#### Overview

**Quantum networks** form an important element of quantum computing and quantum communication systems. In general, quantum networks allow for the transmission of quantum information (quantum bits, also called qubits), between physically separated quantum processors. A quantum processor is a small quantum computer being able to perform quantum logic gates on a certain number of qubits.

#### Overview of the elements of quantum network

The basic structure of a quantum network and more generally a quantum internet is analogous to classical networks. First, we have end nodes on which applications can ultimately be run. These end nodes are quantum processors of at least one qubit. Some applications of a quantum internet require quantum processors of several qubits as well as a quantum memory at the end nodes.

Second, to transport qubits from one node to another, we need communication lines. For the purpose of quantum communication, standard telecom fibres can be used. For networked quantum computing, in which quantum processors are linked at short distances, one typically employs different wavelength depending on the exact hardware platform of the quantum processor.

Third, to make maximum use of communication infrastructure, one requires optical switches capable of delivering qubits to the intended quantum processor. These switches need to preserve quantum coherence, which makes them more challenging to realize than standard optical switches.

Finally, to transport qubits over long distances one requires a quantum repeater. Since qubits cannot be copied, classical signal amplification is not possible and a quantum repeater works in a fundamentally different way than a classical repeater.

#### Quantum networks for computation

In the domain of quantum computing, being able to send qubits from one quantum processor to another allows them to be connected to form a quantum computing cluster. This is often referred to as networked quantum computing, or distributed quantum computing. Here, several less powerful quantum processors are connected together by a quantum network to form one much more powerful quantum computer. This is analogous to connecting several classical computers to form a computer cluster in classical computing. Networked quantum computing offers a path towards scalability for quantum computers, since more and more quantum processors can naturally be added over time to increase the overall quantum computing capabilities. In networked quantum computing, the individual quantum processors are typically separated only by short distances.

#### Quantum networks for communication

In the realm of quantum communication, one wants to send qubits from one quantum processor to another over long distances. This way local quantum networks can be intra connected into a quantum internet. A quantum internet supports many applications, which derive their power from the fact that by transmitting qubits one can create quantum entanglement between the remote quantum processors. Most applications of a quantum internet require only very modest quantum processors. For most quantum internet protocols, such as for example quantum key distribution in quantum cryptography, it is sufficient if these processors are capable of preparing and measuring only a single qubit at a time. This is in contrast to quantum computing where interesting applications can only be realized if the (combined) quantum processors have more qubits that can be simulated easily on a classical computer (more than around 60). The reason why quantum internet applications only need very small quantum processors of often just a single qubit, is because quantum entanglement can already be realized between just two qubits. A simulation of an entangled quantum system on a classical computer cannot simultaneously provide both the same security and speed.

#### Communication lines: physical layer

Over long distances, the primary method of operating quantum networks is to use optical networks and photon-based qubits. Optical networks have the advantage of being able to re-use existing optical fiber. Alternately, free space networks can be implemented that transmit quantum information through the atmosphere or through a vacuum.

#### Fiber optic networks

Optical networks using existing telecommunication fiber can be implemented using hardware similar to existing telecommunication equipment. At the sender, a *single photon* source can be created by heavily attenuating a standard telecommunication laser such that the mean number of photons per pulse is less than 1. For receiving, an avalanche photodetector can be used. Various methods of phase or polarization control can be used such as interferometers and beam splitters. In the case of entanglement based protocols, entangled photons can be generated through spontaneous parametric down-conversion. In both cases, the telecom fiber can be multiplexed to send non-quantum timing and control signals.

#### Free space networks** **

*Free space quantum networks operate similar to fiber optic networks but rely on line of sight between the communicating parties instead of using a fiber optic connection. Free space networks can typically support higher transmission rates than fiber optic networks and do not have to account for polarization scrambling caused by optical fiber.*

Importantly, free space communication is also possible from a satellite to the ground. A quantum satellite capable of distribution entanglement over a distance of 1203 km has been demonstrated. These satellites can play an important role in linking smaller ground based networks over larger distances.

#### Repeaters

Long distance communication is hindered by the effects of signal loss and decoherence inherent to most transport mediums such as optical fiber. In classical communication, amplifiers can be used to boost the signal during transmission, but in a quantum network amplifier cannot be used since qubits cannot be copied – known as the no-cloning theorem. That is, to implement an amplifier, the complete state of the flying qubit would need to be determined, something which is both unwanted and impossible.

#### Trusted repeaters

An intermediary step which allows the testing of communication infrastructure are trusted repeaters. Importantly, a trusted repeater cannot be used to transmit qubits over long distances. Instead, a trusted repeater can only be used to perform quantum key distribution with the additional assumption that the repeater is trusted. Consider two end nodes A and B, and a trusted repeater R in the middle.

A true quantum repeater allows the end to end generation of quantum entanglement, and thus – by using quantum teleportation – the end to end transmission of qubits. In quantum key distribution protocols, one can test for such entanglement. This means that when making encryption keys, the sender and receiver are secure even if they do not trust the quantum repeater. Any other application of a quantum internet also requires the end to end transmission of qubits, and thus a quantum repeater.

Quantum repeaters allow entanglement and can be established at distant nodes without physically sending an entangled qubit the entire distance.

In this case, the quantum network consists of many short distance links of perhaps tens or hundreds of kilometres. In the simplest case of a single repeater, two pairs of entangled qubits are established: and located at the sender and the repeater, and a second pair and located at the repeater and the receiver. These initial entangled qubits can be easily created, for example through parametric down conversion, with one qubit physically transmitted to an adjacent node. At this point, the repeater can perform a bell measurement on the qubits and thus teleporting the quantum state of onto . This has the effect of “swapping” the entanglement such that and are now entangled at a distance twice that of the initial entangled pairs. It can be seen that a network of such repeaters can be used linearly or in a hierarchical fashion to establish entanglement over great distances.

Hardware platforms suitable as end nodes above can also function as quantum repeaters. However, there are also hardware platforms specific only to the task of acting as a repeater, without the capabilities of performing quantum gates.

#### Error correction

Error correction can be used in quantum repeaters. Due to technological limitations, however, the applicability is limited to very short distances as quantum error correction schemes capable of protection qubits over long distances would require an extremely large number of qubits and hence extremely large quantum computers.

Errors in communication can be broadly classified into two types: Loss errors (due to optical fiber/environment) and operation errors (such as depolarization, dephasing etc.). While redundancy can be used to detect and correct classical errors, redundant qubits cannot be created due to the no-cloning theorem. As a result, other types of error correction must be introduced such as the Shor code or one of a number of more general and efficient codes. All of these codes work by distributing the quantum information across multiple entangled qubits so that operation errors as well as loss errors can be corrected.^{[17]}

In addition to quantum error correction, classical error correction can be employed by quantum networks in special cases such as quantum key distribution. In these cases, the goal of the quantum communication is to securely transmit a string of classical bits. Traditional error correct such as Hamming codes can be applied to the bit string before encoding and transmission on the quantum network.