System and method for allocating quantum entanglement

Abstract

A nested network includes a plurality of nodes, each including higher and lower level quantum systems. An intra-node optical network may be configured to interconnect the quantum systems of each of the nodes. An inter-node optical network may be configured to interconnect the higher energy level quantum systems of the plurality of nodes. The higher energy level quantum system may be selectively connected to the intra-node optical network or the inter-node optical network. Each quantum system may include one or more proxy qubits and one or more customer qubits. Entanglement of quantum systems in different nodes may be performed by performing parallel attempts to entangle quantum states of multiple pairs of the higher energy level quantum systems and transfer the entanglement to a lower energy level quantum system of each node after successful entanglement of a pair.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Application No. 63 / 364,246, filed on May 5, 2022, and entitled “SYSTEMS AND METHODS FOR DISTRIBUTING QUANTUM ENTANGLEMENT”, which is hereby incorporated by reference herein for all purposes. For the United States of America, this application claims the benefit of U.S. Application No. 63 / 364,246, filed on May 5, 2022, and entitled “SYSTEMS AND METHODS FOR DISTRIBUTING QUANTUM ENTANGLEMENT” under 35 U.S.C. §119, which is hereby incorporated by reference herein for all purposes. Technical Field

[0003] The present technology relates to quantum information and in particular to systems and methods for entangling quantum states of quantum systems. Background Art

[0004] In distributed quantum computing and other applications of quantum mechanics, it is desirable to provide quantum systems with quantum states that are entangled with each other (e.g., multiple pairs of quantum systems with corresponding quantum states that form Bell pairs). A pair of quantum systems may be entangled ("two-body entanglement") or three or more quantum systems may be entangled ("many-body entanglement").

[0005] A multi-body entangled state can be created by entangling the quantum states of a pair of quantum systems and then extending the entanglement to other quantum systems. For example, the quantum states of the first, second, and third quantum systems can be entangled by first entangling the quantum states of a pair of the quantum systems (e.g., the first and second quantum systems) and then entangling the other (e.g., the third) of the quantum systems with one of the pair of quantum systems (e.g., the first or second quantum system). This process can be repeated to add additional quantum systems to the multi-body entangled state.

[0006] Entangled quantum states have many applications. For example, in quantum computing, Bell pairs can be consumed to perform remote quantum gates between qubits, teleporting qubits between different quantum systems. Entangled quantum systems can also be used in quantum cryptography, timekeeping, and other applications.

[0007] Realizable quantum systems cannot be completely isolated from their environment. Therefore, over time, the interaction between a quantum system prepared in a specific quantum state and the environment causes random changes in the quantum state of the quantum system. This process is called decoherence. Decoherence will eventually cause entangled quantum systems to lose their entanglement.

[0008] There are a variety of known protocols that can be applied to entangle the quantum states of two quantum systems. Some of these protocols are probabilistic in nature (meaning that each attempt to entangle two quantum systems using such protocols has a certain probability of failure). An example protocol for creating entanglement between quantum systems is described below:

[0009] • SD Barrett et al., PRA 71, 060310R (2005).

[0010] Many protocols for entangling two spaced-apart quantum systems are optically mediated. In such protocols, a single photon having a quantum state that is related to the quantum state of the two quantum systems (e.g., a photon emitted by a quantum transition in one or both of the quantum systems) can be transported via an optical path to a location where an interaction with one or more photons or an interaction among one or more photons may occur. In particular, if the optical path is lossy, any individual attempt to entangle the quantum systems may fail. The average number of attempts required to entangle the quantum systems will increase with the loss of the optical path.

[0011] Some entanglement protocols are inherently probabilistic. In the case of such protocols, any individual entanglement attempt may fail with a probability that depends on the details of the protocol.

[0012] Entanglement protocols typically involve several steps. When an entanglement attempt fails, the quantum states of the associated quantum systems may be unknown, and it is necessary to re-initialize the quantum systems involved and start the process again for creating the desired entangled state.

[0013] The above problem is particularly serious in the case where the goal is to create a multi-body entangled state through an entanglement sequence, because if any entanglement attempt in the sequence fails, the entire sequence must be started again. The probability of successfully creating a multi-body entangled state decreases with the number of entanglement operations required to create the desired multi-body entangled state.

[0014] The above factors make creating and distributing quantum entanglement challenging because a failed entanglement attempt destroys any entanglement that had been established prior to the point of failure.

[0015] A strategy for constructing entangled states using probabilistic entanglement protocols is "proxy entanglement". Proxy entanglement involves two sets of quantum systems, namely an "proxy" quantum system and a "client" quantum system. In proxy entanglement, the quantum states of two or more proxy quantum systems can be entangled and then transferred to the corresponding client quantum system. The agents may be entangled through a probabilistic entanglement protocol. The transfer of entangled states to the client may be deterministic. A failed attempt to entangle two agents may be followed by a reset of the agent, which can be done without destroying the state of the corresponding client.

[0016] Proxy entanglement does not eliminate the damage to the coherent states stored in client qubits caused by failed entanglement attempts, because resetting the proxy can decohere the client qubits. After a certain number of failed entanglement attempts, the client qubits will decohere due to the interaction with the corresponding proxy qubits, so that any quantum states stored in the client will be lost.

[0017] When performing a probabilistic entanglement process, it is usually necessary to know whether each entanglement attempt is successful. A predictive entanglement protocol can be used. In a predictive entanglement protocol, successful entanglement can be indicated ("predicted") by detecting one or more photons. The loss of a predictive photon in a detection circuit may mean that a successful entanglement attempt must be considered a failure. Unfortunately, photon loss in a photonic circuit becomes more likely as the complexity of the circuit and most significantly the connectivity increases. Therefore, how to manage the loss of predictive photons can be a very important problem that interferes with the execution of quantum circuits that require multiple remote entanglement steps.

[0018] There is a need for systems and methods that facilitate the construction of entangled quantum states for quantum computing and other applications. There is a particular need for such systems and methods that can reliably create and distribute entanglement using lossy optical paths and / or probabilistic entanglement protocols. Summary of the invention

[0019] The present invention comprises several aspects. These include:

[0020] Methods for creating and distributing entangled quantum states;

[0021] Systems for creating and distributing entangled quantum states;

[0022] Multi-layer quantum networks;

[0023] Methods for transferring quantum states and / or quantum gates among nodes or cells of a multi-layer quantum network.

[0024] One aspect of the present invention provides a method for establishing and distributing quantum entanglement. The method includes: providing a first and a second node, each node including one or more alpha quantum systems and a plurality of higher energy level quantum systems. The alpha and higher energy level quantum systems of each node are interconnected by an intra-node optical network, and the higher energy level quantum system of the first node can be connected to at least the corresponding higher energy level quantum system of the second node through an inter-node optical network. The method attempts to establish quantum entanglement of the quantum states of each of the first plurality of pairs of the higher energy level quantum systems by means of the inter-node optical network. Each of the plurality of pairs includes one of the plurality of higher energy level quantum systems of the first node and a corresponding counterpart of the plurality of higher energy level quantum systems of the second node. The method includes: detecting the success of entangling the quantum states of the entangled pairs in the plurality of pairs of higher energy level quantum systems; and at each of the first node and the second node, using the corresponding intra-node optical network to transfer the entanglement of the corresponding higher energy level quantum system of the entangled pair of higher energy level quantum systems to the quantum state of the selected one of the alpha quantum systems of the corresponding node.

[0025] In some embodiments, the attempts to establish quantum entanglement of the plurality of pairs of quantum states of different ones of the higher energy level quantum systems are performed simultaneously.

[0026] In some embodiments, the α and higher energy level quantum systems each include a proxy element having a proxy state and a client element having a client state, and the method includes: entangling the proxy state of the one of the multiple pairs of higher energy level quantum systems; transferring the entanglement to the client state of the higher energy level quantum system of the one of the multiple pairs of higher energy level quantum systems; and transferring the entanglement to the client state of the selected one of the α quantum systems of the first node.

[0027] In some embodiments, transferring the entanglement to the client state of the higher energy level quantum system of the one of the plurality of pairs of higher energy level quantum systems comprises performing a quantum SWAP gate on the higher energy level quantum system of the one of the plurality of pairs of higher energy level quantum systems.

[0028] In some embodiments, performing the quantum SWAP gate for each of the higher energy level quantum systems of the one of the plurality of pairs of higher energy level quantum systems comprises facilitating switching from a state to a state by applying an RF pulse to the respective one of the higher energy level quantum systems of the one of the plurality of pairs of higher energy level quantum systems. To status of transitions, and vice versa.

[0029] In some embodiments, transferring the entanglement to the client state of the selected one in the alpha quantum system of the first node includes: at the first node, entangling the proxy state of the one of the pair of higher-energy-level quantum systems of the first node with the proxy state of the selected one in the alpha quantum system of the first node; at the first node, transferring the entanglement of the client state of the higher-energy-level quantum system of the one of the multiple pairs of higher-energy-level quantum systems of the first node to the client state of the selected one in the alpha quantum system of the first node.

[0030] In some embodiments, the method includes entangling, at the second node, the proxy state of the one of the pair of higher-energy-level quantum systems of the second node with the proxy state of the selected one of the alpha quantum systems of the second node; and transferring, at the second node, the entanglement of the client state of the higher-energy-level quantum system of the one of the multiple pairs of higher-energy-level quantum systems of the second node to the client state of the selected one of the alpha quantum systems of the second node.

[0031] In some embodiments, transferring the entanglement of the client state of the β quantum system of one of the multiple pairs of β quantum systems of the first and / or second nodes to the client state of the corresponding selected one of the α quantum systems of the first and / or second nodes comprises performing a quantum teleportation process.

[0032] In some embodiments, the proxy state and the client state include first and second spin states, respectively.

[0033] In some embodiments, the first spin state comprises an electronic spin state.

[0034] In some embodiments, the second spin state comprises a nuclear spin state.

[0035] In some embodiments, for at least one of the first and second nodes, transferring the entanglement of the corresponding higher energy level quantum system of the entangled pair of higher energy level quantum systems to the quantum state of a selected one of the α quantum systems of the corresponding node using the optical network within the corresponding node includes transferring the entanglement to the selected one of the α quantum systems, including sequentially transferring the entanglement from the corresponding higher energy level quantum system to one or more intermediate energy level quantum systems and from one of the one or more intermediate energy level quantum systems to the selected α quantum system.

[0036] In some embodiments, the one or more intermediate energy level quantum systems include a beta quantum system, and the intra-node optical network includes an optical link directly connecting the alpha quantum system to the beta quantum system.

[0037] In some embodiments, the quantum system is embedded in a crystalline substrate.

[0038] In some embodiments, the quantum system includes a luminescent center.

[0039] In some embodiments, the higher energy level quantum systems each comprise a T center.

[0040] In some embodiments, each of the first and second nodes includes at least five of the higher-energy level quantum systems, and the method includes attempting in parallel to establish quantum entanglement of the quantum state of each of the at least five of the higher-energy level quantum systems of the first node with the quantum state of a corresponding counterpart of the multiple higher-energy level quantum systems of the second node.

[0041] In some embodiments, each of the first and second nodes includes at least ten of the higher-energy-level quantum systems, and the method includes attempting in parallel to establish quantum entanglement of the quantum state of each of at least ten of the beta quantum systems of the first node with the quantum state of a respective counterpart of the plurality of higher-energy-level quantum systems of the second node.

[0042] In some embodiments, the method includes teleporting a quantum gate or quantum state from the first node to the second node using the entanglement of the quantum states of the respective selected ones in the alpha quantum system.

[0043] In some embodiments, the method includes configuring the intra-node network of the first node to provide an optical connection between the higher energy level quantum system and the selected one of the alpha quantum systems or a beta quantum system associated with the selected one of the alpha quantum systems.

[0044] In some embodiments, the first node includes N higher energy level quantum systems, and each of the N higher energy level quantum systems is connected to a corresponding port of a first optical switch, the first optical switch is operable to selectively couple the higher energy level quantum system to the intra-node optical network or the inter-node optical network, and configuring the intra-node network of the first node includes operating the first optical switch to connect the higher energy level quantum systems of the entangled ones of the multiple pairs of higher energy level quantum systems to the intra-node optical network of the first node.

[0045] In some embodiments, the first node includes M alpha quantum systems and each of the M alpha quantum systems is coupled to a corresponding port of a second optical switch, and configuring the intra-node network of the first node includes operating the second optical switch to connect the selected one of the alpha quantum systems and the higher-energy-level quantum systems belonging to the entangled ones of the multiple pairs of higher-energy-level quantum systems.

[0046] In some embodiments, the method includes expanding the entanglement of the entangled persons in the multiple pairs of higher energy level quantum systems to provide a many-body entangled state of three or more of the higher energy level quantum systems.

[0047] In some embodiments, the three or more of the higher energy level quantum systems in the many-body entangled state include higher energy level quantum systems in at least the first node, the second node, and a third node.

[0048] In some embodiments, the intra-node optical network is characterized by a loss of less than 3 dB.

[0049] In some embodiments, the inter-node optical network is characterized by a loss greater than 3 dB.

[0050] In some embodiments, the method includes maintaining resources of at least one entangled pair of the higher energy level quantum system by continuing to attempt to establish quantum entanglement of multiple pairs of quantum states of the higher energy level quantum system via the inter-node optical network at a rate sufficient to replace entangled pairs of the higher energy level quantum system that are consumed by quantum decoherence or cease to be entangled.

[0051] In some embodiments, the method includes providing a third node comprising one or more alpha quantum systems and a plurality of higher energy level quantum systems, and attempting to establish quantum entanglement of a second plurality of pairs of quantum states of each of the higher energy level quantum systems by means of the inter-node optical network, wherein each of the second plurality of pairs comprises one of the plurality of higher energy level quantum systems of the first node and a corresponding counterpart of the plurality of higher energy level quantum systems of the third node.

[0052] Another aspect of the present invention provides a quantum network comprising a plurality of nodes or cells. Each node or cell comprises: at least one alpha quantum system, a plurality of higher energy level quantum systems, and an intra-node optical network optically coupled to the at least one alpha quantum system and the plurality of higher energy level quantum systems. The inter-node optical network can be configured to provide a plurality of optical paths, each of which optically connects the corresponding pair of higher energy level quantum systems. Each of the plurality of pairs comprises one of the higher energy level quantum systems of the first of the nodes and the corresponding higher energy level quantum system of the second of the nodes. The controller is configured to: simultaneously perform an attempt to entangle the higher energy level quantum system of each of the plurality of pairs of β quantum systems via the inter-node optical network; upon detecting the entanglement of the higher energy level quantum systems of the entangled persons in the plurality of pairs of higher energy level quantum systems, transfer the entangled states of the entangled persons in the plurality of pairs of higher energy level quantum systems to a selected alpha quantum system in the one or more alpha quantum systems of the first of the nodes and / or a selected alpha quantum system in the one or more alpha quantum systems of the second of the nodes via the intra-node optical network.

