Method for establishing quantum communication channel, control program, computer-readable data carrier, control unit, quantum device, quantum network, apparatus and quantum computing arrangement

Abstract

A method, a control program, a computer-readable data carrier, a control unit, a quantum device, a quantum network, an apparatus and a quantum computing arrangement for establishing a quantum communication channel for transmitting quantum data units between a source quantum device and a destination quantum device, the method comprises the steps of: requesting at least one quantum path between a first quantum device and a second quantum device; establishing at least two quantum defined channels between respective two quantum devices, each quantum device being designated to implement at least one quantum path; providing at least two quantum links by entangling at least one qubit of each of the respective two quantum devices connected by the at least two quantum defined channels; and synchronizing the quantum devices providing the at least two quantum defined channels in time to simultaneously provide at least one quantum path via the at least two quantum links for establishing a quantum communication channel.

Description

TECHNICAL FIELD

[0001] The present specification relates to the field of quantum computing. In particular, the present disclosure relates to a method for establishing a quantum communication channel for transmitting quantum data units between a source quantum device and a destination quantum device in a quantum computing arrangement, a control program for controlling a quantum computing arrangement, a computer readable data carrier, a control unit for controlling at least one quantum device in a quantum computing arrangement, a quantum device for a quantum computing arrangement, a quantum network for a quantum computing arrangement, an apparatus such as a satellite, an aircraft and / or a communication station and a quantum computing arrangement. BACKGROUND

[0002] A quantum internet aims to allow the transmission of quantum bits (qubits) between any pair of quantum devices, allowing the exchange of quantum information to support several applications, including distributed quantum computing, secure communication, and precision sensing (see R. Van Meter, Quantum networking. John Wiley & Sons, 2014). Similar to a classical internet, a quantum internet consists of network components such as communication links and routers (see N. Sangouard, R. Dubessy and C. Simon, “Quantum repeater based on single trapped ion,” Physical Review A, vol. 79, no. 4, p. 042340, 2009). However, due to fundamental differences between classical bits and quantum bits, quantum network components behave very differently from classical network devices.

[0003] For example, qubits cannot be copied, which precludes retransmission as a tool to overcome qubit loss. In order to allow for the exchange of qubits, it is necessary to first create quantum entanglement between a qubit held by the sender and a qubit held by the receiver. Once this entanglement has been created, quantum teleportation (see C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wotters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Physical review letters, vol. 70, no. 13, p. 1895, 15 1993) can then be used to send the qubit, which consumes the entanglement, meaning that the qubit must be re-established before the next one can be sent. All of this process is possible by using a routing entanglement protocol (see M. Caleffi, “Optimal routing for quantum networks,” IEEE Access, vol. 5, pp. 22 299 - 22 312, 2017).

[0004] Many routing and forwarding protocols in classical data networks, such as the Internet, can not be directly applicable to quantum networks. For example, the network layer of the Internet mainly uses a connectionless datagram approach. The quantum no-cloning theorem makes quantum information unable to be copied and retransmitted, and thus the datagram approach cannot be applied.

[0005] The virtual circuit model can be more suitable for quantum networks. In this case, and in order to provide the conditions for entanglement exchange, a connection (virtual circuit) is established before communication, and the path nodes are determined to ensure the entanglement resources required for communication. Entanglement exchange allows quantum repeaters to generate long-range entanglement by connecting short-range entangled pairs.

[0006] In classical networks, routing protocols are usually based on link state and distance vector algorithms. However, in quantum networks, link states are probabilistic and vary in different time slots. Furthermore, there is no time for global link state broadcast or distance vector convergence, as entanglement established on different quantum links will decay quickly. Moreover, quantum links cannot be shared by multiple source-destination pairs, which is allowed in classical networks. Therefore, the shortest paths calculated in classical routing will not always be available.

[0007] It is a challenging problem to efficiently design a routing entanglement protocol, i.e., because the number of entangled pairs of qubits available on a link or path at any one time is limited. This means that when the amount of qubits to be transmitted over a single quantum path is larger than the capacity of that path, meaning the number of entangled pairs available, the excess number of qubits must wait for the path nodes to regenerate entangled pairs before being transmitted. This problem leads to increased latency of data qubits in memory, leading to decoherence and reduced fidelity, which means that quantum networks should have a timeliness property, aiming to reduce the time quantum bits need to spend in memory in order to reduce decoherence.

[0008] Entanglement routing aims to allow long distance end-to-end communication of data qubits. However, it faces several challenges, such as no-cloning and decoherence. The no-cloning theorem states that quantum data cannot be copied, and decoherence is the gradual loss of coherence due to interactions between the system and the environment, which leads to loss of quantum data. This limits the time entangled qubits can be stored in quantum repeater memory.

