Methods for establishing and distributing quantum entanglements, and quantum networks

Abstract

The nested network includes a plurality of nodes, each including a high-level and a low-level quantum system. The intra-node optical network can be configured to interconnect the quantum systems of each of the nodes. The inter-node optical network can be configured to interconnect the high-level quantum systems of the plurality of nodes. The high-level quantum system can be selectively connected to the intra-node optical network or the inter-node optical network. Each quantum system can include one or more broker qubits and one or more client qubits. Entanglement of quantum systems in different nodes can be performed by attempting to entangle the quantum states of pairs of high-level quantum systems in parallel, and upon successful entanglement of one pair, transfer the entanglement to the low-level quantum systems of each node.

Description

Technical Field

[0001] Cross - Reference to Related Applications This application claims priority from U.S. Patent Application No. 63 / 364,246, filed on May 5, 2022, entitled SYSTEMS AND METHODS FOR DISTRIBUTING QUANTUM ENTANGLEMENT, the content of which is incorporated herein by reference for all purposes. For purposes of the United States of America, this application claims the benefit under 35 U.S.C. § 119 of U.S. Patent Application No. 63 / 364,246, filed on May 5, 2022, entitled SYSTEMS AND METHODS FOR DISTRIBUTING QUANTUM ENTANGLEMENT, the content of which is incorporated herein by reference for all purposes.

[0002] This technology relates to quantum information, and more particularly, to systems and methods for entangling the quantum states of quantum systems.

Background Art

[0003] In distributed quantum computing and other applications of quantum mechanics, it may be desirable to provide quantum systems that have quantum states that are entangled with each other (e.g., pairs of quantum systems each having a quantum state that forms a Bell pair). Pairs of quantum systems can be entangled ("two - particle entanglement"), or more than two quantum systems can be entangled ("multi - particle entanglement").

[0004] A multi-particle entangled state can be entangled by the quantum states of pairs of quantum systems and then generated by extending the entanglement to other quantum systems. For example, the quantum states of the first, second, and third quantum systems can first be entangled by the quantum state of one pair of the quantum systems (e.g., the first and second quantum systems), and then another one (e.g., the third) quantum system can be entangled by entangling with one of the pairs of the quantum systems (e.g., the first or second quantum system). This process can be repeated to add further quantum systems to the multi-particle entangled quantum state.

[0005] Entangled quantum states can have many applications. For example, in quantum computing, Bell pairs can be consumed to execute remote quantum gates between qubits and teleport qubits between different quantum systems. Entangled quantum systems can also have applications in quantum cryptography, applications for time measurement, and other applications.

[0006] A realizable quantum system cannot be completely isolated from its environment. As a result, the interaction between a quantum system prepared in a particular quantum state and the environment causes random changes to the quantum state of the quantum system. This process is called decoherence. Decoherence will ultimately cause the loss of their entanglement in the entangled quantum systems.

[0007] There are various known protocols that can be applied to entangle the quantum states of two quantum systems. Some of these protocols are inherently probabilistic (this means that each attempt to entangle two quantum systems using such a protocol has a certain probability of failure). Examples of protocols for generating entanglement between quantum systems are ·S.D.Barrett,et al,PRA71,060310R(2005) is described in

[0008] Many protocols for entangling two separated quantum systems are optically mediated. In such protocols, a single photon having a quantum state related to the quantum states of the two quantum systems (e.g., a photon emitted by a quantum transition in one or both of the quantum systems) can be conveyed via an optical path to a location where interaction with one or more photons can occur. Particularly when there are many losses in the optical path, individual attempts to entangle the quantum systems may fail. The average number of attempts required to entangle the quantum systems will increase with the degree of loss in the optical path.

[0009] Some entanglement protocols are inherently probabilistic. When such protocols are used, individual entanglement attempts may fail with a probability that depends on the details of the protocol.

[0010] Entanglement protocols generally involve several steps. When an entanglement attempt fails, the quantum state of the associated quantum systems may be unknown, and it may be necessary to re-initialize the associated quantum systems and restart the process for generating the desired entangled state.

[0011] The above problems are particularly acute when aiming to generate a multi-particle entangled state by an entanglement sequence, because if any attempt at entanglement in the sequence fails, the entire sequence must be restarted. The likelihood of successfully generating a multi-particle entangled state decreases with the number of entanglement operations required to generate the desired multi-particle entangled quantum state.

[0012] The above factors make the generation and distribution of quantum entanglement difficult because if an entanglement attempt fails, any entangled state established up to the point of failure is destroyed.

[0013] A strategy for constructing an entangled state using a probabilistic entanglement protocol is "broker entanglement". Broker entanglement involves two of the quantum systems of a "broker" quantum system and a "client" quantum system. In broker entanglement, the quantum states of two or more broker quantum systems are entangled, and the entanglement can then be transferred to the corresponding client quantum systems. The broker can be entangled by a probabilistic entanglement protocol. The transfer of the entangled state to the client can be deterministic. If an attempt to entangle two brokers fails, a reset of the broker may follow that can be done without destroying the state of the corresponding client.

[0014] Since resetting the broker can cause the client qubits to decohere, broker entanglement does not eliminate damage to the coherent state stored in the client qubits from failed entanglement attempts. After several failed attempts at entanglement, the client qubits will become decohered by interaction with the corresponding broker qubits, and as a result, any quantum state stored in the client will be lost.