[0053] In some embodiments, the alpha and higher energy level quantum systems each include a proxy element having a proxy state and at least one client element having a client state.

[0054] In some embodiments, the controller is further configured to: execute a protocol for entangling the proxy states of the multiple pairs of higher-energy level quantum systems; execute a protocol for transferring the entanglement to the client states of the higher-energy level quantum systems of the entangled ones in the multiple pairs of higher-energy level quantum systems when the proxy states of the entangled ones in the multiple pairs of higher-energy level quantum systems are entangled; execute a protocol for entangling the proxy states of the higher-energy level quantum systems of the entangled ones in the multiple pairs of higher-energy level quantum systems of the first node with the proxy states of the selected ones in the alpha quantum system of the first node; execute a protocol for transferring the entanglement of the client states of the higher-energy level quantum systems of the entangled ones in the multiple pairs of higher-energy level quantum systems of the first node to the client states of the selected ones in the alpha quantum system of the first node.

[0055] In some embodiments, the proxy state and the client state include first and second spin states, respectively.

[0056] In some embodiments, the first spin state comprises an electronic spin state.

[0057] In some embodiments, the second spin state comprises a nuclear spin state.

[0058] In some embodiments, the proxy element and the client element have a fixed spatial relationship in each of the alpha quantum systems.

[0059] In some embodiments, the strength of the hyperfine coupling between the proxy element and the client element is the same for each of the alpha quantum systems.

[0060] In some embodiments, each of the alpha quantum systems and / or each of the higher energy level quantum systems are embedded in a crystalline substrate.

[0061] In some embodiments, the quantum system includes a luminescent center.

[0062] In some embodiments, the higher energy level quantum systems each comprise a T center.

[0063] In some embodiments, the inter-node optical network is more lossy than the intra-node optical networks of the first and second nodes.

[0064] In some embodiments, the intra-node optical network is characterized by a loss of less than 3 dB.

[0065] In some embodiments, the inter-node optical network is characterized by a loss greater than 3 dB.

[0066] In some embodiments, each of the nodes comprises at least five of the higher energy level quantum systems.

[0067] In some embodiments, for each of the plurality of nodes, the intra-node network includes an optical mixer having first and second input ports and a first output port, and a single photon detector at each of the output ports, and the controller is configured to configure the intra-node network to optically couple the selected alpha quantum system to the first input port of the optical mixer and optically connect the higher energy level quantum system of the entangled pair to the second input port of the optical mixer.

[0068] In some embodiments, each of the plurality of nodes comprises a first optical switch having a plurality of input ports and an output port optically connected to the first input port of the optical mixer, each of the plurality of input ports being optically connected to a corresponding one of the one or more alpha quantum systems of the node.

[0069] In some embodiments, for each of the plurality of nodes, the intra-node network includes a single photon detector at each of the output ports having first and second input ports and first and second output ports, and the controller is configured to configure the intra-node network to optically couple a quantum system between the selected α quantum system and the higher energy level quantum system of the entangled pair to the first input port of the optical mixer, and to optically connect the higher energy level quantum system of the entangled pair to the second input port of the optical mixer.

[0070] In some embodiments, each of the plurality of nodes comprises a first optical switch having a plurality of input ports and an output port optically connected to the first input port of the optical mixer, each of the plurality of input ports being optically connected to a corresponding one of a plurality of quantum systems of the node.

[0071] In some embodiments, each of the plurality of nodes comprises a second optical switch having a plurality of input ports and an output port optically connected to the second input port of the optical mixer, each of the plurality of input ports being optically connected to a corresponding one of the plurality of higher energy level quantum systems of the node.

[0072] Another aspect of the present invention provides a method for distributing quantum entanglement, the method comprising: providing a plurality of cells, each of the cells comprising a plurality of quantum systems, the plurality of quantum systems including: a plurality of higher-energy-level quantum systems, each of which can be selectively connected to an inter-cell optical network or an intra-cell optical network; and one or more alpha quantum systems, which can be connected to the intra-cell optical network; configuring the inter-cell optical network to connect a plurality of pairs of the higher-energy-level quantum systems in pairs, wherein each of the plurality of pairs comprises two of the higher-energy-level quantum systems and the two higher-energy-level quantum systems are in different ones of the cells; attempting to establish quantum entanglement of the quantum states of each of the plurality of pairs of the higher-energy-level quantum systems by means of the inter-cell optical network.

[0073] In some embodiments, the plurality of cells includes three or more of the cells, and for at least one of the cells, the plurality of higher energy level quantum systems includes one or more higher energy level quantum systems paired with a corresponding higher energy level quantum system of a first other of the cells and one or more higher energy level quantum systems paired with a corresponding higher energy level quantum system of a second other of the cells.

[0074] In some embodiments, attempting to establish quantum entanglement of the quantum states of each of the plurality of pairs of the higher energy level quantum systems is performed simultaneously for at least five of the plurality of pairs.

[0075] In some embodiments, the method includes maintaining at least a set number of the plurality of pairs of the higher energy level quantum systems in an entangled state and automatically replenishing the entangled pairs in response to entanglement of the plurality of pairs being depleted.

[0076] In some embodiments, the method includes automatically replenishing the entangled pair in response to a predetermined time having passed since entanglement of one of the entangled pair.

[0077] In some embodiments, the method includes detecting the success of entangling the quantum states of the entangled pairs in the multiple pairs of higher-energy-level quantum systems; and at each of the first cell and the second cell in the multiple cells, transferring the entanglement of the corresponding higher-energy-level quantum system of the entangled pair of the higher-energy-level quantum systems to the quantum state of a selected one of the α quantum systems of the corresponding cell using the corresponding intra-cell optical network.

[0078] In some embodiments, the α quantum system and the higher-energy-level quantum system each include a proxy element having a proxy state and a client element having a client state, and the method includes: entangling the proxy state of the higher-energy-level quantum system of one of the multiple pairs of higher-energy-level quantum systems; transferring the entanglement of the proxy state to the client state of the higher-energy-level quantum system of the one of the multiple pairs of higher-energy-level quantum systems.

[0079] Another aspect of the present invention provides a system for distributing quantum entanglement. The system includes a plurality of cells. Each of the cells includes a plurality of quantum systems, the plurality of quantum systems comprising: a plurality of higher energy level quantum systems, each of which can be selectively connected to an inter-cell optical network or an intra-cell optical network; and one or more lower energy level quantum systems, which can be connected to the intra-cell optical network. The system includes a controller, the controller being operable to: configure the inter-cell optical network to connect multiple pairs of the higher energy level quantum systems in pairs, wherein each of the multiple pairs includes two of the higher energy level quantum systems and the two higher energy level quantum systems of each of the multiple pairs are in different ones of the cells; and use the inter-cell optical network to perform a non-deterministic quantum entanglement protocol on the higher energy level quantum system of each of the multiple pairs of the higher energy level quantum systems.

[0080] In some embodiments, the inter-cell optical network comprises a plurality of optical mixers, each of the optical mixers having first and second input ports, and configuring the inter-cell optical network comprises, for each of the plurality of pairs, coupling the higher energy level quantum system of the pair to the first and second input ports of a corresponding one of the plurality of optical mixers.

[0081] In some embodiments, each of the cells comprises a first optical switch operable to selectively couple each of the higher energy level quantum systems of the cell to the inter-cell optical network or the intra-cell optical network.

[0082] In some embodiments, each of the cells comprises a second optical switch operable to selectively connect one of the lower energy level quantum systems of the cell to any of the plurality of higher energy level quantum systems of the cell.

[0083] In some embodiments, the one of the higher energy level quantum systems is a beta quantum system, and the cell includes an alpha quantum system connectable to the beta quantum system through the intra-cell optical network.

[0084] In some embodiments, the alpha quantum system and the beta quantum system each include a proxy element having a proxy state and a client element having a client state.

[0085] In some embodiments, the proxy state and the client state include first and second spin states, respectively.

[0086] In some embodiments, the first spin state comprises an electronic spin state.

[0087] In some embodiments, the second spin state comprises a nuclear spin state.

[0088] In some embodiments, the quantum system is embedded in a crystalline substrate.

[0089] In some embodiments, the quantum system includes a luminescent center.

[0090] In some embodiments, the higher energy level quantum systems each comprise a T center.

[0091] Another aspect of the present invention provides a hierarchical quantum network, which includes a plurality of quantum systems. Each of the quantum systems includes an agent element and a client element. The plurality of quantum systems are associated with an optical network to provide a hierarchical topology, wherein: a first plurality of the quantum systems designated as α quantum systems are each associated with one of a plurality of corresponding nodes; a second plurality of the quantum systems designated as β quantum systems are each associated with a corresponding one of the nodes. Each of the nodes has a corresponding intra-node optical network. The β quantum system can be selectively connected to a corresponding one of the plurality of intra-node optical networks or one of at least one inter-node optical network. A controller is configured to: entangle a pair of the β quantum systems by executing a probabilistic entanglement protocol, the pair including the first and second of the β quantum systems, wherein the first and second β quantum systems in the pair are respectively associated with first and second different ones of the nodes; and apply the resulting entangled quantum states of the pair of the β quantum systems to teleport the quantum state of the α quantum system of the first node or a quantum gate involving the α quantum system of the first node to the second node.

[0092] In some embodiments, the intra-node optical network is characterized by a loss probability of single photons that is lower than a loss probability of single photons of the at least one inter-node optical network.

[0093] In some embodiments, the intra-node optical network includes a third plurality of the quantum systems designated as gamma quantum systems each associated with a corresponding one of the nodes, and the intra-node network is configurable to provide optical links connecting a plurality of pairs of the gamma quantum systems, wherein each of the plurality of pairs of gamma quantum systems includes a first gamma quantum system and a second gamma quantum system, wherein the first and second gamma quantum systems of each of the plurality of pairs are respectively associated with different ones of the nodes, and the inter-node optical network is further configurable to provide an optical link connecting the first and second gamma quantum systems in each pair to at least one of the beta quantum systems of the respective node.

[0094] In some embodiments, the intra-node optical networks can each be configured to establish an optical connection between the α quantum system of the corresponding node and the β quantum system of the corresponding node, each of the optical connections including an interaction unit having first and second inputs respectively arranged to receive photon states originating from the connected α and β quantum systems and first and second outputs respectively arranged to deliver photons to first and second single-photon detectors, the interaction unit being configured to allow interference between the photon states originating from the connected α and β quantum systems.

[0095] Another aspect of the present invention provides a hierarchical quantum network, which includes quantum systems arranged into at least three layers. The hierarchical quantum network includes: a top layer, which includes a plurality of the quantum systems designated as top-layer quantum systems; a bottom layer, which includes a plurality of the quantum systems designated as bottom-layer quantum systems distributed among a plurality of cells; one or more intermediate layers, each of the intermediate layers including a corresponding plurality of the quantum systems designated as middle-layer quantum systems; and an optical network, which can be configured to provide an optical link chain, the optical link chain extends from the first of the bottom-layer quantum systems in the first of the cells to the second of the bottom-layer quantum systems in the second of the cells by means of the middle-layer quantum systems and the top-layer quantum systems. The optical network includes a plurality of intra-cell optical networks each associated with a corresponding one of the cells and an inter-cell optical network configurable to provide an optical link, the optical link connecting the quantum system associated with the cell with others in the quantum system located outside the cell. The optical link chain includes: an optical link connecting the first bottom layer quantum system to the first one of the middle layer quantum systems; an optical link connecting the second bottom layer quantum system to the second one of the middle layer quantum systems; a top layer optical link connecting a pair of the first and second ones of the top layer quantum systems; one or more optical links connecting the first middle layer quantum system directly or indirectly to the first top layer quantum system; and one or more optical links connecting the second middle layer quantum system directly or indirectly to the second top layer quantum system. The controller is configured to distribute quantum entanglement to the first and second middle layer quantum systems by executing a predicted entanglement protocol to entangle the quantum states of the first and second top layer quantum systems and extend the entanglement to the first and second middle layer quantum systems.

[0096] In some embodiments, the controller is further configured to: entangle the quantum states of each of the multiple pairs of the top-layer quantum systems; extend the entanglement of each of the multiple pairs of the top-layer quantum systems to a corresponding pair of the intermediate-layer quantum systems; and purify the entanglement of the entangled pairs of intermediate-layer quantum systems.

[0097] In some embodiments, the controller is configured to cause teleportation of the quantum state of the first underlying quantum system to the second underlying quantum system using the entanglement of the quantum states of the first and second intermediate layer quantum systems.

[0098] In some embodiments, the controller is configured to cause teleportation of a quantum gate controlled by the first underlying quantum system using the entanglement of the quantum states of the first and second intermediate layer quantum systems to apply the quantum gate to the second underlying quantum system.

[0099] Other aspects and example embodiments are illustrated in the drawings and / or described in the description below.

[0100] It is emphasized that the invention relates to all combinations of features described above, even if these features are recited in different claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] The accompanying drawings illustrate non-limiting example embodiments of the invention.

[0102] Figure 1 is a schematic depiction of a system in accordance with a simple example embodiment of the present technology.

[0103] Figure 1A is a schematic depiction of example nodes that may be used in a system of the present technology.

[0104] Figure 2 is a flow chart of a method according to an example embodiment.

[0105] Figure 3 is a block diagram of a hardware implementation of an instance node.

[0106] Figure 4 is a block diagram of a hardware implementation of an example inter-node network.

[0107] Figure 5 is a schematic cross-section of a substrate supporting a quantum system and a device used to work with the quantum states of the quantum system.

[0108] Figure 6 is an example energy level diagram of a quantum system that may be incorporated into systems in accordance with the present technology.

[0109] Figure 7 is a flow chart illustrating a method for creating and distributing entanglement applicable to the case where individual quantum systems include proxy elements and client elements.

[0110] Figure 8 is a schematic illustration showing an example sequence of interactions that can be applied to create entanglement of alpha-client qubits in a system in accordance with the present technology.

[0111] Fig. 8A is an example energy level diagram with annotations showing one way to initialize a quantum system in a desired state.

[0112] Figure 8B , 9 9A are quantum circuit diagrams illustrating, respectively, a sequence for entangling the α-client qubits of two nodes; a sequence for creating multi-body entanglement of several qubits; and a sequence for teleporting a quantum CNOT gate.

[0113] Fig.10is a schematic illustration showing an example network with three layers of a quantum system.

[0114] Fig. 10A , 10B 10C is a diagram showing an example interconnect topology that may be present in a system as described herein.

[0115] Fig.11 is a graph illustrating the effect of the number of parallel entanglement attempts on the time required to establish an entangled pair of qubits.

[0116] Fig.12 is a graph illustrating the effect of photon loss on the fidelity of entangled states.