[0009] Quantum routing protocols known from the prior art aim to decide the optimal path before generating end-to-end entanglement. Quantum routing is more complex than routing in classical networks, because it not only needs to consider classical metrics, such as path length, cost and throughput, to calculate the best path, but also needs to consider the required end-to-end quantum fidelity. In this context, there are several quantum routing proposals from the prior art that aim to find alternative entanglement paths for each connection, which can include operations to improve communication efficiency by purifying quantum links in order to achieve the required fidelity threshold.

[0010] While quantum routing algorithms are a new emerging research field, several proposals already exist, most of which aim at identifying a single path, as described in: Marcello Caleffi, 2017, in “Optimal routing for quantum networks”, IEEE Access 5 (2017), 22299-22312; Kaushik Chakraborty, David Elkouss, Bruno Rijsman, and Stephanie Wehner, 2020, in “Entanglement Distribution in a Quantum Network, a Multi-Commodity Flow-Based Approach”, (2020) or Zhang, L., Liu, Q., in “Optimisation of the routing protocol for quantum wireless Ad Hoc network”, IET Quant. Comm. 1-8 (2021). https: / / doi.org / 10.1049 / qtc2.12028, while others aim at supporting multiple paths end-to-end, which however can overlap, as described in: Li C., Li T., Liu Y. X., et al. in “Effective routing design for remote entanglement generation on quantum networks [J], npj Quantum Information, 2021, 7(1)”.

[0011] The choice between centralized and distributed quantum routing depends on the specific requirements and constraints of the quantum network. As also mentioned in Skrzypczyk, Matthew and Stephanie Wehner, in “An Architecture for Meeting Quality-of-Service Requirements in Multi-User Quantum Networks”, ArXiv abs / 2111.13124 (2021), centralized quantum routing involves a central entity that computes the optimal path for the quantum information transmission. This approach can be efficient in terms of resource utilization, as the central entity has a global view of the network state. However, it can face scalability issues in large networks due to the need for global information and the possibility of a single point of failure. On the other hand, distributed quantum routing involves each node making routing decisions based on local information. As there is no single point of failure, this approach can be more scalable and robust to failures. However, it can have limitations in the efficient use of resources, as the nodes lack a global view of the network.

[0012] Most of the approaches proposed according to the state of the art follow a centralized model that focuses on the operation of a centralized control system, such as a software-defined network (SDN), which has all the essential information about the network, such as the network topology, the resources of each edge network, and the success probability of entanglement on different links. This is the case of the work proposed by Caleffi (see above), which is related to a routing algorithm that tries to find the optimal path between a source and a destination based on a routing metric called end-to-end entanglement rate. Both path selection algorithms are centralized algorithms and work under the assumption that each node has information about the entire network.

[0013] In the centralized approach, the central controller collects information about the source-destination pair and identifies the optimal set of edges to create the external links. These links can also be used as backup options in case of failure. Thereafter, the central controller needs to instruct the relevant nodes to establish the computed external links. However, it seems that not all links can be successfully created despite the allocated resources. Therefore, the external controller needs to receive reports from the nodes on the successfully established external links, determine the most efficient way to form the entanglement path based on the reports. Once the external and entanglement paths are established, the central controller informs the source that they can transmit the qubits through the entanglement connection before the end of the current time slot. However, due to the time-consuming central operation, i.e., the collection of global information and the need for the central controller to act on all quantum devices, it can happen that the total operation lasts longer than the coherence time of the deployed qubits. SUMMARY

[0014] Thus, it can be seen as an object to provide a reproducible, reliable and efficient way for enabling communication in a quantum computing arrangement, in particular, it can be seen as an object to provide an entanglement routing mechanism capable of generating and utilizing multiple paths in order to maximize the number of simultaneous pairs of quantum users and their expected throughput. This object is solved by the subject matter of the independent claims.

[0015] According to an aspect, there is provided a method for establishing a quantum communication channel in a quantum computing arrangement for transmitting quantum data units between a source quantum device and a destination quantum device, the method comprising the steps of: requesting at least one quantum path between a first quantum device and a second quantum device; establishing at least two quantum bounded channels between respective two quantum devices each designated for enabling the at least one quantum path; providing at least two quantum links by entangling at least one qubit of each of the respective two quantum devices connected by the at least two quantum bounded channels; and synchronizing in time the quantum devices providing the at least two quantum bounded channels for simultaneously providing the at least one quantum path via the at least two quantum links for establishing the quantum communication channel.

[0016] According to an aspect, there is provided a control program for controlling a quantum computing arrangement, comprising instructions which, when executed by a control unit, cause the control unit to implement a corresponding method.

[0017] According to an aspect, there is provided a computer readable data carrier having stored thereon a corresponding control program.

[0018] According to an aspect, there is provided a control unit for controlling at least one quantum device in a quantum computing arrangement, the control unit being configured to implement a corresponding method of a corresponding computer readable data carrier and / or comprising a corresponding computer readable data carrier.

