of node 2. For this plot, ${\gamma }_1(t)$ is the same as in Fig. 3, ${\tau }_s=2L_s/v_{\mathrm{g}}=0.15t_{\mathrm{p}}$, $t_{\mathrm{p}}=20{\gamma }^{-1}$, $r_s=\sqrt{1-t_s^2}=0.6$, and a detuning $\delta ={\omega }_1-{\omega }_2=\gamma$ between the two local oscillators has been assumed. The green dashed line shows the unperturbed wave packet for $r_s=0$. (c) Shape of the recovery pulse ${\gamma }_2(t)=|{\gamma }_2(t)|e^{-i2{\varphi }_2(t)}$ with a final phase ${\varphi }_2(2t_{\mathrm{p}})\simeq 2.03\times \delta t_{\mathrm{p}}$ obtained from a numerical optimization of the state transfer problem. (d) Plot of the resulting evolution of the population of each oscillator for an initial state $|{\psi }_q⟩=|1⟩$. The dashed line shows the population in the second oscillator for the original pulse ${\gamma }_2(t)$ given in Fig. 3.