[0117] definition

[0118] "Connected" in the context of quantum systems means "connected" by an optical path, optical link, optical waveguide, or optical network extending between the quantum systems. "Connected" includes situations where the optical path, optical link, optical waveguide, or optical network is operable to carry photons or photon states emitted by each of the quantum systems to locations (e.g., optical mixers, optical beam splitters, optical coupling waveguides, etc.) where the photons or photon states can interact (e.g., interfere) with each other. For example, two quantum systems are "connected" when the optical network is configured to deliver photons originating from each of the optical systems to an interaction unit having first and second inputs, respectively, arranged to receive photon states originating from the connected quantum systems, and first and second outputs, respectively, arranged to deliver photons to first and second single photon detectors, wherein the interaction unit is configured to allow interference between photon states originating from the connected quantum systems.

[0119] "Entanglement" describes a situation where the quantum states of individual quantum systems in a group of two or more quantum systems cannot be described independently of the quantum states of the other quantum systems in the group. An equivalent definition of an entangled state is a state of multiple quantum systems that cannot be decomposed into the states of the individual quantum systems that make it up. For example, two entangled particles may each have a quantum state that is a superposition of spin-up and spin-down, while the combined spin of the two particles is constrained to be zero. Entanglement can even exist between quantum systems separated by very large distances.

[0120] "Highly entangled state" means a state that is maximally entangled or close to maximally entangled. Bell pairs are an example of a highly entangled state.

[0121] "Qubit" means a quantum system having a first and a second quantum state that can be used to represent quantum information and that can exist in quantum superposition. Examples of quantum systems that can be used as qubits include: particles with spin (e.g., electrons, atomic nuclei, holes), where different spin states can represent information; particles with exciton states, where the absence or presence of excitons can represent information; particles with different orbital states (e.g., electrons), where the orbital state occupied by the particle represents information, and the like.

[0122] "Triple-state particle" refers to a quantum system with three or more quantum states that can be used to represent quantum information and can exist in quantum superposition. Particles with a spin greater than 1 / 2 can be used as triple-state particles, for example.

[0123] "Proxy quantum system" means a quantum system that is applied as a conduit to deterministically transfer quantum states to another quantum system (client quantum system).

[0124] "Client quantum system" means a quantum system that receives a transfer of quantum states from a proxy quantum system.

[0125] "Quantum system" means a system that has practical applications for storing and / or manipulating quantum information. A quantum system supports multiple quantum states and superpositions of at least two supported quantum states. Examples of quantum systems are spins (e.g., electron spins, nuclear spins), qubits, tri-state particles, quantum dots, damage centers (e.g., T, I, and M centers), NV centers, impurity atoms in silicon or other substrates, and collections of two or more of these. In some embodiments, a quantum system is used as a qubit. For example, a quantum system may consist of or include a spin having two spin states, and the spin may be used as a qubit to store and manipulate information represented by individual ones or superpositions of the two spin states. DETAILED DESCRIPTION

[0126] Throughout the following description, specific details are set forth in order to provide a more thorough understanding of the present invention. However, the present invention may be practiced without these details. In other examples, well-known elements are not shown or described in detail to avoid unnecessarily obscuring the present invention. Therefore, the description and the accompanying drawings are considered to be illustrative rather than restrictive.

[0127] One application of the present technology is to establish entanglement between quantum systems connected by an optical path (e.g., optical waveguides, optical fibers, open space, etc.). In some embodiments, the optical path is non-deterministic, meaning that the same photon or photon state emitted into the optical path may be affected in different ways by propagation along the optical path. For example, some photons or photon states may be lost by the optical path, or some photons or photon states may experience different changes in phase / polarization or other properties as they propagate along the optical path.

[0128] In some embodiments, the optical path is lossy (i.e., the probability that a photon delivered into one end of the optical path will reach the other end of the optical path is less than about 50% (corresponding to a 3 dB loss). In some embodiments, the optical path has a loss in the range of about 3 dB to about 40 dB (corresponding to a probability that a single photon will traverse the optical path without loss in the range of about 50% to about 0.01%).

[0129] Probabilistic entanglement protocols can be applied to establish entanglement of quantum systems connected by optical paths. The probability of successful entanglement from one execution of the probabilistic entanglement protocol varies with the details of the protocol and the probability that a single photon created when executing the protocol will be detected. In some embodiments, the probability that any single execution of the probabilistic entanglement algorithm will result in entanglement is less than about 13%. Some embodiments perform the probabilistic entanglement protocol over a lossy optical link, where the probability of successful entanglement from one iteration of the entanglement is within about 10 -7 % to about 20%.

[0130] The present technology provides a method that can be applied to alleviate the problems described in the background section. This method involves providing multiple quantum systems connected by optical paths and simultaneously performing an entanglement protocol for multiple pairs of quantum systems, wherein each of the multiple pairs includes a quantum system connected by an optical path.

[0131] Once the quantum system of any of the multiple pairs is successfully entangled, the goal of obtaining quantum system entanglement at either end of the optical path is achieved. The entangled pairs can then be applied as a resource, for example, to teleport quantum states or quantum gates from one end of the optical path to the other; to quantum cryptography; or for any other application of entanglement.

[0132] In a preferred embodiment, the execution of the entanglement protocol is automated. A computer system can coordinate the steps of executing the entanglement protocol for different pairs of quantum systems, and can determine when the entanglement of the quantum systems of any of the multiple pairs has been established. In some embodiments, the entanglement attempts are performed substantially continuously, so that at any given time, one or more of the multiple pairs of qubits are entangled and available as resources. In some embodiments, the entanglement attempts are performed on demand and because any practical number of entanglement attempts can be performed simultaneously, the time required to establish an entangled pair of quantum systems is significantly reduced compared to the case where the entanglement attempts are continuously repeated for a single pair of quantum systems until entanglement has been achieved.

[0133] Without loss of generality, quantum systems at either end of an optical path may be considered to belong to a "node" or "cell". The present techniques may be applied to establish entanglement among quantum systems at different nodes and / or distribute entanglement to one or more other quantum systems within a node. The nodes are not required to be physically separated by any particular distance, but they may be separated by any distance, including distances ranging from very large distances to very small distances.

[0134] Figure 1 An example system 100 is described according to an example implementation of the present technology. The system 100 can be applied to efficiently construct entangled states. The system 100 includes a plurality of nodes 102. Figure 1 A simple example is shown in which system 100 includes a quantum system associated with three nodes 102. However, system 100 may have from two up to any practical number of nodes 102.

[0135] Each node 102 includes a plurality of quantum systems. Figure 1 Quantum systems 20A and 20B are included (collectively or generically referred to as quantum system 20 ). System 100 may operate as described herein to create entanglement among two or more of quantum systems 20B in two or more of nodes 102 .

[0136] To explain the operation of system 100, it is convenient to consider the case where each quantum system 20 is a qubit. Quantum systems 20 are not limited to qubits (e.g., as in other examples described herein, they may include triads or systems combining two or more qubits and / or triads). As described below (see, e.g., Figure 7 ), in some embodiments, each quantum system 20 includes an element that can act as an agent and an element that can act as a client. By way of example only, the agent element may include an electron spin and the client element may include a nuclear spin.

[0137] For example, quantum system 20 can be implemented by particles that possess intrinsic spin. Different spin states can correspond to different calculated values. Because quantum system 20 is a quantum system, they are not limited to being in a specific spin state. For example, a particle with spin 1 / 2 can be observed to have spin up or spin down relative to any selected axis. However, a particle can have a quantum state that is a specific superposition of spin up and spin down.

[0138] The system 100 includes optical paths connecting different nodes 102. In the illustrated embodiment, the optical paths are provided by a reconfigurable inter-node optical communication network 110. The network 110 is highly connected and is specifically configurable to simultaneously provide multiple optical links between any two nodes 102 in the system 100, such that each of the optical links provides an optical path that optically couples one quantum system 20B in a first one of the nodes 102 to one quantum system 20B in another one of the nodes 102.

[0139] Entanglement may be created between multiple pairs of quantum systems 20B in different nodes 102, for example as described above. For applications where many-body entanglement is desired, this entanglement may optionally be extended to many-body entanglement of groups of three or more quantum systems 20B.

[0140] In the illustrated embodiment, each node 102 includes one or more additional quantum systems 20A. Specifically, each node 102 includes a group 104 consisting of a plurality of quantum systems 20B and a group 106 consisting of one or more other quantum systems 20A.

[0141] Quantum system 20A may be referred to as an "α" quantum system and quantum system 20B may be referred to as a "β" quantum system. This nomenclature reflects the idea that quantum systems 20 of system 100 may be viewed as logically arranged into "layers" (e.g., α layer and β layer), wherein quantum systems 20 belonging to each layer may play different roles. For example, β quantum system 20B may be applied to establish entanglement between different nodes 102 and α quantum system 20A may be used in operations that consume entanglement provided by β quantum system 20B. This nested layer structure may be extended to three or more layers (e.g., α, β, γ layers).

[0142] In each node 102, a low-loss optical network 112 connects the beta quantum system 20B of the node 102 to the alpha quantum system 20A of the node 102. In some embodiments, the low-loss optical network 112 includes a low-loss optical path 113 connecting each of the beta quantum systems 20B to each of the alpha quantum systems 20A. The low-loss optical path 113 facilitates the application of deterministic quantum operations among the quantum systems 20A, 20B of any node 102.

[0143] The quantum systems 20 of nodes 102 are not required to be in any particular spatial relationship to each other. The quantum systems 20 of nodes 102 are interconnected by low-loss optical network 112, and the beta quantum system 20B of node 102 can be connected to quantum systems outside node 102 by means of optical communication network 110. The optical links provided by networks 110 and 112 can be of any practical length, from small to very large.

[0144] The nodes 102 may be spatially separated from each other, but this is not mandatory in all embodiments. Embodiments are possible where the quantum systems 20 of two or more distinct nodes 102 are at intermixed locations (e.g., distributed in the same area of ​​a substrate). Other embodiments are possible where the quantum systems 20 of distinct nodes 102 are more widely separated (e.g., located on different substrates, in different refrigerators, in different buildings, etc.). Quantum systems 20 belonging to the same node 102 may be spaced closely together and / or widely distributed.

[0145] Figure 1A A very simple example of one node 102-1 is shown. Node 102-1 includes two or more beta quantum systems and one or more alpha quantum systems. In this example, node 102-1 includes two beta quantum systems 20B (individually identified as 20B-1 and 20B-2) and four alpha quantum systems 20A (individually identified as 20A-1 to 20A-4). Each beta quantum system 20B is optically connected or connectable to a corresponding waveguide 111 of an inter-node network 110 (portions of waveguides 111-1 and 111-2 are shown). Each alpha quantum system 20A and each beta quantum system 20B is optically connected or connectable to a waveguide 113 of a low-loss optical network 112.

[0146] System 100 includes additional elements as described elsewhere herein, including a controller 118 that coordinates the operation of system 100. Controller 118 may, for example, be configured to: set and / or manipulate the quantum state of quantum system 20, and / or control optical networks 110 and / or 112 to provide desired optical connectivity between quantum systems 20.

[0147] The mechanisms for setting and manipulating the quantum states of quantum systems 20 may depend on the properties of quantum systems 20 and may include, for example, mechanisms to generate bias and / or local magnetic fields, radiation sources (e.g., optical radiation, radio frequency radiation, such as, for example, microwave radiation) that may be delivered to quantum systems 20 individually and / or in groups, mechanisms for applying electric fields to individual quantum systems 20, etc. Controller 118 may, for example, be configured to initialize any of quantum systems 20 to a desired quantum state by applying a combination of optical and / or radio frequency pulses to quantum systems 20, as is known in the art. Example coordination tasks that controller 118 may be configured to perform include: performing single-qubit control operations, processing results of single-qubit measurements, and dynamically reconfiguring optical network 110 and / or optical network 112 as needed to optimize network connections for creating and distributing entanglement.

[0148] Figure 2is a flow chart outlining a method 200 for creating entanglement between a selected alpha quantum system 20A of a first one of the nodes 102 and a selected alpha quantum system 20A of a second one of the nodes 102 .

[0149] In block 202 , the network 110 is configured to pairwise optically connect each of the plurality of beta quantum systems 20B of the node 102A to a corresponding one of the plurality of beta quantum systems 20B of the node 102B in a manner that facilitates entanglement of each pair of beta quantum systems 20B.

[0150] In block 204, two nodes (eg, nodes 102A and 102B—see Figure 2A ) is initialized to a quantum state suitable for a probabilistic entanglement protocol that is to be applied in an attempt to entangle the quantum states of multiple pairs of quantum systems 102B.

[0151] In block 206, the method 200 begins attempting to entangle each pair of beta quantum systems 20B. These attempts may be performed in parallel (e.g., at the same or overlapping times). The attempts to entangle different pairs of beta quantum systems 20B may be asynchronous or synchronous. Each entanglement attempt may include applying a sequence of operations of a protocol to entangle the corresponding pair of beta quantum systems 20B. The protocol may be a probabilistic protocol. For example, each entanglement attempt may include the steps of applying an entanglement protocol as described in SD Barrett et al., PRA 71, 060310R (2005).

[0152] Block 206 is repeated until at least one of the plurality of pairs of beta qubits is confirmed to have been successfully entangled, as determined at block 206A. In some embodiments, success at block 206A is detected by detecting a predictive pattern of photon detection events at an optical detector corresponding to one of the plurality of pairs of beta quantum systems 20B.

[0153] Figure 2A An example optical path 111 of a network 110 is illustrated that is optically connected between two quantum systems 20B through a suitable optical coupler 117. Optical path 111 includes an optical mixer 116 where single photon states associated with quantum system 20B may be interfered. Single photon detectors 118A and 118B are operable to detect photons in a pattern that indicates entanglement (or indicates that an entanglement attempt was unsuccessful).

[0154] Any of the entanglement attempts initiated in block 206 may fail. The failure may be due to any reason, including loss of photons in network 110, improper initialization of quantum system 20B, etc. Network 110 may suffer from significant optical losses (e.g., due to factors such as the distance between nodes 102, optical losses associated with switches used to configure network 110 to provide the desired connections, less than 100% efficiency of single photon detectors, etc.). For example, failure of an entanglement attempt may be detected by observing a photon detection pattern that does not correspond to successful entanglement at corresponding optical detectors 118A and 118B and / or observing a photon detection pattern that does correspond to successful entanglement at detector 116.

[0155] If the entanglement attempt of a pair of beta quantum systems 20B fails, block 206 may reinitialize each of the pair of beta quantum systems 20B and attempt to entangle the pair of beta quantum systems again. At the end of block 206, at least one pair of beta quantum systems 20B (including one beta quantum system 20B in node 102A and one beta quantum system 20B in node 102B) is entangled. For example, block 206 may be completed when successful entanglement of at least one pair of beta quantum systems 20B is indicated.

[0156] Because many entanglement attempts can be performed in parallel, the amount of time expected to obtain at least one pair of entangled β quantum systems 20B can be significantly reduced compared to a situation in which serial attempts are made to entangle a pair of β quantum systems 20B.