[0019] According to an aspect, there is provided a quantum device for a quantum computing arrangement, the quantum device being configured to implement a corresponding method and / or being adapted to be controlled by a corresponding control unit.

[0020] According to an aspect, there is provided a quantum network for a quantum computing arrangement, the quantum network being configured to implement a corresponding method and / or comprising at least one corresponding control unit and / or at least one corresponding quantum device.

[0021] According to an aspect, there is provided an apparatus, such as a satellite, an aircraft and / or a communication station, configured to participate in a quantum computing arrangement, comprising at least one corresponding control unit, at least one corresponding quantum device and / or at least one corresponding quantum network.

[0022] According to an aspect, there is provided a quantum computing arrangement configured to implement a corresponding method according to at least one of the claims, comprising at least one corresponding control unit, at least one corresponding quantum device, at least one corresponding quantum network and / or at least one corresponding apparatus.

[0023] The source quantum device can be a first quantum device configured as a sender and the destination quantum device can be a second quantum device configured as a receiver, connected to each other via a quantum communication channel for transmitting information in the form of quantum data units. The quantum path can provide at least a part, a section and / or a segment of the quantum communication channel.

[0024] A quantum channel (e.g. photonic) can be used to transfer quantum information between stationary qubits in neighboring quantum devices. A device can allocate qubits to a quantum channel such that no qubit is allocated to more than one channel. A channel is said to be bounded when neighboring devices allocate qubits to both ends of it. There can be more than one bounded channel between two devices. Neighboringness is created via a direct optical link (e.g. fiber, free-space optics) between two quantum repeaters or via a shared optical medium (e.g. a satellite). The channel is characterized by a quantum channel state, which can for example reflect the quality of the channel.

[0025] The control unit or network controller can aim to send updates to all quantum devices, when necessary, about i) the current source-destination communication pairs that need to establish long-distance entanglement; ii) the amount of end-to-end entanglement needed (throughput) for each source-destination pair; iii) the priority of the source-destination pairs. The controller can assign a priority to each source-destination pair based on the required throughput and some operational metrics (e.g. assign high priority to source-destination pairs with high throughput or assign equal cost to each end-to-end entanglement). Finally, all source-destination pairs should have different priorities. Communication between the quantum devices and the network controller, which can be installed in a satellite, is done via a classical communication link.

[0026] The quantum devices can be connected to each other via quantum channels and to the Internet via classical channels. Each quantum device has a certain number of stationary qubits arranged in a quantum memory. The quantum devices can be configured as and / or comprise at least one quantum processor and / or at least one quantum repeater. The quantum processor can be a quantum device with behavior similar to an end host in the classical Internet. The quantum repeater can be a quantum device that allows the establishment of quantum entanglement between any pair of remote quantum processors. The quantum repeater can support long-distance entanglement via quantum switching. The quantum repeater can exchange control information via the Internet.

[0027] The quantum computing arrangement can be configured as and / or comprise a quantum network of quantum devices. The apparatus can comprise and / or participate in the quantum computing arrangement. The quantum network can be established within and / or external to the apparatus.

[0028] The present solution allows to ensure the timeliness property of the quantum communication channel through multiple paths simultaneously to solve the entanglement routing problem. The resulting entanglement routing mechanism is able to generate and exploit multiple paths in order to maximize the number of simultaneous quantum user pairs and their expected throughput. The proposed routing is able to work with any entanglement generation process, reacting to on-demand requests for end-to-end quantum paths between any pair of quantum devices at different time slots. At each time slot, the algorithm finds contention-free paths for the current source-destination quantum pair. This set of paths is "contention-free" when the routing mechanism is able to satisfy the on-demand requests while avoiding the allocation of the same quantum resources to different paths.

[0029] The proposed mechanism follows a decentralized operation based on classical techniques, as these can be more likely to be implemented in quantum technologies in the near future. These techniques aim to first find a path from the source to the destination and then distribute entanglement links along this path. The difference between these approaches comes from the path selection algorithm.

[0030] In contrast, for example, R. Van Meter, T. Satoh, T. D. Ladd, W. J. Munro, and K. Nemoto, in “Path selection for quantum repeater networks,” Networking Science, vol. 3, no. 1-4, pp. 82-95, 2013 define a cost metric across each communication link and then use Dijkstra’s algorithm to find the optimal path between a source and a destination. However, Dijkstra’s algorithm can only find the shortest path when the routing metric is additive, which can not happen in quantum networks. Following a different approach, M. Pant, H. Krovi, D. Towsley, L. Tassiulas, L. Jiang, P. Basu, D. Englund, and S. Guha, in “Routing entanglement in the quantum internet,” npj Quantum Information, vol. 5, no. 1, p. 25, 2019 propose a greedy multi-path routing algorithm for distributing entanglement. However, multi-path routing algorithms can not be scalable for larger networks with multiple demands. Methods based on a primary path and selected alternative paths can scale better while still bringing the advantage of utilizing multiple paths.

