Networks connecting quantum processors
Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum processors. A quantum processor is a machine able to perform quantum circuits on a certain number of qubits. Quantum networks work in a similar way to classical networks. The main difference is that quantum networking, like quantum computing, is better at solving certain problems, such as modeling quantum systems.
Basics.
Quantum networks for computation.
Networked quantum computing or distributed quantum computing works by linking multiple quantum processors through a quantum network by sending qubits in between them. Doing this creates a quantum computing cluster and therefore creates more computing potential. Less powerful computers can be linked in this way to create one more powerful processor. This is analogous to connecting several classical computers to form a computer cluster in classical computing. Like classical computing, this system is scalable by adding more and more quantum computers to the network. Currently quantum processors are only separated 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 creating quantum entangled qubits, information can be transmitted between the remote quantum processors. Most applications of a quantum internet require only very modest quantum processors. For most quantum internet protocols, such as 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 be realized only if the (combined) quantum processors can easily simulate more qubits than a classical computer (around 60). Quantum internet applications require only small quantum processors, often just a single qubit, 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 the same security and speed.
Overview of the elements of a quantum network.
The basic structure of a quantum network and more generally a quantum internet is analogous to a classical network. First, we have end nodes on which applications are ultimately 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, different wavelengths are chosen 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, one requires a quantum repeater to transport qubits over long distances. Repeaters appear in between end nodes. Since qubits cannot be copied (No-cloning theorem), classical signal amplification is not possible. By necessity, a quantum repeater works in a fundamentally different way than a classical repeater.
Elements of a quantum network.
End nodes: quantum processors.
End nodes can both receive and emit information. 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. The quantum state being stored can either be the relative spin of an electron in a magnetic field or the energy state of an electron. They can also 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. NV centers can be utilized at room temperatures. Small scale quantum algorithms and quantum error correction has already been demonstrated in this system, as well as the ability to entangle two and three quantum processors, and perform deterministic quantum teleportation.
Another possible platform are quantum processors based on ion traps, which utilize radio-frequency magnetic fields and lasers. In a multispecies trapped-ion node network, photons entangled with a parent atom are used to entangle different nodes. 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.
Communication lines: physical layer.
Over long distances, the primary method of operating quantum networks is to use optical networks and photon-based qubits. This is due to optical networks having a reduced chance of decoherence. 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. This fiber can be either single-mode or multi-mode, with single-mode allowing for more precise communication. 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.
In 2020 a team of researchers affiliated with several institutions in China has succeeded in sending entangled quantum memories over a 50-kilometer coiled fiber cable.
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. However, over long distances, free space communication is subject to an increased chance of environmental disturbance on the photons.
Free space communication is also possible from a satellite to the ground. A quantum satellite capable of entanglement distribution over a distance of 1,203 km has been demonstrated. The experimental exchange of single photons from a global navigation satellite system at a slant distance of 20,000 km has also been reported. These satellites can play an important role in linking smaller ground-based networks over larger distances. In free-space networks, atmospheric conditions such as turbulence, scattering, and absorption present challenges that affect the fidelity of transmitted quantum states. To mitigate these effects, researchers employ adaptive optics, advanced modulation schemes, and error correction techniques. The resilience of QKD protocols against eavesdropping plays a crucial role in ensuring the security of the transmitted data. Specifically, protocols like BB84 and decoy-state schemes have been adapted for free-space environments to improve robustness against potential security vulnerabilities.
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 formula_1. Similarly, R and B run quantum key distribution to generate a key formula_2. A and B can now obtain a key formula_3 between themselves as follows: A sends formula_3 to R encrypted with the key formula_1. R decrypts to obtain formula_3. R then re-encrypts formula_3 using the key formula_2 and sends it to B. B decrypts to obtain formula_3. A and B now share the key formula_3. The key is secure from an outside eavesdropper, but clearly the repeater R also knows formula_3. 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.
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 kilometers. In the simplest case of a single repeater, two pairs of entangled qubits are established: formula_12 and formula_13 located at the sender and the repeater, and a second pair formula_14 and formula_15 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 formula_13 and formula_14 thus teleporting the quantum state of formula_13 onto formula_15. This has the effect of "swapping" the entanglement such that formula_12 and formula_15 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 protecting 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.
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 correction codes 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