[0157] As discussed elsewhere herein, in some embodiments, the beta quantum system 20B may include two or more elements (e.g., one or more electron spins and / or one or more nuclear spins) each having a different quantum state. In such cases, the steps of method 200 may be applied to individual ones of these elements. For example, block 206 may be completed when the quantum state of an electron spin (or nuclear spin) element of one beta quantum system 20B is entangled with the quantum state of a corresponding electron spin (or nuclear spin) in a counterpart in the beta quantum system 20B.

[0158] Figure 3 1 is a block diagram showing an example implementation of a single node 102 having N alpha quantum systems 20A and M beta quantum systems 20B. In this example embodiment, a switch 128 may be operated to connect the beta quantum system 20B to the inter-node network 110 or the intra-node network 112. For the purpose of generating entanglement with the beta quantum systems of other nodes 102, the switch 128 may be operated to connect some or all of the beta quantum systems 20B to the inter-node network 110. For the purpose of transferring entanglement to a selected one of the alpha quantum systems 20A, the switch 128 may be configured to connect one or more beta quantum systems 20B to the intra-node network 112.

[0159] Intra-node network 112 allows any pair consisting of one of beta quantum systems 20B and one of alpha quantum systems 20A to connect to optical mixer 130 (which may, for example, include a beam splitter). Optical mixer 130 has two outputs each connected to a corresponding single photon detector (140-1 and 140-2).

[0160] exist Figure 3 In an embodiment of the present invention, the intra-node network 112 includes: an M×1 optical switch 132 that allows any of the beta quantum systems 20B1-1 to 20B-M to be connected to one input of the optical mixer 130; and an N×1 optical switch 134 that allows any of the alpha quantum systems 20A-1 to 20A-N to be connected to a second input of the optical mixer 130. The optical switches 128, 130, and 132 can be controlled by the controller 118.

[0161] In some embodiments, some or all of the switches 128 are initially configured to connect corresponding beta quantum systems 20B to corresponding optical links of the inter-node network 110. An attempt is made to entangle the beta quantum systems 20B with corresponding external quantum systems outside the node 102. Upon detecting entanglement of one of the beta quantum systems 20B with the corresponding external quantum system, the corresponding switch 128 may be configured to connect the entangled beta quantum system 20B to the intra-node network 112 and the switch 132 may be configured to provide an optical connection between the entangled beta quantum system 20B and the optical mixer 130.

[0162] In the event that it is desired to transfer the entanglement of the entangled beta quantum system 20B to a selected one of the alpha quantum systems 20A of the node 102, the switch 134 may then be configured to provide an optical connection from the selected alpha quantum system 20A to the optical mixer 130. The entanglement may then be transferred to the selected alpha quantum system 20A as described elsewhere herein.

[0163] Figure 41 is a block diagram illustrating an example construction of an inter-node network 110. In this example, P nodes 102-1 to 102-P each have M ports that each correspond to a β quantum system 20B. These ports are respectively connected to corresponding ports of an MP×MP optical switch 150. A plurality of optical mixers 152, each having two input ports and two output ports, are also connected to the optical switch 150. Each of the output ports of each mixer 152 is connected to a corresponding single photon detector 140. The switch 150 may be operated to connect one β quantum system 20B of one node 102 to a first input port of one of the optical mixers 152, and to connect another β quantum system 20B of a second node 102 to a second input port of one of the optical mixers 152. The photons detected at the corresponding detectors 140 may indicate the entanglement of the β quantum systems 20B of the first and second nodes optically coupled to the mixers 152.

[0164] In some operating modes, the optical switch 150 may be configured to connect a plurality (e.g., 2 to M) of the M ports of a first one of the nodes 102 to first input ports of a corresponding plurality of mixers 152, and to connect the same number of ports of a second one of the nodes 102 to second input ports of the corresponding plurality of mixers 152.

[0165] In some operating modes, the optical switch 150 may be configured to connect a first plurality (e.g., 2 to M) of the M ports of a first one of the nodes 102 to the first input ports of the corresponding plurality of mixers 152, and to connect a port of one of the plurality of other nodes 102 to each of the second input ports of the corresponding plurality of mixers 152. Such a mode may be used to simultaneously create entanglement of the beta quantum system 20B of the first one of the nodes 102 with the beta quantum systems of the plurality of other nodes 102.

[0166] The beta quantum system 20B and the alpha quantum system 20A may, for example, comprise matter qubits - as opposed to "flying" qubits (photons). In a preferred embodiment, the beta quantum system 20B and the alpha quantum system 20A comprise luminescence centers in a substrate such as silicon. For example, the alpha and beta quantum systems 20B and 20A may each be provided by a luminescence center or collection of luminescence centers in a substrate.

[0167] For example, the luminescence center may include a luminescence center selected from the following: a defect, such as a T center, an I center or an M center, or a nitrogen-carbon center, or an Al1 or Ga1 center, or a radiation damage center with an unpaired ground state spin; or an impurity, such as a selenium or tellurium or sulfur atom or other double donor impurities.

[0168] In any embodiment, some or all quantum systems may be the same. For example, all alpha quantum systems, all beta quantum systems, all gamma quantum systems, all quantum systems in a cell or node, all quantum systems that may be connected by a particular optical link or network, or all quantum systems may have the same structure (e.g., provided by the same type of luminescent center).

[0169] Figure 5 A structure 50 is schematically illustrated that provides an environment for an example quantum system 20, which may be an alpha quantum system 20A or a beta quantum system 20B. In some embodiments, quantum system 20 includes a luminescent center 52 in a substrate 54. Substrate 54 may, for example, include a silicon or diamond substrate.

[0170] Substrate 54 is preferably formed of a material made of atoms that do not have a net nuclear spin. For example, substrate 54 may include purified silicon 28 (i.e., silicon that is greater than 92.23% silicon 28). In some embodiments, the material of substrate 42 is at least 96% or 99% or 99.5% or 99.9% (by atomic number) silicon 28.

[0171] Figure 5 A magnet 56 is shown that is operable to change the magnitude of the magnetic field at the location of the quantum system 20 (and thus change the energy difference between the spin-up state and the spin-down state of a spin, such as an electron spin or a nuclear spin of the quantum system 20). A control circuit 56A is connected to control the adjustable magnet 56. One or more bias magnets 56B (which may be permanent magnets) near the quantum system 20 may enhance the magnetic field from the adjustable magnet 56. The magnet 56B may be deposited, for example, on or in or near the substrate 54.

[0172] Figure 5 Also shown is an antenna 57 (e.g., comprising one or more coils) that can be driven by an RF signal source 57A to manipulate the quantum state of the quantum system 20 through a resonant effect (e.g., electron spin resonance—“ESR”) as known to those skilled in the art. The RF signal source 57A can be controlled to produce radiation pulses, such as π pulses or π / 2 pulses, that when delivered manipulate the quantum state of the quantum system 20. The antenna 57 can, for example, be integrated into or onto a substrate in which the quantum system 20 is positioned, or positioned sufficiently close to the quantum system 20 to deliver RF radiation to the quantum system 20 that is suitable for manipulating the quantum state of the quantum system 20 in a desired manner.

[0173] Figure 5Also shown is a narrowband light source 58 arranged to illuminate the location of the quantum system 20. The light source 58 may, for example, emit light having a wavelength corresponding to an optical transition of the quantum system 20. The transition may, for example, include the promotion of an electron from a ground state to an excited state, the creation of an exciton, a spin flip transition, etc. The light source 58 may, for example, include a laser. The laser may be tunable to emit light having wavelengths corresponding to different optical transitions of the quantum system 20.

[0174] Figure 5 Also shown are electrodes 59A and a variable potential circuit 59B configured to apply a controllable potential difference between electrodes 59A. Circuit 59B can be controlled to change the electric field at the location of quantum system 20. The electric field can shift the energy level of quantum system 20 (e.g., through the Stark effect).

[0175] Structure 50 includes optical structure 60 including waveguide 60A and resonant cavity 60B. Cavity 60B enhances optical coupling between quantum system 20 and waveguide 60A. Waveguide 60A may, for example, optically couple quantum system 20 to intra-node network 112 and / or inter-node network 110.

[0176] The substrate 54 is housed within a refrigerator 59 capable of cooling the substrate 54 to a cryogenic temperature. In some embodiments, the operating temperature of the structure 44 may be very low (eg, a few mK or a few Kelvin).

[0177] The controllable elements of the system 50 , such as the magnet control circuit 56A, the RF signal source 57A, the light source 58 , and / or the variable potential circuit 59B, may be controlled by the controller 118 .

[0178] Figure 6 61H and 61L may correspond, for example, to spin-up and spin-down states of unpaired spins (e.g., electrons, nuclei, or holes). For example, energy levels 61H and 61L may be the result of hyperfine splitting caused by the interaction between nuclear and electron spins at the location of quantum system 20 or splitting caused by another magnetic field at the location of quantum system 20.

[0179] States 62H and 62L may, for example, correspond to spin-up and spin-down states, respectively, of unpaired spins (e.g., of electrons, nuclear spins, or holes). States 62H and 62L may be related to states 61H and 61L, respectively, by orbital or exciton transitions. The energy difference between states 62H and 61H or between states 62L and 61L may correspond to photon energy at an optical wavelength.

[0180] like Figure 6, the energy difference ΔE1 between states 61H and 62H is different from the energy difference ΔE2 between states 61L and 62L. In some embodiments, the difference between ΔE1 and ΔE2 corresponds to a frequency difference sufficient to provide spin-selective coupling of the spins of quantum system 20 to optical structure 60 (e.g., by having resonator 60B have a resonant frequency corresponding to one of ΔE1 and ΔE2, wherein the Q factor of resonator 60B is sufficiently high and the difference between ΔE1 and ΔE2 is sufficiently large so that photons having an energy corresponding to the other of ΔE1 and ΔE2 are not properly coupled to resonator 60B). For example, the difference between ΔE1 and ΔE2 may be at least about 1 MHz (i.e., about 6.6×10 -28 J) or more typically at least about 100 MHz. In some embodiments, the difference between ΔE1 and ΔE2 is at least 1 GHz (i.e., about 6.6×10 -25 J).

[0181] For example, when provided with optical photons 66 having a wavelength (or equivalently frequency or energy) corresponding to ΔE1, quantum system 20 may absorb one of photons 66 and transition from state 61H to state 62H. Quantum system 20 may then transition from state 61H to 62H and emit photon 66 having the same energy ΔE1.

[0182] Since the quantum system 20 is a quantum system, the quantum system 20 is not necessarily in a clear quantum state. Instead, the quantum system 20 may be in a superposition of different states (e.g., a superposition of states 61H and 61L). Moreover, the state of the quantum system 20 and the optical photon 66 may be together in a superposition of states in which the quantum system 20 has and has not yet emitted a photon or otherwise interacted with a photon. In general, the quantum state of the quantum system consisting of the quantum system 20 together with the optical photon 66 covers a wide variety of possible interactions between the quantum system 20 and the optical photon 66. Therefore, the quantum states of the quantum system 20 and the optical photon 66 may be entangled.

[0183] A more detailed example of a method according to the present technology will now be described. In this example, each of the alpha quantum system 20A and the beta quantum system 20B includes at least two elements. Each of the elements has an independently controllable quantum state and quantum information can be selectively transferred among the elements of each quantum system 20. For example, each of the quantum systems 20 may include at least one electron spin and at least one nuclear spin that can each be applied to store quantum information.

[0184] In some embodiments, some or all quantum systems are provided by structures in which a proxy element and one or more client elements have a fixed spatial relationship. For example, a quantum system may be provided by a luminescent center comprising atoms having a configured spatial arrangement, wherein an electron spin associated with one of the atoms may be applied as a proxy element and a nuclear spin associated with one or more of the atoms may be applied as one or more client elements. In some embodiments, for some or all quantum systems, the hyperfine interactions between the proxy elements and the client elements of the quantum systems have the same strength. This may be, for example, a situation in which each of a group of quantum systems comprises substantially the same arrangement of atoms, such that the distances between the proxy elements and the client elements are substantially the same.

[0185] symbol Indicates the combined quantum state of a quantum system including both the electron (or hole) spin represented by the first arrow and the nuclear spin represented by the second arrow. The electron or hole spins are down and the nuclear spin is spin up.

[0186] In some embodiments, one of the elements of quantum system 20 is used as a proxy and another element of quantum system 20 may be used as a client. Proxy elements may be used to exchange quantum information with other quantum systems 20. Client elements may be used to store quantum information in quantum system 20. Client elements may have a longer decoherence time than proxy elements.

[0187] With this arrangement, the quantum states of the proxy elements of a pair of beta quantum systems 20B in different nodes 102 ("proxy quantum states") can be entangled as described above. The entangled proxy quantum states can then be transferred to the client elements of the beta quantum systems 20B. This frees up the proxy elements of each beta quantum system 20B for transferring entanglement to the alpha quantum system 20A.

[0188] Transferring entanglement from beta quantum system 20B to alpha quantum system 20A may involve creating entanglement between beta quantum system 20B and a proxy element of alpha quantum system 20A to which the entanglement is to be transferred.

[0189] Figure 7 is a flow chart of an example method 250 of creating entanglement between proxy elements of a pair of beta quantum systems 20B and then distributing that entanglement to client elements of a selected alpha quantum system 20A.

[0190] The resulting entanglement (e.g., entangled Bell pair states) may then be consumed for any purpose. Such consumption may, for example, take the form of a remote quantum gate operated on one or more client elements of the alpha quantum system 22. For example, such a remote quantum gate may be used to expand a pre-existing entangled state to a many-body entangled state of three or more qubits.

[0191] In block 252 of method 250 , network 110 is configured to pairwise optically connect each of the plurality of beta quantum systems 20B of node 102A to a corresponding one of the plurality of beta quantum systems 20B of node 102B in a manner that facilitates entanglement of each pair of beta quantum systems 20B.

[0192] In block 254, two nodes (eg, nodes 102A and 102B—see Figure 2A ) are initialized to quantum states suitable for a probabilistic entanglement protocol to be applied in an attempt to entangle the quantum states of multiple pairs of proxy elements of quantum system 102B.

[0193] In block 256, attempts are made to entangle each pair of proxy elements of beta quantum system 20B. These attempts may be made in parallel for different pairs (e.g., at the same or overlapping times). The attempts to entangle different pairs of proxy elements of beta quantum system 20B may be asynchronous or synchronous. Block 256 may apply any suitable entanglement protocol (e.g., a probabilistic and / or predictive protocol as described elsewhere herein).

[0194] Block 256 is repeated until it is confirmed that the proxy element of at least one of the plurality of pairs of beta quantum systems 20B has been successfully entangled, as determined at block 256A. In some embodiments, success at block 256A is detected by detecting a predictive pattern of photon detection events at an optical detector corresponding to one of the plurality of pairs of beta quantum systems 20B.