[0031] Therefore, the routing mechanism according to the present solution enables to find alternative path segments between any pair of quantum devices while knowing the available quantum resources. Therefore, it is possible to increase the number of quantum devices with good throughput (number of end-to-end entanglements) while taking into account the decoherence rate of qubits. The proposed mechanism allows the quantum network to generate entanglement on demand, reacting only when a request arrives. The reactive nature of the proposed mechanism aims to avoid computing potential candidate path segments that can conflict with quantum resources later, which can happen when all potential paths are computed before knowing their resource requirements.

[0032] Considering that the performance of centralized shortest path routing algorithms as proposed in E. W. Dijkstra, in “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269-271, 1959, highly depends on the network topology making them less reactive to topology changes - which can occur more frequently when using long quantum satellite links - the proposed mechanism can be decentralized in order to make it less dependent on the network topology.

[0033] In view of the above, the proposed solution has many advantages compared to other approaches aiming at supporting entanglement routing. For example, the solution avoids the generation of single points of failure. It enables to exploit edges with multiple qubits in order to support purification. It enables to avoid resource conflicts between different simultaneous paths. It has a low dependency on the network topology. It scales better than other multipath approaches known in the art.

[0034] Further developments can be derived from the dependent claims and the following description. Many features described with reference to the method can be implemented as device features and vice versa. Thus, the description provided in the context of the method for establishing a quantum communication channel also applies in an analogous manner to the control unit, the quantum device, the quantum network, the apparatus and / or the quantum computing arrangement, respectively. In particular, the steps of the method and the mentioned components involved therein can be implemented as functions of the control unit, the quantum device, the quantum network, the apparatus and / or the quantum computing arrangement, and their functions can be implemented as method steps.

[0035] According to an embodiment of the method, the method further comprises a step of providing a setup message to be received by the quantum devices designated for implementing the quantum paths. The setup message can be sent by the control unit to the respective quantum devices. The quantum devices designated for establishing the quantum communication channel can be configured as quantum routers. The setup message can be followed by an announcement message providing information on the status of local and bounded and unbounded channels, e.g. with an indication of bounded source-destination pairs. Thereby, the setup message allows to efficiently and reliably set up the quantum devices involved when establishing the quantum communication channel.

[0036] According to an embodiment of the method, the method further comprises the step of establishing a first set of quantum links for providing at least two alternative quantum communication channels. A pairing list of source-destination pairs of quantum devices and corresponding quantum channels can be managed. The quantum channels can be prioritized in the list by means of a corresponding priority value or parameter. The pairing list can comprise information on bound and unbound channels, which can be kept as different sections of the pairing list and / or subsets of the pairing list. The quantum devices can update the pairing list according to unserved source-destination pairs for removing end-to-end entanglement along corresponding quantum paths. Thereby, the pairing list allows for an efficient and reliable establishment of involved quantum devices when establishing quantum communication channels.

[0037] According to an embodiment of the method, the method further comprises the step of evaluating at least one quantum path best suited for establishing a quantum communication channel. The quantum communication channel can be established by means of the at least one quantum path which has been calculated to be best suited for establishing a quantum communication channel. The evaluation can further involve calculating a distance between a quantum path for providing a quantum communication channel and at least a theoretical main path. This further contributes to providing reliable communication via corresponding quantum communication channels.

[0038] According to an embodiment of the method, the method further comprises the step of triggering a timer for synchronizing quantum devices. A corresponding time interval established by means of the timer can determine an actual quantum data unit transmission rate. Thus, the timer allows for reliably establishing quantum communication channels at a desired and / or required quantum data unit transmission rate.

[0039] According to an embodiment of the method, the method further comprises the step of sending a data request message with a source quantum device to a quantum device providing at least two quantum bound channels for providing information on resources of the quantum device required for establishing a quantum communication channel. The data request message allows for evaluating an availability of resources of the quantum device providing at least two quantum bound channels. Thereby, the data request message allows for an efficient and reliable establishment of involved quantum devices when establishing quantum communication channels.

[0040] According to an embodiment of the method, the method further comprises the step of providing at least one link state message indicating a quality of at least two quantum links represented by a time-to-live value representing an average level of fidelity of the at least two quantum links. The at least one link state message can trigger a calculation and / or provision of the time-to-live value. The time-to-live value can be considered as a core parameter for evaluating a quality of the at least two quantum links. Thereby, the at least one link state message and the time-to-live value further contribute to an efficient and reliable establishment of quantum communication channels.

[0041] According to an embodiment of the method, the method further comprises the step of exchanging entanglement of qubits within at least one quantum device establishing at least two quantum links. The exchange can be performed by placing an internal link between the qubits of two local quantum links. The quantum device acting as a repeater that is also a splitter can perform the exchange on the recovered path when receiving a link state message from a neighbor on the best path. This further helps to establish quantum communication channels efficiently and reliably. BRIEF DESCRIPTION OF DRAWINGS

[0042] The subject matter will be described with reference to the following drawings in which like elements are referred to with like numerals, and where:

[0043] Figure 1 is a schematic representation of a computing arrangement.

