# Quantum network

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.

## Basics

### 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[1] 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[2]). 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 can not simultanously provide both the same security and speed.

### 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 fibers 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.

## Applications

A quantum internet supports numerous applications, enabled by quantum entanglement. In general, quantum entanglement is well suited for tasks that require coordination, synchronization or privacy.

Examples of such applications include quantum key distribution[3][4], clock synchronization,[5] protocols for distributed system problems such as leader election or byzantine agreement[citation needed], extending the baseline of telescopes,[6] as well as position verification, secure identification and two-party cryptography in the noisy-storage model. A quantum internet also enables secure access to a quantum computer[7] in the cloud. Specifically, a quantum internet enables very simple quantum devices to connect to a remote quantum computer in such a way that computations can be performed there without the quantum computer finding out what this computation actually is.

## Elements of a quantum network

### End nodes: quantum processors

Telecommunication lasers and parametric down-conversion combined with photodetectors can be used for quantum key distribution. In this case, the end nodes can in many cases be very simple devices consisting only of beamsplitters and photodetectors.

However, for many protocols more sophisticated end nodes are desirable. These systems provide advanced processing capabilities and can also be used as quantum repeaters. Their chief advantage is that they can store and retransmit quantum information without disrupting the underlying quantum state, and perform quantum logic gates.

One way of realizing such end nodes is by using color centers in diamond, such as the Nitrogen-vacancy center. This system forms a small quantum processor featuring several qubits. Small scale quantum algorithms and quantum error correction[8] has already been demonstrated in this system, as well as the ability to entangle two remote[9] quantum processors, and perform deterministic quantum teleportation.[10]

Another possible platform are quantum processors based on Ion traps Also, cavity quantum electrodynamics (Cavity QED) is one possible method of doing this. In Cavity QED, photonic quantum states can be transferred to and from atomic quantum states stored in single atoms contained in optical cavities. This allows for the transfer of quantum states between single atoms using optical fiber in addition to the creation of remote entanglement between distant atoms.[11][12]

### 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.[13]

#### 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.[14]

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 [15] 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 amplifiers 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 and R now perform quantum key distribution to generate a key ${\displaystyle k_{AR}}$. Similarly, R and B run quantum key distribution to generate a key ${\displaystyle k_{RB}}$. A and B can now obtain a key ${\displaystyle k_{AB}}$ between themselves as follows: A sends ${\displaystyle k_{AB}}$ to R encrypted with the key ${\displaystyle k_{AR}}$. R decrypts to obtain ${\displaystyle k_{AB}}$. R then re-encrypts ${\displaystyle k_{AB}}$ using the key ${\displaystyle k_{RB}}$ and sends it to B. B decrypts to obtain ${\displaystyle k_{AB}}$. A and B now share the key ${\displaystyle k_{AB}}$. The key is secure for an outside eavesdropper, but clearly the repeater R also knows ${\displaystyle k_{AB}}$. This means that any subsequent communication between A and B does not provide end to end security, but is only secure as long as A and B trust the repeater R.

#### Quantum repeaters

Diagram for quantum teleportation of a photon

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.[16]

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: ${\displaystyle |A\rangle }$ and ${\displaystyle |R_{a}\rangle }$ located at the sender and the repeater, and a second pair ${\displaystyle |R_{b}\rangle }$ and ${\displaystyle |B\rangle }$ 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 ${\displaystyle |R_{a}\rangle }$ and ${\displaystyle |R_{b}\rangle }$ thus teleporting the quantum state of ${\displaystyle |R_{a}\rangle }$ onto ${\displaystyle |B\rangle }$. This has the effect of "swapping" the entanglement such that ${\displaystyle |A\rangle }$ and ${\displaystyle |B\rangle }$ 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.[17]

Hardware platforms suitable as end nodes above can also function as quantum repeaters. However, there are also hardware platforms specific only[18] 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 amount 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.[19]

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.

#### Entanglement purification

Quantum decoherence can occur when one qubit from a maximally entangled bell state is transmitted across a quantum network. Entanglement purification allows for the creation of nearly maximally entangled qubits from a large number of arbitrary weakly entangled qubits, and thus provides additional protection against errors. Entanglement purification (also known as Entanglement distillation has already been demonstrated in Nitrogen-vacancy centers in diamond.[20]

## Current status

### Quantum internet

At present, there is no network connecting quantum processors, or quantum repeaters deployed outside a lab.

Updates: In contrast with its notoriously restrictive internet policies, China seems to be taking the lead on developing next-generation internet communications. The city of Jinan is set to become the hub of this quantum communications network that will boost Beijing-Shanghai internet when the project is launched by the end of August. It is set to become the world’s first “unhackable” internet communications network. Futurism July 25, 2017

A quantum telecommunication network has been put into service in Wuhan, capital of central China's Hubei Province. October 31, 2017 (Xinhua)

### Quantum key distribution networks

Several test networks have been deployed that are tailored to the task of quantum key distribution either at short distances (but connecting many users), or over larger distances by relying on trusted repeaters. These networks do not yet allow the end to end transmission of qubits, or the end to end creation of entanglement between far away nodes.

Major quantum network projects and QKD protocols implemented
Quantum network Start BB84 BBM92 E91 DPS COW
DARPA QKD network 2001 Yes No No No No
SECOCQ QKD network in Vienna 2003 Yes Yes No No Yes
Tokyo QKD network 2009 Yes Yes No Yes No
Hierarchical network in Wuho, China 2009 Yes No No No No
Geneva area network (SwissQuantum) 2010 Yes No No No Yes
DARPA Quantum Network
Starting in the early 2000s, DARPA began sponsorship of a quantum network development project with the aim of implementing secure communication. The network became operational within the BBN Technologies laboratory in late 2003 and was expanded further in 2004 to include nodes at Harvard and Boston Universities. The network consists of multiple physical layers including fiber optics supporting phase-modulated lasers and entangled photons as well free-space links.[21][22]
SECOQC Vienna QKD network
From 2003 to 2008 the Secure Communication based on Quantum Cryptography (SECOQC) project developed a collaborative network between a number of European institutions. The architecture chosen for the SECOQC project is a trusted repeater architecture which consists of point-to-point quantum links between devices where long distance communication is accomplished though the use of repeaters.[23]
Chinese hierarchical network
In May 2009, a hierarchical quantum network was demonstrated in Wuhu, China. The hierarchical network consists of a backbone network of four nodes connecting a number of subnets. The backbone nodes are connected though an optical switching quantum router. Nodes within each subnet are also connected though an optical switch and are connected to the backbone network though a trusted relay.[24]
Geneva area network (SwissQuantum)
The SwissQuantum network developed and tested between 2009 and 2011 linked facilities at CERN with the University of Geneva and hepia in Geneva. The SwissQuantum program focused on transitioning the technologies developed in the SECOQC and other research quantum networks into a production environment. In particular the integration with existing telecommunication networks, and its reliability and robustness.[25]
Tokyo QKD network
In 2010, a number of organizations from Japan and the European Union setup and tested the Tokyo QKD network. The Tokyo network build upon existing QKD technologies and adopted a SECOQC like network architecture. For the first time, one-time-pad encryption was implemented at high enough data rates to support popular end-user application such as secure voice and video conferencing. Previous large-scale QKD networks typically used classical encryption algorithms such as AES for high-rate data transfer and use the quantum-derived keys for low rate data or for regularly re-keying the classical encryption algorithms.[26]

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