[0195] Block 257 transfers the entanglement established in block 256 to the client elements (eg, nuclear spins) of the entangled beta quantum system 20B. After block 257, at least one pair of client qubit states of the beta quantum system 20B are entangled.

[0196] Block 258 configures the network 112 to optically couple each of the entangled beta quantum systems 20B to the selected alpha quantum system 20A in the same node 102 .

[0197] Block 259 uses the optical connection of block 258 to entangle the quantum state of the proxy element of the entangled beta quantum system 20B with the proxy element of the corresponding selected alpha quantum system 20A.

[0198] The quantum entanglement protocol used to implement block 259 may operate probabilistically. However, because network 112 may be a low-loss optical network, successful entanglement may be predicted more quickly than would be expected on a more lossy optical network 110. Block 259 may repeat the entanglement attempt until successful entanglement is predicted.

[0199] Block 260 uses the entanglement created in block 259 to transfer the entanglement of the client element of the entangled beta quantum system 20B to the proxy element of the corresponding alpha quantum system 20A (e.g., by quantum teleportation). After block 260, the proxy qubit states of at least one pair of alpha quantum systems 20A (where the pair of alpha quantum systems 20A are in different nodes 102) are entangled.

[0200] Block 261 transfers the entanglement of the proxy element of the selected alpha quantum system 20A to the client element of the selected alpha quantum system 20A. After block 261, the client qubit states of the selected alpha quantum system 20A (where the selected alpha quantum systems 20A of the pair are in different nodes 102) are entangled. The resulting entanglement of the client element of the alpha quantum system 20A in the different node 102 may then be consumed.

[0201] In some embodiments, the alpha quantum system 20A is used as a computing resource. For example, the controller 118 may be configured to cause the system 100 to perform a quantum computing algorithm by initializing the alpha quantum system 20A to be in a selected initial quantum state, manipulating the quantum state of the alpha quantum system 20A, applying quantum gates to the alpha quantum system 20A, and entangle the alpha quantum systems 20A with each other and / or with alpha quantum systems 20A in other nodes 102 (e.g., as described above).

[0202] In method 250 , electron spins may be used in the role of agents (ie, agent components may include electron spins) and nuclear spins may be used in the role of clients (ie, client components may include nuclear spins).

[0203] For example, quantum systems 20 may each include a T center. Within a T center, quantum information may be moved among the electron spins of the T center and one or more nuclear spins of the T center. In some embodiments, the electron spins serve as proxy qubits and the nuclear spins serve as client qubits.

[0204] Figure 8 A simple system 80 is shown that includes two nodes 102-1 and 102-2. One beta quantum system 20B is shown for each of the nodes 102. One alpha quantum system 20A is shown for each of the nodes 102. Each beta quantum system 20B includes a proxy element 81B and a client element 82B. Each alpha quantum system 20A includes a proxy element 81A and a client element 82A.

[0205] In this example, the proxy elements 81A, 81B include electron spins (e) and the client elements 82A, 82B include nuclear spins (n). For example, each of the quantum systems 20A, 20B may include a T center. The client elements 82A, 82B may be provided by the nuclear spins of the T center. The proxy elements 81A, 81B may be provided by the electron spins of the T center. The present technology is not limited to these choices of proxy and client elements. The quantum system 20 may take any of a variety of forms that include elements suitable for application as proxy elements and client elements.

[0206] System 80 may include additional elements. For example, system 80 may include additional nodes, additional quantum systems, additional electron spins, and / or additional nuclear spins (not shown). For example, each of nodes 102-1 and 102-2 of system 80 may each include a number of beta quantum systems 20B.

[0207] Assume that it is desired to entangle the quantum state of client element 82A of selected alpha quantum system 20A of node 102-1 with the quantum state of client element 82A of corresponding selected alpha quantum system 20A of node 102-2. An example approach to achieve this entanglement includes several main steps involving interactions 84-1 through 84-5. Figure 8B is a diagram that symbolically indicates these interactions.

[0208] exist Figure 8B In , quantum states are indicated by the symbol Ψ marked with a subscript that identifies a particular element of an individual quantum system 20. For the beta quantum system 20B, the subscript contains "20B". For the alpha quantum system 20A, the subscript contains "20A". For the proxy element, the subscript contains "e". For the client element, the subscript contains "n". Figure 8B , 9 In the quantum circuit diagram of 9A, the symbol E represents the entanglement process, the symbol M represents measurement, the symbol H represents a Hadamard gate, the symbol X represents X measurement, the symbol Z represents Z measurement and the symbol + indicates a CNOT gate.

[0209] For the purpose of this example, the quantum systems 20A, 20B have Fig. 8A The ground state energy level indicated in . Figure 8 Annotated to schematically illustrate interactions 84 (showing interactions 84-1 through 84-5) in parallel with the blocks of method 250. Prior to interaction 84-1, beta quantum systems 20B are initialized. Initialization may, for example, include placing each of quantum systems 20B in the same ground state.

[0210] Fig. 8A The description includes initializing the beta quantum system 20B by placing the proxy element 81B corresponding to An example of state 86C, where g indicates the ground state, ↑ indicates that the electron spin is up and Indicates nuclear spin is up.

[0211] This initialization may include, for example, optically exciting each of beta quantum systems 20B with light having a wavelength corresponding to transition 85-1 from either of states 86A and 86B to excited state 75. Transition 85-1 may, for example, include an electron orbital transition.

[0212] For example, light may be delivered from an appropriately tuned laser.The quantum state of proxy element 81B may transition from excited state 75 to state 86C (which may be an initialized desired state) or 86D (an undesired state) via transition 85-2.

[0213] The RF driver may be applied to stimulate transition 85-3 from state 86D back to state 86A or 86B. The RF driver may have a frequency corresponding to the energy difference between state 86D and state 86A or 86B. Once quantum system 20B drops to state 86C, it remains in state 86C because no transitions to other states are available.

[0214] For example, light and RF drivers may be applied for a period sufficient to initialize the beta quantum system 20B. The required period may be determined by simulation or experiment. Typically, delivering light and RF drivers for a period of about 10 microseconds or less is sufficient.

[0215] The proxy element (electron spin) in each of quantum systems 20B can then be placed in a superposition of electron spin up and electron spin down (eg, state: ). The Sqrt(X) gate may be applied, for example, by applying an RF pulse of about 10 ns (e.g., in the range of about 1 ns to about 1 μs) to induce a π / 2 rotation about the X axis in a Bloch sphere representation of the quantum state of the electron spin. Suitable pulse durations may be determined by simulation or experiment. The RF pulse may have a frequency corresponding to the energy difference between states 86C and 86A.

[0216] Interaction 84-1 entangles the quantum states of proxy elements 81B (electron spins) of beta quantum system 20B. In some embodiments, multiple quantum systems 20B in each of nodes 102-1 and 102-2 are initialized and attempts are made in parallel to entangle the quantum states of multiple pairs of proxy elements of these quantum systems, as described above.

[0217] For example, entanglement can be achieved by applying a light pulse having a wavelength selected to correspond to a spin-selective optical transition to an excited state (e.g., 75) to each of the beta quantum systems 20B. "Spin selectivity" means that the transition occurs only for one electron spin state. If a transition occurs, a photon is emitted when the excited state decays. For example, the light may have a wavelength corresponding to the transition 85-1. The length of the light pulse may be selected so that only a single photon will be released. For example, the light pulse may have a duration on the order of 1 ns.

[0218] Those skilled in the art will recognize that there is a possibility of relaxing from excited state 75 to one of states 86A or 86B and to one of states 86C or 86D. The probability of each of these outcomes is determined by the "branching ratio." Typically, the branching ratio is such that the probability of relaxing back to one of states 86A or 86B is in the range of ˜0% to about 10%, while the probability of relaxing to one of states 86C and 86D is in the range of about 90% to ˜100%.

[0219] During the initialization of quantum system 20 (as described above), transition 85-1 may be triggered many times, causing relaxation to occur many times. Therefore, even if the probability of relaxing to state 86C or 86D is low, given enough cycles, the probability that the state of quantum system 20 will be initialized to state 86C is high (close to 100%).

[0220] However, the entanglement protocol may involve invoking transition 85-1 only once. Therefore, the probability that executing the entanglement protocol may cause a random change in the quantum state of quantum system 20 (e.g., by flipping electron spins) is finite, where the probability (which may be small) is determined by the branching ratio.

[0221] Since the beta quantum systems 20B are each initialized to a quantum state involving a superposition of electron spin up and electron spin down, the expected resulting combined state of the electron spin and any emitted photon is a superposition of a state in which the electron spin is up and one photon has been emitted and a state in which the electron spin is down and no photon has been emitted.

[0222] Any emitted photon states are routed through the network 110 to an optical mixer (e.g., 152) that permits interference of photon states emitted by the paired beta quantum system 20B. The optical mixer may, for example, include free space optics and / or integrated optics. The delivery of optical pulses to the quantum system 20B is timed so that any emitted photon states will have a chance to interact with each other in the optical mixer. A single photon detector at the output port of the optical mixer is monitored to detect when exactly one photon is detected.

[0223] Next, a π RF pulse is delivered to each of the β quantum systems 20B. The π pulse rotates the quantum states of the electrons in quantum systems 71A and 71B by 180 degrees about the X axis in the Bloch sphere representation. The steps of applying a light pulse having a wavelength selected to correspond to a spin-selective optical transition and detecting any emitted photons are then repeated.

[0224] A single detected photon following each light pulse indicates entanglement of the quantum states of the electrons of the paired beta quantum system 20 B. If photons are detected in any other combination (eg, zero photons or two photons at any stage), the entanglement process is restarted.

[0225] In interaction 84-2, entanglement is transferred to client element 82B (nuclear spin) of beta quantum system 20B. For example, interaction 84-2 can be caused to transfer the entanglement of the electron spin to the nuclear spin by applying a SWAP gate between the electron spin in paired beta quantum system 20B and the nuclear spin of quantum system 20B. Applying the SWAP gate can, for example, include applying an RF pulse tuned to a frequency corresponding to the energy difference between states 86A and 86D for a duration sufficient to facilitate the transition from state 86A to state 86D. To status The pulse length of the SWAP gate can be determined from simulations and / or experiments and can be, for example, of the order of 100 ns (e.g., in the range of 10 ns to 1 μs). In order to implement the SWAP gate in this manner, it is necessary to be able to induce a crossover transition between states 86A and 86D. Some quantum systems containing T centers are characterized by hyperfine tensor anisotropies that facilitate driving such crossover transitions.

[0226] The advantage of transferring the entanglement to the nuclear spin of quantum system 71 may be that the nuclear spin is generally better isolated from the environment than the electron spin and thus the decoherence time of the nuclear spin may be significantly longer than the decoherence time of the electron spin. Moreover, transferring the entanglement to the nuclear spin of beta quantum system 20B releases the electron spin of quantum system 20B for the next step.

[0227] In interactions 84-3 and 84-4, entanglement is transferred to the proxy element (e.g., electron spin) 81A of the alpha quantum system 20A in each of the nodes 102-1 and 102-2. In interaction 84-3, the quantum state of the electron spin of the beta quantum system 20B is entangled with the quantum state of the electron spin of the selected alpha quantum system 20A. These entanglements can be caused by the same steps described above for entangling the quantum state of the electron spin of the beta quantum system 20B, except that the collection and detection of photons in each case is performed on the intra-node optical network 112, and the initialization process described above is modified so that only the proxy element (electron spin) of the beta quantum system 20B and the corresponding selected alpha quantum system 20A is initialized. In this modified initialization process, the quantum system 20B can be excited with light having a wavelength equal to the transition 85-1 from either state 86A and 86B to the excited state 75. As transition 85-2 cycles, the non-zero probability of relaxing into states 86C and 86D via transition 85-2 then leaves the proxy spin in state |↑>. Thus, this process initializes the proxy element 82B to a known state while minimally perturbing the quantum state of the corresponding client element (e.g., nuclear spin) 82B. Typically, it is sufficient to deliver light for a period of about 1 microsecond or less.

[0228] In interaction 84-4, the quantum state of the client element 82B (e.g., nuclear spin) of the beta quantum system 20B is teleported to the proxy element 81A (e.g., electron spin) of the corresponding selected alpha quantum system 20A in each of the nodes 102-1 and 102-2. This can be done independently in the nodes 102-1 and 102-2. The teleportation consumes the entanglement of the proxy elements 81A, 81B of the alpha and beta quantum systems 20A, 20B.

[0229] For example, teleportation in each node may include performing local Bell state measurements on the electron spins and nuclear spins of the beta quantum system 20B.

[0230] Bell state measurements can be performed, for example, by the following sequence of actions:

[0231] 1. Apply the CNOT gate to the electron spin of the β quantum system 20B using the nuclear spin of the β quantum system 20B as a control.

[0232] 2. Perform a Z measurement on the electron spin of the β quantum system 20B.

[0233] 3. If the Z measurement results in an even-parity state: apply a π rotation to the electron spin corresponding to the α quantum system 20A.

[0234] 4. Perform an X measurement (ie, a projection measurement into the X basis) on the nuclear spins of the beta quantum system 20B.

[0235] 5. Apply feedforward to the electron spins of the β quantum system 20B.

[0236] If the nuclear spin is up, then the CNOT gate flips the electron spin. Otherwise, the CNOT gate does nothing. Fig. 8A It can be seen that the CNOT gate represents a transition from state 86C to state 86A. The CNOT gate may be implemented, for example, by applying an RF pulse having a frequency selected to correspond to the energy difference between states 86A and 86C for a duration selected to interchange states 86A and 86C. This duration may be determined by simulation and / or experimental calibration. The duration may be, for example, on the order of 10 μs (e.g., a period in the range of 100 ns to 100 μs).

[0237] Performing a Z measurement on the electron spin of the beta quantum system 20B may include using resonance, spin-selective optical cycles, and photon detection. If a photon is detected, the result of the measurement is that the electron spin has a state corresponding to a spin-selective transition. Such a measurement may include applying light having a wavelength that resonates with the spin-selective transition for a time sufficient to generate and detect photons. Preferably, for better measurement fidelity, the measurement generates and detects multiple photons. For example, the measurement may involve applying light for a time sufficient to generate and detect enough photons to confirm the spin state at at least a threshold fidelity (e.g., 90% fidelity or higher). In some example embodiments, light is applied for a period of approximately 10 ns (e.g., in the range of 1 ns to 50 ns). The duration of the pulse may be determined based on simulation and / or experiment.

[0238] Performing an X measurement of client element 81B (e.g., nuclear spins) may include, for example, applying a π / 2 pulse on the nuclear transition to rotate the X Bloch sphere projection onto the Z axis and then using a resonant spin-selective optical cycle of the proxy spins while applying an RF driver with a frequency equal to the spacing between states 86C and 86A to measure the spin-up population of the nuclear spins of beta quantum system 20B. The π / 2 pulse may, for example, have a duration of approximately 10 μs (e.g., in the range of 1 to 100 μs). The resonant spin-selective optical cycle may, for example, have a duration of approximately 10 μs (e.g., in the range of 5 to 50 μs).