[0044] Figure 2 is a schematic representation of a quantum computing arrangement preparing to establish at least one quantum communication channel.

[0045] Figure 3 is a schematic representation of a quantum computing arrangement having at least one established quantum communication channel.

[0046] Figure 4 is a schematic representation of steps of a method for establishing a quantum communication channel. DETAILED DESCRIPTION

[0047] The following detailed description is merely exemplary in nature and is not intended to limit the application and the application's use. Furthermore, there is no intention to be bound by any theory presented in the preceding background or the following detailed description. Representations and illustrations in the drawings are schematic and not to scale. Identical reference numerals designate identical elements. A more complete understanding of the described subject matter can be had by reference to the drawings and the following detailed description.

[0048] Figure 1A schematic representation of a computing arrangement 1 is shown, comprising a plurality of quantum devices 2 and respective control units 3, which can be provided with interface modules 4 to connect the quantum devices 2 and / or control units 3 to control elements 5, which can be connected to each other via respective transmission lines 6, which can be configured to transport any kind of information, data, power and / or energy, including photonic links. Thus, the transmission lines 6 can involve any suitable wired, wireless and / or optical communication means, including lines, cables, transceivers, antennas, satellite antennas, etc. In the present example, the quantum devices 2 and respective control units 3 can be provided to apparatuses 7, such as ground stations 8 and / or vehicles 9 on the ground G, including aircraft 9a and / or satellites 9b. Thus, the apparatuses 7 can comprise respective computer systems 10, which can comprise the quantum devices 2, control units 3, interface modules 4, control elements 5 and / or transmission lines 6, as desired or required by their respective applications, e.g. for implementing quantum computations, secure communications and / or precision sensing of certain parameters and / or values by means of the control elements 5, such as for quantum sensing of accelerations, gravitation, magnetic effects, photonic effects, radiation, rotations, etc., and then computing by means of the quantum devices 2, which are configured for establishing quantum networks Q via respective quantum communication channels C and / or classical or conventional networks N by means of respective transmission lines 6.

[0049] A computer program 11 for controlling the computing device 10 can be stored on a computer-readable data carrier 12, which can take the form of a computer-readable medium 13 and / or data carrier signal 14. The computer system 10 can comprise the quantum devices 2, control units 3, interface modules 4, control elements 5 and / or transmission lines 7, computer program 11, computer-readable data carrier 12, which can be adapted to exchange data between the respective aforementioned components. The control elements 9 can be any kind of data source, such as measurement elements, classical sensors, quantum sensor output devices and / or actuators of any of the apparatuses 7. Thus, the quantum devices 2 involved can act as source A quantum devices 2 in the sense of a sender, destination B quantum devices 2 as quantum processors P in the sense of a receiver, which behave similarly to end hosts in a classical network environment, and / or as quantum repeaters R (see Fig. 2) allowing to establish quantum entanglement between any pair of remote quantum processors P (see Fig. 3). Figure 2 and 3 ).

[0050] Figure 2A schematic representation of a quantum computing arrangement 1 is shown which is preparing to establish at least one quantum communication channel C in a quantum network Q. The quantum computing arrangement 1 comprises a plurality of quantum devices 2, each quantum device 2 comprising a plurality of qubits q which can be linked to each other via quantum defining channels K as shown by dashed lines. In addition, the quantum devices 2 can be linked to each other via network channels O of a conventional network N as shown by dashed lines, which can be provided in the form of an internet infrastructure, for example, with respective transmission lines 6. The quantum network Q and the conventional network N can be controlled by means of at least a respective control unit 3.

[0051] Figure 3 A schematic representation of a quantum computing arrangement within at least one established quantum communication channel C in a quantum network Q is shown. Based on quantum defining channels K, quantum links K are established in the figure represented by solid lines by entangling at least one qubit q of each of the respective 2 quantum devices 2 designated for implementing at least one quantum path J in the figure represented by a straight solid line, which can comprise a plurality of path segments M in the figure represented by dashed lines. By synchronizing the quantum devices 2 which provide the quantum defining channels K simultaneously via quantum links L, a respective quantum communication channel C can be provided based on the quantum path J.

[0052] The quantum devices 2 providing a source A and a destination B of information transmitted along a quantum path J and / or a quantum communication channel C can be configured as quantum processors P. Any of the quantum devices 2 arranged along a quantum communication channel C between a source A and a destination B can function as a quantum repeater R. In order to allow information to pass through the quantum repeater R, a respective pair of qubits q in the quantum repeater R is undergoing a swap X.

