INSIGHTS

6 min read

#### by Hassan Shapourian

##### Published on 09/12/2023

##### Last updated on 02/05/2024

##### Published on 09/12/2023

##### Last updated on 02/05/2024

Future optical networks empowered with quantum communication capabilities are one of the pillars of quantum technologies. Beyond facilitating the transmission of classical signals, these networks unlock the potential for exchanging quantum information, ushering in transformative possibilities such as unconditional security, distributed quantum computing, and distributed sensing. In this blog post, we discuss the initial steps to elevate a conventional optical network infrastructure into a quantum-enabled network—a process we term "quantum network planning." For more details check out our paper.

Before delving into details, it's worth revisiting some fundamental concepts (see our earlier blog post for more details). A paramount challenge in realizing quantum communication (through optical fiber) over long distance stems from the signal attenuation (or photon loss). The principles of quantum mechanics preclude the straightforward application of classical techniques like signal amplification. To address this issue, several schemes, collectively known as quantum repeaters, have emerged over the years, drawing inspiration from their classical counterparts. The core concept is to place a number of repeater stations at intermediate distances to effectively counteract the photon loss. These quantum repeater schemes are generally divided into two categories in terms of the type of required communications: two-way and one-way repeaters.

Compared to one-way repeaters which require forward quantum error correction, two-way repeaters feature simpler quantum hardware and can handle longer distances but come with two drawbacks: latency and congestion. Nevertheless, until the advent of a compact quantum computer equipped with quantum error correction capabilities, two-way repeaters remain the preferred contender for long-distance quantum communication. It's worth recalling that the aim of two-way schemes is to distribute end-to-end entanglement links connecting pairs of end users. This overarching objective is why these schemes are often coined as "entanglement distribution networks."

As mentioned, quantum networks use optical communication links. In envisioning a pragmatic and economical approach to constructing these networks, a compelling strategy is then to capitalize on our already established optical network infrastructure. The first step to build entanglement distribution networks in an existing infrastructure entails the art of identifying optimal sites for embedding quantum hardware.

A natural candidate for these strategic positions is the existing routers and EDFAs (erbium-doped fiber amplifier) across the optical network fabric. We formulate the repeater placement problem as an integer linear programming (ILP) problem. Our framework takes an existing network topology with possible locations for quantum hardware as an input and solve the allocation problem with the objective of maximizing the quantum network utility. As a result, it yields how many repeaters are needed, where to place them, and how to allocate quantum hardware resources such as quantum memories to different user pairs. We further obtain the minimum value for the coherence time of quantum memories.

Our framework is designed based on two key principles:

**Fairness**: The network throughput for user pairs are determined according to their end-to-end distance. For instance, user pairs with similar distances receive similar entanglement bit (ebit) rates. If such user pairs use the same repeater node, then quantum memories will be distributed equally between them.

**Efficiency**: More quantum repeaters are not necessarily better. Since quantum hardware is noisy, putting more repeaters on a path increases the overall noise level. Our framework takes into account not only the ebit generation rate but also the quality of end-to-end entanglement (using final state fidelity).

Let us illustrate what our network planning framework does through a toy example. Consider an existing optical network in the form of a linear chain with two users at the end.

Our optimization scheme finds that we need to upgrade the middle node to a quantum repeater as shown below.

We further apply our quantum network planning framework to several real-world network topologies including Energy Sciences Network (ESnet). We consider 6 user pairs in the East Coast and the Midwest. The ESnet core and edge nodes are shown in Figure 3 as green circles and red squares (here, we used the network graph representation introduced in Figures 1 and 2). Since the original links are long (greater than hundred miles), we have augmented the network graph by adding auxiliary nodes so that no optical links are longer than 60mi. We assume we can use at most 20 quantum repeaters across the network.

The optimal solution for the ESnet is shown in the lower panel of Figure 3. The longest link in the solution is approximately 125mi long which implies that we need the 10,000 quantum memories at each quantum repeater (for multiplexing) with at least 2 millisecond coherence time to achieve an average network throughput of 3 ebits per request. To put numbers in perspective, coherence time for quantum memories spans a wide range from microseconds to hours depending on the technology. The most promising candidate in terms of potential for scalability and multiplexing is color center defects in crystals with the coherence time of nearly 10 milliseconds (c.f. Table VI of this review article).

**Conclusion**

We developed a framework to guide the first steps of planning a quantum network using the existing optical network infrastructure and formulated it as an optimization problem (in the form of ILP).

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