[0239] Feed forward may include: if the X measurement of the client element 82B (e.g. (nuclear spin)) of the beta quantum system 20B reveals an even parity (e.g. |-> state - i.e., the state ), then the [z] gate is applied to the electron spin of the β quantum system for a π rotation about the Z axis of the Bloch sphere. Otherwise, if the X measurement reveals an odd parity (e.g., a |+> state—that is, the state ), then do nothing. Applying the [z] gate may, for example, include modifying the energy of a proxy element 81B (e.g., an electron spin) of the beta quantum system 20B, such as by applying an electric field or changing a magnetic field for a period of time sufficient to allow the state to accumulate a phase shift of π radians or by advancing the phase of the state in phase tracking software.

[0240] In interaction 84-5, entanglement is transferred to client element (nuclear spin) 82A of alpha quantum system 20A. After the quantum state of the nuclear spin of beta quantum system 20B has been transferred to the electron spin of alpha quantum system 20A (e.g., as described above), entanglement may be transferred to the nuclear spin of alpha quantum system 20A, as indicated by interaction 84-5. This may be performed in the same manner as described above with respect to interaction 84-2.

[0241] The methods described above are not limited to the case where the alpha and beta quantum systems 20A and 20B include electron spins and nuclear spins. The methods can be more generally applied to the case where nodes 102A and 102B have available alpha and beta quantum systems that can be used to transfer quantum information as described. Moreover, those skilled in the art will recognize that the described methods can be altered by using other combinations of quantum gates and manipulations that produce equivalent results.

[0242] Creating a multi-body entangled state

[0243] Fig. 9 A method for creating a many-body entangled state involving three or more qubits that can be located in different nodes is described. Fig. 9 The horizontal line in the figure indicates that the initial quantum state |ψ i > individual qubits, where iε{1,…,6}. Fig. 9 , H indicates a Hadamard gate. CNOT gates 90 are applied sequentially to add additional qubits to the entangled state. Each CNOT gate 90 is controlled by the top qubit to which it is connected.

[0244] Because individual qubits may be in different nodes, the CNOT gate may be implemented as a teleported non-local CNOT gate, as described, for example, in J. Eisen, Phys. Rev. A, 62, 052317, 2000. A teleportation gate between two nodes may employ a pair of entangled qubits that may be entangled as a resource, for example using the techniques described above.

[0245] Fig. 9A Schematic illustration of the use of the entangled state |ψ A > and |ψ B >Implement a teleported CNOT gate between quantum states |ψ1> and |ψ2>.

[0246] Segmented Architecture - Instance Characteristics and Changes

[0247] It should be appreciated that segmenting a distributed quantum network (e.g., a quantum computer) into a nested network having multiple layers (e.g., α and β layers or α, β, and γ layers, etc.) can advantageously provide an increased rate of achieving entanglement between higher energy level (e.g., "β" and / or "γ") quantum states by simultaneously performing attempts to entangle multiple pairs of higher energy level (e.g., "β" and / or "γ") quantum states.

[0248] Fig.10 An example quantum network 200 is shown having three layers of quantum systems (alpha quantum system 20A, beta quantum system 20B, and gamma quantum system 20C). In this example, the inter-node optical network 110 includes an optical network 110C that can be applied to establish entanglement among the gamma quantum system 20C and an optical network 110B that can be applied to establish entanglement among the quantum system 20B.

[0249] Network 110 also includes node 202, which includes both gamma quantum system 20C and beta quantum system 20B, along with optical network 212, which can be applied to extend entanglement from quantum system 20C to quantum system 20B (e.g., in a manner similar to intra-node network 112 of node 102). Optical network 212 can, for example, be a low-loss optical network similar to network 112.

[0250] In some embodiments, optical network 110C is significantly more lossy than optical networks 110B or 112. In some embodiments, the time required to establish entanglement of multiple pairs of gamma quantum systems 20C is reduced by simultaneously attempting entanglement of a relatively greater number of pairs of quantum systems 20C as compared to the number of pairs of beta quantum systems 20B for which entanglement attempts are simultaneously attempted using optical network 110B.

[0251] In a network with three or more layers (e.g., α, β, and γ), each layer may have different functionality. Quantum systems in the lowest energy level (e.g., α) layer may be used to store and manipulate quantum information (e.g., to perform quantum computations). One or more quantum systems in the highest layer (e.g., γ) may be used to establish entanglement between different cells. Quantum systems in the middle layer (e.g., β) may be used to isolate the lowest layer quantum systems from the highest layer quantum systems, and to distill and / or purify the entanglement generated in the highest layer quantum systems.

[0252] For example, entanglement may be established between multiple pairs of quantum systems at an "entanglement layer" (e.g., a γ layer). Entanglement may be transferred to a "distillation / purification layer" (e.g., a β layer), where multiple pairs of entangled quantum systems are transformed to obtain a smaller number of maximally entangled pairs. Purification or distillation may be performed using any suitable purification / distillation process. The maximally entangled pairs of the β quantum systems may then be consumed to perform processing at the lowest "computation" layer (e.g., by teleporting quantum states and / or quantum gates between cells).

[0253] Figures 10A to 10C are additional non-limiting examples of possible topologies for systems as described herein. Fig. 10A The system 200-1 is schematically shown in which the nodes or cells 102 each include an alpha quantum system 20A and a plurality of beta quantum systems 20B. The intra-node network 110 may be configured to provide an optical link associating the beta quantum system of one of the nodes 102 with one of the plurality of corresponding beta quantum systems in two or more other nodes 102. This architecture facilitates establishing entanglement among the beta quantum systems 20B of any pair of nodes 102 in the system 200-1.

[0254] Fig. 10B An example node 102 of a system 200-2 is schematically shown. The system 200-2 may have any number of nodes 102. The node 102 includes a quantum system 20A and a corresponding beta quantum system 20B interconnected by an optical network 112. In this example, the beta quantum system 20B serves as an intermediary between the alpha quantum system 20A and a plurality of gamma quantum systems 20C. This configuration may provide improved isolation of the quantum state of the alpha quantum system 20A from noise caused by the operation of the gamma quantum system 20C (e.g., in order to perform an entanglement protocol involving the gamma quantum system 20C).

[0255] Fig. 10C An example node 102 of system 200 - 3 is shown schematically. Fig. 10C The nodes and Fig. 10B The optical network of the node is similar to that of , except that the node includes a plurality of beta quantum systems 20B each associated with a corresponding alpha quantum system 20A, and the optical network of the node allows each of the beta quantum systems 20B to selectively connect to any one of the plurality of gamma quantum systems 20C. Fig. 10C The nodes of may be scaled to include any number of pairs of corresponding α / β quantum systems, where each of the β quantum systems may be selectively connected to any of two, three, or more γ quantum systems 20C via the optical network 110B.

[0256] In which network 112 connects each α quantum system 20A to a corresponding β quantum system 20B (e.g. Fig. 10B and 10CIn a system described in ) (rather than being connected to any other alpha or beta quantum system), network 112 has low connectivity and can provide a relatively very low probability of photon loss.

[0257] The rate at which entanglement between two β-β qubits or two γ-γ qubits increases is (1–(1-p)^N), where p is the probability of a single channel succeeding in any given attempt and N is the number of β-β channels attempted for entanglement in parallel. Fig.11 is an example graph of this function for the case where the probability of achieving entanglement in any attempt is 10%. This increase in entanglement rate can lead to faster operating speeds for distributed quantum information processing.

[0258] In some embodiments, entanglement of beta quantum systems can be generated speculatively, either continuously or periodically or otherwise. This is particularly useful in cases where the entangled beta quantum systems have long coherence times (e.g., 100 microseconds or longer). In such cases, multiple pairs of entangled beta quantum systems can be immediately used as resources that can be used, for example, to teleport quantum states among nodes, teleport gates among nodes, extend entanglement to existing nodes, and the like.

[0259] The nested network can also be designed to provide a protective layer between the β quantum system and the α quantum system to prevent noise and interference. Computational qubits (e.g., represented by the quantum state of the α quantum system) can be isolated from the noise associated with probabilistic entanglement gates (such as can be used to create entanglement of remote quantum systems), especially when probabilistic gates are applied across highly connected mappings. This problem still exists even when using a quantum system that incorporates proxy qubits and client qubits and proxy qubits of different quantum systems are entangled using probabilistic entanglement gates. Even in this arrangement, due to the coupling between the proxy qubits and the client qubits, the client qubits will inevitably be disturbed by the probabilistic entanglement attempts involving the corresponding proxy qubits. These disturbances increase constructively with each attempt of the probabilistic entanglement protocol, so the combined magnitude of the disturbance increases with the loss of the link in the attempt to entangle the proxy qubits.

[0260] As connectivity grows, links tend to grow more lossy. The quantum states of client qubits that are regularly exposed to these perturbations will be quickly corrupted. This makes such client qubits unsuitable for use as computational qubits. With a nested architecture as described herein, in which the alpha quantum system can host computational qubits, those computational qubits are isolated from perturbations associated with a large number of entanglement attempts over a relatively lossy inter-node network (e.g., network 110).

[0261] Instead, the alpha quantum system may be exposed to a relatively low-loss photonic link of an intra-node network (e.g., network 112). This reduces the number of entanglement attempt cycles experienced by the alpha quantum system. The beta quantum system is not necessarily used for computation. Therefore, the quantum states of the beta quantum system (agents and clients) are free to reset whenever they are damaged. In addition, the beta quantum system client does not need the existence of eigenstates that contain computational information and may therefore be less susceptible to perturbations associated with entanglement attempts.

[0262] Fig.12 is a graph indicating the impact of this isolation. Fig.11 The curves in are based on simulations of the residual fidelity of an entangled two client qubit state as a function of photon loss after the network has gone through the necessary phase of probabilistic entanglement to add additional quantum systems to the entangled state. Since high connectivity generally means high photon loss, operating with low loss in the alpha network (e.g., 112) and allowing high photon loss on the beta network (e.g., 110) produces a highly connected and effectively low-loss entangled network.

[0263] Example Application

[0264] The foregoing description illustrates the principles and building blocks that enable the construction of a variety of systems. Some such systems may have fixed configurations. Some such systems may have dynamically variable configurations.

[0265] The system as described herein may be caused to operate in a range of alternative operating modes (eg, which may be determined by the configuration of the controller 118). For example:

[0266] • β-β entanglement attempts between multiple β quantum systems of one node and multiple β quantum systems of another node can be performed in parallel.

[0267] • β-β entanglement attempts between one node and the β quantum systems of two or more other nodes can be performed in parallel (parallel entanglement attempts are not mandatory to occur between the same two nodes).

[0268] The number of quantum systems configured to be used as beta quantum systems in one or several specific nodes may vary. For example, individual quantum systems in a node may be used as alpha quantum systems and then reconfigured to be used as beta quantum systems or vice versa.

[0269] The system may be operated to maintain an entangled resource, wherein a supply of a desired number of entangled quantum systems is created and remains available. For example, the system may be configured to create an entangled group of two or more quantum systems, wherein each group includes quantum systems belonging to two or more nodes. The number and configuration of entangled quantum systems provided to different nodes may vary to suit demand. For example, such entanglement may be utilized to teleport gates or quantum states between nodes, to create entanglement of alpha quantum states in different nodes, and the like. The system may be configured to keep entangled resources available (e.g., by automatically creating a replacement group of entangled quantum systems before the entanglement of an existing group of entangled quantum systems is expected to be lost due to decoherence or other effects),

[0270] By establishing entanglement among higher-level quantum systems (e.g. gamma optical systems) interconnected by additional optical links,

[0271] The system may be expanded or connected to other systems such as the systems described herein.

[0272] The system may change its operation based on the performance of the optical link. For example, the performance of the inter-node network 110 (e.g., loss)

[0273] The system may be configured to monitor the performance of one or more optical links and change its operation in response to that performance, such as by attempting to entangle more pairs of beta quantum systems in parallel, and / or keeping a greater resource of entangled beta quantum systems available and / or using a different entanglement protocol when the performance of an optical link is poor.

[0274] As described herein, the difference between "alpha" and "beta" quantum systems is their connectivity. An alpha quantum system is connected to a relatively low-loss inter-node network 112, while a beta quantum system can selectively connect to either the inter-node network 110 (which may be lossy relative to the inter-node network 112) and the intra-node network 112.

[0275] In some embodiments, all quantum systems hosting qubits (or a large number of quantum systems hosting qubits greater than the number of quantum systems typically used simultaneously as beta quantum systems) may be selectively connected to inter-node network 110 or intra-node network 112 (e.g., via switch 128). In such embodiments, any of the selectively connectable quantum systems may be used as a beta quantum system (e.g., by exercising control to selectively connect the quantum system to inter-node network 110 at some times and to intra-node network 112 at other times), or as an alpha quantum system (e.g., by connecting the quantum system to intra-node network 112 at all times or only at selected times). In such embodiments, a particular quantum system may be used as an alpha quantum system at some times and as a beta quantum system at other times.

[0276] In some embodiments, one or more qubits of one or more β quantum systems are temporarily configured as α quantum systems (e.g., by disconnecting from the inter-node network 110). For example, such qubits can be used as auxiliary qubits in quantum computations performed using qubits of the α quantum system.

[0277] In some embodiments, two or more different entanglement protocols are applied at different times and / or between different pairs of quantum systems. For example, entanglement between multiple pairs of beta quantum systems can be performed using a protocol that produces high-fidelity entanglement at the expense of entanglement bandwidth (e.g., a beta-beta connection can be performed using a two-photon Barrett-Kok entanglement scheme). In the same system, entanglement between a pair of alpha quantum systems and a beta quantum system ("alpha-beta entanglement") can be performed using a single-photon heralded protocol (this protocol can sacrifice fidelity to obtain a very high entanglement bandwidth, thereby minimizing the number of entanglement attempts to achieve entanglement). In some embodiments, other entanglement protocols are used to establish entanglement by means of particularly lossy connections (e.g., connections between node networks extending between cryostats or over long distances, or connections connecting multiple beta networks to form a 'gamma' network layer of a larger system).

[0278] Techniques may vary. For example, it is not mandatory to create entanglement of beta quantum systems 21 on demand. In some embodiments, the controller 118 operates to continuously attempt to create entanglement between beta quantum systems 21 of different nodes 102. In this mode of operation, entangled pairs of beta quantum systems may be more or less continuously available as resources.

[0279] The system described herein has a variety of applications, such as distribution of encryption keys; distributed quantum computing; transmission of quantum information; storage and retrieval of quantum information, etc.