[0053] On such a topology of a quantum communication arrangement 1, a requested end-to-end quantum path J can be created by first establishing a set of quantum links L by entangling the qubits q of the established quantum defining channels K and by causing the quantum devices 2 to perform entanglement swaps X to effectively extend the established entanglement to two remote quantum devices 2, as Figure 3 shown, which shows a host end-to-end path J with two replaceable segments M. With the resulting end-to-end entanglement, one quantum device 2 can transmit the state of a data qubit q to the other quantum device 2 without the need to physically transport the data qubit q itself, thereby destroying the entanglement in the process. The ebits involved in such a proof can correspond to the entanglement content in a two-qubit state of maximum entanglement (Bell state).

[0054] In order to maintain entanglement simultaneously in adjacent quantum links L, the quantum repeaters R need to be synchronized in time. This can be achieved by using a synchronization protocol, e.g. via an internet synchronization protocol of the network channel O which can be provided and / or controlled by the control unit 3. This synchronization procedure allows the quantum repeaters R to work based on time slots whose duration ensures that the established entanglement does not decohere within a certain time slot. At each time slot, a routing algorithm is able to find an end-to-end path for the current source-destination pair while resources are still available in the network and to avoid conflicts in the access to available resources.

[0055] Figure 4 A schematic representation of the steps S of the method for establishing a quantum communication channel C is shown. Certain steps S can involve respective decisions D. An exemplary operation of the proposed routing protocol can involve three phases, namely a first phase I, a second phase II and / or a third phase III.

[0056] The first phase I can involve a procedure to construct the most suitable topology for the quantum network Q. In a first step 1 of the first phase I, all involved quantum devices 2 can receive a setup message U from the control unit 3 with information about the current source-destination pairs for which long distance entanglement is required, the throughput per source-destination pair (number of end-to-end entanglements) and / or the quality of each end-to-end entanglement. Based on this information, the quantum repeaters R can calculate the best quantum path J per source-destination pair based on a suitable quantum metric (e.g. a path weight given in an order proportional to the minimum number of parallel quantum bounded channels K available between any pair of adjacent quantum repeaters R in that quantum path J to the quality of the end-to-end entanglement) while avoiding resource conflicts. Since all quantum repeaters R can run the same decision procedure, all quantum repeaters R can have the same view on the overall calculation of the best quantum path J.

[0057] In the present example, the first phase I can comprise the following steps S encompassing respective operations which can be performed by each of the involved quantum repeaters R: To disengage from an idle mode SO of the quantum network Q, in a first step SI each quantum repeater R can perform a data exchange with adjacent quantum repeaters R over a classical network channel O, in a second step an announcement message V with information about the status of local unbounded and bounded channels (with an indication of bounded source-destination pairs) can be propagated to all quantum repeaters R in the quantum network Q in a third step S3, each of the involved quantum repeaters R can calculate the best quantum path J per source-destination pair of quantum devices 2 based on the collected topology, quantum channel status information and metrics such as minimum hop count and maximum overall channel quality.

[0058] A fourth step S4, each quantum repeater R involved can bind the qubit q to the local channel selected for the estimated best quantum path J starting from the source-destination pair with the highest priority. The quantum bounded channel K can be marked with the ID of the source-destination pair of the quantum device 2 and can then be removed from the list of unbounded local channels. In a fifth step S5, all repeaters can update the list of unserved source-destination pairs, removing the end-to-end entanglement preserved in steps S2 and S3. Each quantum repeater R involved can repeat steps 1, 2 and 3 while there are still unserved source-destination pairs that can be decided in the respective first decision D1.

[0059] A second phase II can involve steps S and decisions D for building the desired and / or required segment topology: after computing the best quantum path J for all source-destination pairs of the quantum device 2, the remaining qubits q and channels can be used to build alternative path segments M to be used as recovery segment paths for each source-destination pair of the quantum device 2. Each recovery path can start and end in a different quantum repeater R of the best quantum path J and can be referred to as quantum network splitter Y (see Figure 3 ). A quantum repeater R configured as quantum network splitter Y must not be more than the number of k network hops away from each other on the main path, as k is also the number of hops for broadcasting entanglement results to ensure consistent exchange decisions in the third phase III. The second phase II can encompass the following operations to be performed by each quantum repeater R:

[0060] In the second phase II, during a sixth step S6, while still having unbounded channels, each quantum repeater R can estimate its distance (number of hops) towards the two quantum network splitters Y located in the best quantum path J of the source-destination pair, starting from the pair with the highest priority. In a seventh step S7, the quantum repeaters R at a distance smaller than the time-to-live (number of hops) of the respective link state message W (used in phase 3) including the quantum network splitters Y can bind the qubit q to the channel towards the quantum network splitter Y, e.g. marking the respective channel as bounded with the ID of the source-destination pair and the label of the segment channel. The creation of the quantum segment M is thus known to the quantum network splitters Y, as all involved quantum repeaters R can run the same recovery algorithm. Then, the quantum repeaters R can repeat steps S1 and S2.

[0061] A third phase III can involve sending data Z to be transmitted. In the third phase III, the quantum relays R can try to create quantum links L on the quantum bound channels K and exchange the X quantum links L assigned to the same end-to-end quantum path J. However, the involved quantum relays R can only have a certain amount of time available to try to create quantum links L on the quantum bound channels K, which can be related to the size of the available memory, because if the memory storage time is not large enough, the reserved links can decohere. Thus, the third phase III can start from an eighth step S8 when the quantum device 2 collocated with the quantum source A sends data requests and / or link state messages W to the involved quantum relays R of the best quantum path J towards the destination B through the network channels O. The quantum device creates as many data request messages W as needed according to the respective number of end-to-end entanglements associated with the source-destination pair of the quantum device 2.

[0062] Each data request message W can comprise a vector of time variables indicating the waiting time to trigger the entanglement process in each quantum relay R in the source-destination pair of the quantum device 2 of the respective quantum path J. The waiting time of each quantum relay R can be computed based on the status of the quantum memory (e.g. included in the announcement message V) and the expected delay towards those quantum relays R (e.g. estimated based on the reception of the announcement message V). The waiting times of all quantum relays R in the respective quantum path J must be equal in order to ensure that the entanglement processes of all quantum channels C are triggered at the same point in time. Furthermore, each data request message W can comprise a variable indicating the number of entanglement processes needed (e.g. associated with the number of data units to be sent) and / or a variable indicating the time interval between each entanglement process (e.g. to indicate the transmission frequency).

[0063] In the third phase III, the following steps S and decisions D can be performed, which can involve respective operations performed by each involved quantum relay R: In an eighth step S8, each involved quantum relay R can receive a data request message W. In a ninth step S9, the creation of the local quantum link can be performed after the assigned waiting time and, if the quantum relay R is configured as a quantum network splitter Y, the data request message W is forwarded in the selected best quantum path J and optionally in the recovery path in a tenth step S10. In an eleventh step S11, after the expiration of the waiting time, the link creation can be completed by, for example, a request in the form of a link state message T sent to the entanglement source or by interfacing with the local entanglement operation. Information about the fidelity of the quantum link L can be stored locally as a respective link state parameter (e.g. in contrast to the link state routing of classical networks, the quantum link state is highly dynamic and non-deterministic).

[0064] After creating the quantum link in the tenth step S11, in a twelfth step S12, each quantum repeater R involved can send a respective link status message T to its neighbors over the network channel O if the link status is below a configured threshold (e.g. set by the control unit 3). The link status message T can be sent with a time to live t. Since entanglement decays quickly, the value of t can be directly proportional to the average fidelity level of the network quantum link L (e.g. the value of t can be estimated and distributed by the control unit 3). In a thirteenth step S13, after establishing the quantum link L, the quantum repeaters R involved can perform an entanglement swap X to establish long distance quantum entanglement on the best quantum path J, thus enabling the transmission of data Z via the respective quantum channel C. In case of missing link status messages T, the swap X can be performed by placing an internal link between the qubits q of two local quantum links within the quantum device 2. The quantum repeaters R, also configured as quantum network splitters Y, can perform the swap X on the recovery path upon receiving a link status message T from a neighbor on the best quantum path J. After sending the data request message W, the quantum device 2 collocated with the quantum source A can send the first quantum data Z as a respective unit after an initial time interval equal to the transmission latency plus a time increment (the time increment is for example estimated based on the time to send another data Z unit after the time interval specified in the data request message W). After that, the quantum network Q can return to the idle mode SO, which can constitute the zeroth step.

[0065] While at least one example embodiment has been presented in the foregoing detailed description, it should be appreciated that a large number of modifications can be made. It should also be appreciated that the example embodiment or embodiments are only examples and are not intended to limit the scope, applicability, or configuration of the application in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing an example embodiment of the application. It will be understood that various changes can be made in the function and arrangement of elements described in the example embodiment without departing from the scope of the claims.

[0066] Additionally, it should be noted that "comprising" or "including" does not exclude any other elements or steps and "a" or "an" does not exclude a plurality or multiple. Further, it should be noted that features or steps described with reference to one or more of the above-described example embodiments can be used in combination with other features or steps of other described example embodiments. Reference signs in the claims should not be construed as limiting the scope of the claims.

[0067] List of reference signs

[0068] 1 quantum communication arrangement

[0069] 2 quantum device

[0070] 3 control unit

[0071] 4 interface module

[0072] 5 control element

[0073] 6 transmission line

[0074] 7 device

[0075] 8 ground station

[0076] 9 vehicle

[0077] 9a aircraft

[0078] 9b satellite

[0079] 10 computer system

[0080] 11 computer / control program

[0081] 12 computer-readable data carrier

[0082] 13 computer-readable medium

[0083] 14 data carrier signal

[0084] q qubit

[0085] t time-to-live

[0086] A source / sender

[0087] B destination / recipient

[0088] C quantum communication channel / quantum path

[0089] D decision

[0090] G ground

[0091] J quantum path

[0092] K quantum bound channel

[0093] L quantum link

[0094] M quantum segment

[0095] N conventional network

[0096] O network channel

[0097] P quantum processor

[0098] Q quantum network

[0099] R quantum repeater

[0100] S step

[0101] T link state message

[0102] U setup message

[0103] V announce message

[0104] W data request message

[0105] X exchange

[0106] Y quantum network shunt

[0107] Z transmit data Z

[0108] I first phase

[0109] II second phase

[0110] III third phase

[0111] D1 unreserved resource?