[0280] Example Implementation of a Controller

[0281] A control system (e.g., controller 118) for implementing the techniques described herein may be implemented using specially designed hardware, configurable hardware, a programmable data processor configured by providing software (which may optionally include "firmware") that can be executed on a data processor, a special-purpose computer, or a data processor that is specially programmed, configured, or constructed to perform one or more steps in the method as explained in detail herein and / or a combination of two or more of these steps. Examples of specially designed hardware are: logic circuits, application specific integrated circuits ("ASICs"), large-scale integrated circuits ("LSIs"), very large-scale integrated circuits ("VLSIs"), and the like. Examples of configurable hardware are: one or more programmable logic devices, such as programmable array logic ("PAL"), programmable logic arrays ("PLAs"), and field programmable gate arrays ("FPGAs"). Examples of programmable data processors are: microprocessors, digital signal processors ("DSPs"), embedded processors, graphics processors, mathematical coprocessors, general-purpose computers, server computers, cloud computers, mainframe computers, computer workstations, and the like. For example, one or more data processors in the control circuitry of the device may implement methods as described herein (e.g., methods for establishing entanglement of qubits in different nodes) by executing software instructions in a program memory accessible to the processors.

[0282] The present technology may also be implemented in the form of a program product containing software instructions that, when executed, cause a data processor to perform the method as described herein. A program product may include any non-transitory medium carrying a set of computer-readable instructions that, when executed by a data processor, cause the data processor to perform the method of the present invention. A program product according to the present invention may be in any of a variety of forms. A program product may include, for example, a non-transitory medium, such as a magnetic data storage medium including a floppy disk, a hard disk drive, an optical data storage medium including a CD ROM, a DVD, an electronic data storage medium including a ROM, a flash RAM, an EPROM, a hard-wired or pre-programmed chip (e.g., an EEPROM semiconductor chip), a nanotechnology memory, or the like. The computer-readable signals on the program product may optionally be compressed or encrypted.

[0283] explain

[0284] Where a component (e.g., a software module, a processor, an assembly, a device, a circuit, etc.) is referenced herein, unless otherwise indicated, reference to that component (including reference to a "meaning") should be interpreted to include any component that performs the function of the described component as an equivalent of that component (i.e., functionally equivalent), including components that are structurally non-equivalent to the disclosed structure that performs the function in the illustrated exemplary embodiments of the invention.

[0285] Unless the context clearly requires otherwise, throughout the description and claims:

[0286] "comprise", "comprising" and similar terms should be construed in an inclusive sense rather than an exclusive or exhaustive sense; that is, in the sense of "including but not limited to";

[0287] "Connected", "coupled" or any variation thereof means any connection or coupling (direct or indirect) between two or more elements; the coupling or connection between elements may be physical, logical or a combination thereof;

[0288] "Herein," "above," "herein below," and words of similar meaning when used to describe this specification shall refer to this specification as a whole rather than to any particular part of this specification;

[0289] · "or" concerning a list of two or more items encompasses all of the following interpretations of the word: any one of the items in the list, all of the items in the list, and any combination of the items in the list;

[0290] The singular forms "a", "an" and "the" also include the meaning of any appropriate plural forms. Unless otherwise stated, these terms ("a", "an" and "the") mean one or more;

[0291] "And / or" is used to indicate that one or both of the stated situations may occur, for example, A and / or B includes (A and B)

[0292] and both (A or B);

[0293] “Approximately” when applied to numerical values ​​means ±10% of the value;

[0294] When a feature is described as "optionally" or "optionally" present or as present "in some embodiments", the disclosure is intended to cover embodiments in which that feature is present and other embodiments in which that feature is not necessarily present and other embodiments in which that feature is excluded. In addition, where any combination of features is described in the application, this statement is intended to be used as an exclusive term related to the combination of features (e.g., "only", "only" or "only").

[0295] and the like) and the premise basis for the use of “negative limitations” to exclude the existence of other features; and

[0296] "First" and "second" are used for descriptive purposes and should not be understood as indicating or implying relative importance or indicating the number of the indicated technical features.

[0297] Words indicating directions (e.g., "vertical," "lateral," "horizontal," "upward," "downward," "forward," "backward," "inwardly," "outwardly," "left," "right," "front," "backward," "top," "bottom," "under," "below," and the like) used in this description and any appended claims (if any) depend on the particular orientation of the device being described and illustrated. The subject matter described herein may be in a variety of alternative orientations. Accordingly, these directional terms are not strictly defined and should not be narrowly interpreted.

[0298] In the case of stating a range of values, the stated range includes all subranges of the range. The statement of a range is intended to support the value being at the endpoints of the range and any intervening values ​​to the tenth of the unit of the lower limit of the range, as well as any subrange or set of subranges of the range, unless the context otherwise clearly dictates or specifically excludes any portion of the stated range. In the case of a stated range that includes one or both endpoints of the range, ranges that exclude either or both of those included endpoints are also included in the present invention.

[0299] Certain values ​​described herein are preceded by "about." In this context, "about" provides literal support for the exact value that follows it, as well as all other values ​​that are close to or approximately equal to that value. Specific values ​​are included in the "about" specifically recited values, where the specific values ​​provide a substantial equivalent of the specifically recited value in the context in which the specifically recited value is presented.

[0300] Specific examples of systems, methods, and devices have been described herein for purposes of illustration. These are merely examples. The techniques provided herein may be applied to systems other than the example systems described above. Within the practice of the present invention, many changes, modifications, additions, omissions, and substitutions are possible. The present invention includes variations of the described embodiments that will be apparent to those skilled in the art, including variations obtained by: replacing features, elements, and / or actions with equivalent features, elements, and / or actions; mixing and matching features, elements, and / or actions from different embodiments; combining features, elements, and / or actions from embodiments as described herein with features, elements, and / or actions of other technologies; and / or omitting combined features, elements, and / or actions from the described embodiments.

[0301] As will be apparent to those skilled in the art after reading this disclosure, each of the individual embodiments described and illustrated herein has discrete components and features that can be readily separated or combined with the features of any other described embodiment without departing from the scope of the invention.

[0302] Any aspects described above with respect to the apparatus may also be applicable to the method and vice versa.

[0303] Any described method can be implemented in the order of the described events or in any other order that is logically possible. For example, although the process or block is presented in a given order, alternative examples can perform routines with steps or adopt systems with blocks in different orders, and some processes or blocks can be deleted, moved, added, subdivided, combined and / or modified to provide alternatives or sub-combinations. Each of these processes or blocks can be implemented in a variety of different ways. Moreover, although the process or block is sometimes shown to be executed serially, these processes or blocks can be executed in parallel, simultaneously or at different times instead.

[0304] Various features are described herein as being present in "some embodiments". Such features are not mandatory and may not be present in all embodiments. Embodiments of the present invention may include zero, any one, or any combination of two or more of such features. Even if such features are shown in different figures and / or described in different sections or paragraphs, the present disclosure contemplates all possible combinations of such features. This is limited to the extent that a particular one of such features is incompatible with the others of such features in the sense that a person of ordinary skill in the art would not be able to construct a practical embodiment combining such incompatible features. Therefore, a description that "some embodiments" have feature A and that "some embodiments" have feature B should be interpreted as an explicit indication that the inventor also contemplates embodiments combining features A and B (unless the description states otherwise or features A and B are not compatible at all).

[0305] Therefore, the following appended claims and claims introduced thereafter are intended to be interpreted as including all such modifications, substitutions, additions, omissions and sub-combinations as can reasonably be inferred. The scope of the claims should not be limited by the preferred embodiments set forth in the examples, but should be given the broadest interpretation consistent with the description as a whole.

Claims

1. A method for establishing and distributing quantum entanglement, the method comprising: Providing first and second nodes, each node comprising one or more alpha quantum systems and a plurality of higher energy level quantum systems, the alpha and higher energy level quantum systems of each node being interconnected via an intra-node optical network, and the higher energy level quantum system of the first node being connectable to at least a corresponding higher energy level quantum system of the second node via an inter-node optical network; attempting to establish quantum entanglement of quantum states of each of a first plurality of pairs of the higher energy level quantum systems by means of the inter-node optical network, wherein each of the plurality of pairs comprises one of the plurality of higher energy level quantum systems of the first node and a respective counterpart of the plurality of higher energy level quantum systems of the second node; detecting success in entangling the quantum states of the plurality of pairs of entangled pairs in the higher energy level quantum systems; At each of the first node and the second node, the entanglement of a respective higher energy level quantum system of the entangled pair of higher energy level quantum systems is transferred to a quantum state of a selected one of the alpha quantum systems of the respective node using the respective intra-node optical network.

2. The method of claim 1, wherein the attempts to establish quantum entanglement of the plurality of pairs of quantum states of different ones of the higher energy level quantum systems are performed simultaneously.

3. The method of claim 1, wherein the alpha and higher energy level quantum systems each include a proxy element having a proxy state and a client element having a client state, and the method comprises: entangle the proxy state of the one of the plurality of pairs of higher energy level quantum systems; transferring the entanglement to the client state of the higher energy level quantum system of the one of the plurality of pairs of higher energy level quantum systems; and The entanglement is transferred to the client state of the selected one in the alpha quantum system of the first node.

4. The method of claim 3, wherein transferring the entanglement to the client state of the higher-energy-level quantum system of the one of the multiple pairs of higher-energy-level quantum systems comprises performing a quantum SWAP gate on the higher-energy-level quantum system of the one of the multiple pairs of higher-energy-level quantum systems.

5. The method of claim 4, wherein performing the quantum SWAP gate for each of the higher energy level quantum systems of the one of the plurality of pairs of higher energy level quantum systems comprises causing a gate to be switched from a state > to state >, and vice versa.

6. The method of any one of claims 3 to 5, wherein transferring the entanglement to the client state of the selected one in the alpha quantum system of the first node comprises: At the first node, entangle the proxy state of the one of the pair of higher energy level quantum systems of the first node with the proxy state of the selected one of the alpha quantum systems of the first node; At the first node, the entanglement of the client state of the higher energy level quantum system of the one of the multiple pairs of higher energy level quantum systems of the first node is transferred to the client state of the selected one of the alpha quantum systems of the first node.

7. The method according to any one of claims 3 to 6, further comprising: At the second node, entangle the proxy state of the one of the pair of higher energy level quantum systems of the second node with the proxy state of the selected one of the alpha quantum systems of the second node; and At the second node, the entanglement of the client state of the higher energy level quantum system of the one of the multiple pairs of higher energy level quantum systems of the second node is transferred to the client state of the selected one of the alpha quantum systems of the second node.

8. The method of any one of claims 3 to 7, wherein transferring entanglement of a client state of a beta quantum system of one of a plurality of pairs of beta quantum systems of the first and / or second nodes to the client state of the corresponding selected one of the alpha quantum systems of the first and / or second nodes comprises performing a quantum teleportation process.

9. The method of any one of claims 7-8, wherein the proxy state and the client state comprise first and second spin states, respectively.

10. The method of claim 9, wherein the first spin state comprises an electron spin state.

11. The method of claim 9 or 10, wherein the second spin state comprises a nuclear spin state.

12. A method according to any one of claims 1 to 11, wherein for at least one of the first and second nodes, transferring the entanglement of the corresponding higher energy level quantum system of the entangled pair of higher energy level quantum systems to the quantum state of a selected one of the alpha quantum systems of the corresponding node using the optical network within the corresponding node includes transferring the entanglement to the selected one of the alpha quantum systems, including sequentially transferring the entanglement from the corresponding higher energy level quantum system to one or more intermediate energy level quantum systems and from one of the one or more intermediate energy level quantum systems to the selected alpha quantum system.

13. The method of claim 12, wherein the one or more intermediate energy level quantum systems include a beta quantum system, and the intra-node optical network includes an optical link directly connecting the alpha quantum system to the beta quantum system.

14. The method of any one of claims 1 to 13, wherein the quantum system is embedded in a crystalline substrate.

15. The method of claim 11, wherein the quantum system comprises a luminescent center.

16. The method of claim 14 or 15, wherein the higher energy level quantum systems each comprise a T centre.

17. A method according to any one of claims 1 to 16, wherein each of the first and second nodes includes at least five of the higher-energy level quantum systems, and the method includes attempting in parallel to establish quantum entanglement of the quantum state of each of the at least five of the higher-energy level quantum systems of the first node with the quantum state of a corresponding counterpart of the multiple higher-energy level quantum systems of the second node.

18. The method of any one of claims 1 to 16, wherein each of the first and second nodes comprises at least ten of the higher-energy level quantum systems, and the method comprises attempting in parallel to establish quantum entanglement of a quantum state of each of at least ten of the beta quantum systems of the first node with a quantum state of a respective counterpart of the plurality of higher-energy level quantum systems of the second node.

19. The method of any one of claims 1 to 18, comprising teleporting a quantum gate or quantum state from the first node to the second node using the entanglement of the quantum states of the respective selected ones in the alpha quantum system.

20. The method of any one of claims 1-19, comprising configuring the intra-node network of the first node to provide an optical connection between the higher energy level quantum system and the selected one of the alpha quantum systems or a beta quantum system associated with the selected one of the alpha quantum systems.

21. The method of claim 20, wherein the first node comprises N higher energy level quantum systems, and each of the N higher energy level quantum systems is connected to a corresponding port of a first optical switch, the first optical switch being operable to selectively couple the higher energy level quantum system to the intra-node optical network or the inter-node optical network, and configuring the intra-node network of the first node comprises operating the first optical switch to connect the higher energy level quantum systems of the entangled ones of the multiple pairs of higher energy level quantum systems to the intra-node optical network of the first node.

22. The method of claim 21, wherein the first node comprises M alpha quantum systems and each of the M alpha quantum systems is coupled to a corresponding port of a second optical switch, and configuring the intra-node network of the first node comprises operating the second optical switch to connect the selected one of the alpha quantum systems and the higher-energy-level quantum systems belonging to the entangled ones of the multiple pairs of higher-energy-level quantum systems.

23. The method of any one of claims 1 to 22, further comprising extending the entanglement of the entangled persons in the multiple pairs of higher energy level quantum systems to provide a many-body entangled state of three or more of the higher energy level quantum systems.

24. The method of claim 23, wherein the three or more of the higher energy level quantum systems in the many-body entangled state include higher energy level quantum systems in at least the first node, the second node, and a third node.

25. The method of any one of claims 1-24, wherein the intra-node optical network is characterized by a loss of less than 3 dB.

26. The method of any one of claims 1-25, wherein the inter-node optical network is characterized by a loss greater than 3 dB.

27. The method of any one of claims 1 to 26, comprising maintaining resources of at least one entangled pair of the higher energy level quantum system by continuing to attempt to establish quantum entanglement of multiple pairs of quantum states of the higher energy level quantum system via the inter-node optical network at a rate sufficient to replace entangled pairs of the higher energy level quantum system that are consumed by quantum decoherence or cease to be entangled.

28. The method of any one of claims 1 to 27, further comprising providing a third node comprising one or more alpha quantum systems and a plurality of higher energy level quantum systems, and attempting to establish quantum entanglement of a second plurality of pairs of quantum states of each of the higher energy level quantum systems by means of the inter-node optical network, wherein each of the second plurality of pairs comprises one of the plurality of higher energy level quantum systems of the first node and a corresponding counterpart of the plurality of higher energy level quantum systems of the third node.