[0112] D2 unqualified channel?

[0113] D3 latency expiration?

[0114] D4 link state threshold reached?

[0115] S0 idle mode

[0116] S1 send / receive setup message

[0117] S2 send / receive announce message

[0118] S3 compute best path

[0119] S4 create qualified channel

[0120] S5 update list of unreserved resources

[0121] S6 compute distance to primary path

[0122] S7 create qualified channel to shunt / relay

[0123] S8 send / receive data request message

[0124] S9 trigger timer for creation of quantum link

[0125] S10 forward data request message

[0126] S11 creation of quantum link

[0127] S12 central link data message

[0128] S13 exchange / establish quantum communication channel

Claims

1. A method for establishing a quantum communication channel (C) in a quantum computing arrangement (1) for transmitting quantum data units (Z) between a source (A) quantum device (2) and a destination (B) quantum device (2), the method comprising the steps of: requesting at least one quantum path (J) between a first quantum device (2) and a second quantum device (2); establishing at least two quantum bounding channels (K) between respective two quantum devices (2) each designated for implementing the at least one quantum path (J); providing at least two quantum links (L) by entangling at least one qubit (q) of each of the respective two quantum devices (2) connected by the at least two quantum bounding channels (K); and synchronizing in time the quantum devices (2) providing the at least two quantum bounding channels (K) for simultaneously providing the at least one quantum path (J) via the at least two quantum links (L) for establishing the quantum communication channel (C).

2. The method according to claim 1, further comprising the step of providing a setup message (U) to be received by the quantum devices (2) designated for implementing the quantum path (J).

3. The method according to claim 1 or 2, further comprising the step of establishing a first set of quantum links (L) for providing at least two alternative quantum communication channels (C).

4. The method according to at least one of claims 1 to 3, further comprising the step of evaluating at least one quantum path (J) best suited for establishing the quantum communication channel (C).

5. The method according to at least one of claims 1 to 4, further comprising the step of triggering a timer for synchronizing the quantum devices (2).

6. The method of at least one of claims 1 to 5, further comprising the step of: sending a data request message (W) with the source (A) quantum device (2) to the quantum devices (2) providing the at least two quantum bounding channels (K) for providing information about resources of the quantum devices (2) required for establishing the quantum communication channel (C).

7. The method according to at least one of claims 1 to 6, further comprising the step of providing at least one link state message (T) indicating a quality of the at least two quantum links (L) represented by a time-to-live value (K) representing an average fidelity level of the at least two quantum links (L).

8. The method of at least one of claims 1 to 7, further comprising the step of: exchanging (X) entanglement of qubits (q) within at least one quantum device (2) for establishing at least two quantum links (L).

9. A control program (11) for controlling a quantum computing arrangement (1), the control program (11) comprising instructions which, when the control program (11) is executed by a control unit (3), cause the control unit (3) to carry out the method according to at least one of claims 1 to 8.

10. A computer readable data carrier (13) having stored thereon the control program according to claim 9.

11. A control unit (3) for controlling at least one quantum device (2) in a quantum computing arrangement (1), the control unit (3) being configured to implement the method according to at least one of claims 1 to 8 and / or comprising the computer-readable data carrier (13) according to claim 10.

12. A quantum device (2) for a quantum computing arrangement (1), the quantum device (2) being configured to implement the method according to at least one of claims 1 to 8 and / or being adapted to be controlled by the control unit (3) according to claim 11.

13. A quantum network (Q) for a quantum computing arrangement (1), the quantum network (Q) being configured to implement the method according to at least one of claims 1 to 9 and / or comprising at least one control unit (3) according to claim 11 and / or at least one quantum device (2) according to claim 12.

14. An apparatus (7), such as a satellite (9b), an aircraft (9a) and / or a communication station (8), the apparatus (7) being configured to participate in a quantum computing arrangement (1), comprising at least one control unit (3) according to claim 11, at least one quantum device (2) according to claim 12 and / or at least one quantum network (Q) according to claim 13.

15. A quantum computing arrangement (1), the quantum computing arrangement (1) being configured to implement the method according to at least one of claims 1 to 8, comprising at least one control unit (3) according to claim 11, at least one quantum device (2) according to claim 12, at least one quantum network (Q) according to claim 13 and / or at least one apparatus (7) according to claim 14.

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