29. A quantum network comprising: Multiple nodes, each node includes: at least one alpha quantum system, a plurality of higher energy level quantum systems; and an intra-node optical network optically coupled to the at least one alpha quantum system and the plurality of higher energy level quantum systems; an inter-node optical network configurable to provide a plurality of optical pathways, each of the optical pathways optically connecting corresponding pairs of the higher energy level quantum systems, each of the plurality of pairs comprising one of the higher energy level quantum systems of a first one of the nodes and a corresponding higher energy level quantum system of a second one of the nodes; and A controller configured to: performing simultaneously via the inter-node optical network an attempt to entangle the higher energy level quantum system of each of a plurality of pairs of beta quantum systems; When entanglement of the higher energy level quantum systems of the entangled ones in the multiple pairs of higher energy level quantum systems is detected, the entangled states of the entangled ones in the multiple pairs of higher energy level quantum systems are transferred to a selected α quantum system among the one or more α quantum systems of the first one in the node and / or a selected α quantum system among the one or more α quantum systems of the second one in the node via the intra-node optical network.

30. The quantum network of claim 29, wherein the alpha and higher energy level quantum systems each comprise a proxy element having a proxy state and at least one client element having a client state.

31. The quantum network of claim 30, wherein the controller is further configured to: executing a protocol for entangling the plurality of pairs of the proxy states of the higher energy level quantum systems; When the proxy states of the entangled persons in the multiple pairs of higher energy level quantum systems are entangled, executing a protocol for transferring the entanglement to the client states of the higher energy level quantum systems of the entangled persons in the multiple pairs of higher energy level quantum systems; executing a protocol for entangling the proxy states of the higher energy level quantum systems of the entanglers in the plurality of pairs of higher energy level quantum systems of the first node with the proxy states of the selected ones in the alpha quantum system of the first node; A protocol is executed for transferring the entanglement of the client states of the higher energy level quantum systems of the entangled ones in the plurality of pairs of higher energy level quantum systems of the first node to the client states of the selected ones in the alpha quantum system of the first node.

32. A quantum network as claimed in any one of claims 30 to 31, wherein the proxy state and the client state comprise first and second spin states, respectively.

33. A quantum network according to claim 32, wherein the first spin state comprises an electron spin state.

34. A quantum network according to claim 32 or 33, wherein The second spin state comprises a nuclear spin state.

35. A quantum network as claimed in any one of claims 32 to 34, wherein the proxy element and the client element have a fixed spatial relationship in each of the alpha quantum systems.

36. A quantum network as claimed in any one of claims 32 to 35, wherein the strength of the hyperfine coupling between the proxy element and the client element is the same for each of the alpha quantum systems.

37. A quantum network as claimed in any one of claims 29 to 36, wherein each of the alpha quantum systems and / or each of the higher energy level quantum systems are embedded in a crystalline substrate.

38. A quantum network according to claim 37, wherein the quantum system comprises a luminescent centre.

39. The method of claim 37 or 38, wherein the higher energy level quantum systems each comprise a T centre.

40. A quantum network as claimed in any one of claims 29 to 39, wherein the inter-node optical network is lossier than the intra-node optical networks of the first and second nodes.

41. A quantum network according to claim 40, wherein the intra-node optical network is characterized by a loss of less than 3 dB.

42. The method of any of claims 40-41, wherein the inter-node optical network is characterized by a loss greater than 3 dB.

43. A quantum network as claimed in any one of claims 29 to 42, wherein each of the nodes comprises at least five of the higher energy level quantum systems.

44. A quantum network according to any one of claims 29 to 43, wherein for each of the plurality of nodes, the intra-node network comprises an optical mixer having first and second input ports and a first output port and a single photon detector at each of the output ports, and the controller is configured to configure the intra-node network to optically couple the selected alpha quantum system to the first input port of the optical mixer and optically connect the higher energy level quantum system of the entangled pair to the second input port of the optical mixer.

45. A quantum network according to claim 44, wherein each of the plurality of nodes comprises a first optical switch having a plurality of input ports and an output port optically connected to the first input port of the optical mixer, each of the plurality of input ports being optically connected to a corresponding one of the one or more alpha quantum systems of the node.

46. ​​A quantum network according to any one of claims 29 to 45, wherein for each of the plurality of nodes, the intra-node network comprises a single photon detector at each of the output ports having first and second input ports and first and second output ports, and the controller is configured to configure the intra-node network to optically couple a quantum system intermediate the selected alpha quantum system and the higher energy level quantum system of the entangled pair to the first input port of the optical mixer, and to optically connect the higher energy level quantum system of the entangled pair to the second input port of the optical mixer.

47. A quantum network according to claim 46, wherein each of the plurality of nodes comprises a first optical switch having a plurality of input ports and an output port optically connected to the first input port of the optical mixer, each of the plurality of input ports being optically connected to a corresponding one of a plurality of quantum systems of the node.

48. A quantum network according to any one of claims 45 to 47, wherein each of the plurality of nodes comprises a second optical switch having a plurality of input ports and an output port optically connected to the second input port of the optical mixer, each of the plurality of input ports being optically connected to a respective one of the plurality of higher energy level quantum systems of the node.

49. A method for distributing quantum entanglement, the method comprising: A plurality of cells are provided, each of the cells comprising a plurality of quantum systems, the plurality of quantum systems comprising: a plurality of higher energy level quantum systems, each of which is selectively connectable to an inter-cell optical network or an intra-cell optical network; and one or more alpha quantum systems connectable to the intra-cell optical network; configuring the inter-cell optical network to connect a plurality of pairs of the higher-energy-level quantum systems in pairs, wherein each of the plurality of pairs includes two of the higher-energy-level quantum systems and the two higher-energy-level quantum systems are in different ones of the cells; Attempting to establish quantum entanglement of the quantum states of each of the multiple pairs of the higher energy level quantum systems by means of the inter-cell optical network.

50. The method of claim 49, wherein the plurality of cells comprises three or more of the cells, and for at least one of the cells, the plurality of higher energy level quantum systems comprises one or more higher energy level quantum systems paired with a corresponding higher energy level quantum system of a first other of the cells and one or more higher energy level quantum systems paired with a corresponding higher energy level quantum system of a second other of the cells.

51. The method of claim 49 or 50, wherein attempting to establish quantum entanglement of the quantum states of each of the multiple pairs of the higher energy level quantum systems is performed simultaneously for at least five of the multiple pairs.

52. The method of any one of claims 49 to 51, comprising maintaining at least a set number of the plurality of pairs of the higher energy level quantum systems in an entangled state and automatically replenishing the entangled pairs in response to entanglement of the plurality of pairs being depleted.

53. The method of claim 52, comprising automatically replenishing the entangled pair in response to a predetermined time having passed since entanglement of one of the entangled pairs.

54. The method of any one of claims 49 to 53, further comprising: detecting success in entangling the quantum states of the plurality of pairs of entangled pairs in the higher energy level quantum systems; At each of a first cell and a second cell of the plurality of cells, entanglement of a respective higher energy level quantum system of an entangled pair of higher energy level quantum systems is transferred to a quantum state of a selected one of the alpha quantum systems of the respective cell using the respective intra-cell optical network.

55. The method of any one of claims 49 to 54, wherein the alpha quantum system and the higher energy level quantum system each include a proxy element having a proxy state and a client element having a client state, and the method comprises: entangle the proxy state of the higher-energy-level quantum system of one of the plurality of pairs of higher-energy-level quantum systems; The entanglement of the proxy state is transferred to the client state of the higher energy level quantum system of the one of the plurality of pairs of higher energy level quantum systems.

56. A system for distributing quantum entanglement, the system comprising: A plurality of cells, each of the cells comprising a plurality of quantum systems, the plurality of quantum systems comprising: a plurality of higher energy level quantum systems, each of which is selectively connectable to an inter-cell optical network or an intra-cell optical network; and one or more lower energy level quantum systems connectable to the intra-cell optical network; A controller operable to: configuring the inter-cell optical network to connect a plurality of pairs of the higher-energy-level quantum systems in pairs, wherein each of the plurality of pairs includes two of the higher-energy-level quantum systems and the two higher-energy-level quantum systems of each of the plurality of pairs are in different ones of the cells; A non-deterministic quantum entanglement protocol is performed on the higher-energy level quantum system of each of the plurality of pairs of the higher-energy level quantum systems using the inter-cell optical network.

57. The system of claim 56, wherein the inter-cell optical network comprises a plurality of optical mixers, each of the optical mixers having first and second input ports, and configuring the inter-cell optical network comprises, for each of the plurality of pairs, coupling the higher energy level quantum system of the pair to the first and second input ports of a corresponding one of the plurality of optical mixers.

58. The system of any one of claims 56-57, wherein each of the cells comprises a first optical switch operable to selectively couple each of the higher energy level quantum systems of the cell to the inter-cell optical network or the intra-cell optical network.

59. The system of claim 58, wherein each of the cells comprises a second optical switch operable to selectively connect one of the lower energy level quantum systems of the cell to any of the plurality of higher energy level quantum systems of the cell.

60. The system of claim 59, wherein the one of the higher energy level quantum systems is a beta quantum system, and the cell comprises an alpha quantum system connectable to the beta quantum system via the intra-cell optical network.

61. The system of claim 59, wherein the alpha quantum system and the beta quantum system each include a proxy element having a proxy state and a client element having a client state.

62. The system of claim 61, wherein the proxy state and the client state comprise first and second spin states, respectively.

63. The system of claim 62, wherein the first spin state comprises an electron spin state.

64. The system of claim 62 or 63, wherein the second spin state comprises a nuclear spin state.

65. The system of any one of claims 56-64, wherein the quantum system is embedded in a crystalline substrate.

66. The system of claim 65, wherein the quantum system comprises a luminescent center.

67. The system of claim 65 or 66, wherein the higher energy level quantum systems each comprise a T center.

68. A hierarchical quantum network comprising: A plurality of quantum systems, each of the quantum systems comprising a proxy element and a client element, the plurality of quantum systems being associated with an optical network to provide a hierarchical topology, wherein: a first plurality of said quantum systems, designated as alpha quantum systems, each associated with one of a plurality of corresponding nodes and connectable to said intra-node optical network associated with said node, each of said nodes having a respective intra-node optical network, a second plurality of said quantum systems, designated as beta quantum systems, each associated with a corresponding one of said nodes and selectively connectable to a corresponding one of said plurality of intra-node optical networks or one of at least one intra-node optical network, and A controller configured to: entangle quantum states of a pair of the beta quantum systems by executing a probabilistic entanglement protocol, the pair comprising a first and a second of the beta quantum systems, wherein the first and second beta quantum systems of the pair are associated with first and second different ones of the nodes, respectively, and The resulting entangled quantum states of the pair of the beta quantum systems are applied to teleport a quantum state of the alpha quantum system of the first node, or a quantum gate involving the alpha quantum system of the first node, to the second node.

69. The hierarchical quantum network of claim 68, wherein the intra-node optical network is characterized by a loss probability of single photons that is lower than a loss probability of single photons of the at least one inter-node optical network.

70. A hierarchical quantum network according to claim 68 or 69, wherein the intra-node optical network includes a third plurality of the quantum systems designated as gamma quantum systems each associated with a corresponding one of the nodes, and the intra-node network is configurable to provide optical links connecting multiple pairs of the gamma quantum systems, wherein each of the multiple pairs of gamma quantum systems includes a first gamma quantum system and a second gamma quantum system, wherein the first and second gamma quantum systems of each of the multiple pairs are respectively associated with different ones of the nodes, and the inter-node optical network is further configurable to provide optical links connecting the first and second gamma quantum systems in each pair to at least one of the beta quantum systems of the corresponding node.

71. A hierarchical quantum network according to any one of claims 68 to 70, wherein the intra-node optical networks are each configurable to establish an optical connection between the alpha quantum system of the corresponding node and the beta quantum system of the corresponding node, each of the optical connections comprising an interaction unit having first and second inputs respectively arranged to receive photon states originating from the connected alpha and beta quantum systems and first and second outputs respectively arranged to deliver photons to first and second single photon detectors, the interaction unit being configured to allow interference between the photon states originating from the connected alpha and beta quantum systems.

72. A hierarchical quantum network comprising a quantum system arranged into at least three layers, the hierarchical quantum network comprising: a top layer comprising a plurality of said quantum systems designated as top layer quantum systems; a bottom layer comprising a plurality of said quantum systems designated as bottom layer quantum systems distributed among a plurality of cells; one or more intermediate layers, each of said intermediate layers comprising a respective plurality of said quantum systems designated as intermediate layer quantum systems; an optical network configurable to provide a chain of optical links extending from a first one of the bottom-layer quantum systems in a first one of the cells to a second one of the bottom-layer quantum systems in a second one of the cells by virtue of the middle-layer quantum system and the top-layer quantum system, the optical network comprising a plurality of intra-cell optical networks each associated with a respective one of the cells and an inter-cell optical network configurable to provide optical links connecting the quantum system associated with a cell with others of the quantum system located outside the cell; The optical link chain comprises: an optical link connecting the first bottom-layer quantum system to a first one of the middle-layer quantum systems; an optical link connecting the second bottom-layer quantum system to a second one of the middle-layer quantum systems; a top optical link connecting a pair consisting of a first and a second in the top quantum system; one or more optical links connecting the first intermediate layer quantum system directly or indirectly to the first top layer quantum system; one or more optical links directly or indirectly connecting the second middle layer quantum system to the second top layer quantum system; and A controller is configured to distribute quantum entanglement to the first and second intermediate quantum systems by executing a predicted entanglement protocol to entangle quantum states of the first and second top-level quantum systems and extend the entanglement to the first and second intermediate-level quantum systems.

73. The hierarchical quantum network of claim 72, wherein the controller is further configured to: entangle a plurality of pairs of quantum states of each of the top quantum systems; extending the entanglement of each of the plurality of pairs of top-layer quantum systems to a corresponding pair of the middle-layer quantum systems; and Purifying the entanglement of the entangled pair of the intermediate layer quantum system.

74. A hierarchical quantum network according to claim 72 or 73, wherein the controller is configured to cause teleportation of the quantum state of the first underlying quantum system to the second underlying quantum system using the entanglement of the quantum states of the first and second intermediate layer quantum systems.

75. A hierarchical quantum network according to claim 72 or 73, wherein the controller is configured to cause teleportation of a quantum gate controlled by the first underlying quantum system using the entanglement of the quantum states of the first and second intermediate layer quantum systems to apply the quantum gate to the second underlying quantum system.

76. Any apparatus or system comprising any new and inventive feature, combination of features, or sub-combination of features described herein.

77. Any method comprising any new and inventive step, action, combination of steps and / or actions, or sub-combination of steps and / or actions described herein.

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