[0015] When performing a probabilistic entanglement process, it is usually necessary to know whether each entanglement attempt has been successful. A heralded entanglement protocol can be used. In a heralded entanglement protocol, the success of entanglement can be indicated ( "heralded") by the detection of one or more photons. The loss of heralded photons in the detection circuit may mean that even if an entanglement attempt is successful, it must be treated as a failure. Unfortunately, as the complexity of the circuit, especially its connectivity, increases, the probability of photon loss also increases. Therefore, how to manage the loss of heralded photons can become a very important problem that hinders the execution of quantum circuits that require multiple remote entanglement stages.

Prior Art Documents

Non-Patent Documents

[0016]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0017] There is a need for systems and methods that facilitate the construction of entangled quantum states for quantum computing and other applications. In particular, there is a need for systems and methods that can reliably generate and distribute entanglement using lossy optical paths and / or probabilistic entanglement protocols.

Means for Solving the Problems

[0018] The present invention includes several aspects. These include · A method for generating and distributing an entangled quantum state, · A system for generating and distributing an entangled quantum state, · A multi-layer quantum network, · A method for transferring quantum states and / or quantum gates between nodes or cells of a multi-layer quantum network, is included.

[0019] One aspect of the present invention provides a method for establishing and distributing entangled quantum states. The method includes providing a first and a second node, each node including one or more alpha quantum systems and a plurality of high-level quantum systems. The alpha quantum systems and high-level quantum systems of each node are interconnected by an intra-node optical network, and the high-level quantum systems of the first node are connectable by an inter-node optical network to at least corresponding high-level quantum systems of the second node. The method attempts to establish quantum entanglement of the quantum states of each of a first plurality of pairs of high-level quantum systems by the inter-node optical network. Each of the pairs includes one of the plurality of high-level quantum systems of the first node and a corresponding one of the plurality of high-level quantum systems of the second node. The method includes detecting success in the entanglement of the quantum states of the entangled pairs among the pairs of high-level quantum systems, and in each of the first and second nodes, using the intra-node optical network of each node to transfer the entanglement of each of the high-level quantum systems of the entangled pairs of high-level quantum systems to a selected one of the quantum states of the alpha quantum systems of each node.

[0020] In some embodiments, attempts to establish quantum entanglement of different ones of the quantum states of the plurality of pairs of high-level quantum systems are performed simultaneously.

[0021] In some embodiments, the alpha and high-level quantum systems each include a broker element having a broker state and a client element having a client state, and the method includes entangling a broker state of one of a pair of high-level quantum systems, transferring the entanglement to a client state of one of the high-level quantum systems of the pair of high-level quantum systems, and transferring the entanglement to a selected one of the client states of the alpha quantum system of the first node.

[0022] In some embodiments, transferring the entanglement to a client state of one of the high-level quantum systems of the pair of high-level quantum systems includes performing a quantum SWAP gate on one of the high-level quantum systems of the pair of high-level quantum systems.

[0023] In some embodiments, performing a quantum SWAP gate on each of one of the high-level quantum systems of the pair of high-level quantum systems includes applying an RF pulse to each of one of the high-level quantum systems of the pair of high-level quantum systems to facilitate a transition from state

Number

Number

[0024] In some embodiments, transferring entanglement to a selected one of the client states of the alpha quantum system of the first node includes entangling, at the first node, one of the broker states of a pair of the high-level quantum systems of the first node with a selected one of the broker states of the alpha quantum system of the first node, and transferring, at the first node, the entanglement of one of the client states of the high-level quantum systems of a pair of the high-level quantum systems of the first node to a selected one of the client states of the alpha quantum system of the first node.

[0025] In some embodiments, the method includes entangling, at the second node, one of the broker states of a pair of the high-level quantum systems of the second node with a selected one of the broker states of the alpha quantum system of the second node, and transferring, at the second node, the entanglement of one of the client states of the high-level quantum systems of a pair of the high-level quantum systems of the second node to a selected one of the client states of the alpha quantum system of the second node.

[0026] In some embodiments, transferring the entanglement of one of the client states of a pair of the beta quantum systems of the first and / or second nodes to a selected one of the client states of the alpha quantum systems of the first and / or second nodes includes performing a quantum teleportation procedure.

[0027] In some embodiments, the broker state and the client state each include a first spin state and a second spin state.

[0028] In some embodiments, the first spin state includes an electron spin state.

[0029] In some embodiments, the second spin state includes a nuclear spin state.

[0030] In some embodiments, for at least one of the first and second nodes, using the respective intra-node optical network, transferring the entanglement of each entangled pair of high-level quantum systems of the high-level quantum system to a selected one of the alpha quantum systems of the respective node includes transferring the entanglement to a selected one of the alpha quantum systems, and sequentially transferring the entanglement from each high-level quantum system to one or more intermediate-level quantum systems and from one of the one or more intermediate-level quantum systems to a selected alpha quantum system.

[0031] In some embodiments, the one or more intermediate-level quantum systems include beta quantum systems, and the intra-node optical network includes an optical link directly connecting the alpha quantum system to the beta quantum system.

[0032] In some embodiments, the quantum system is embedded in a crystal substrate.

[0033] In some embodiments, the quantum system includes a luminescent center.

[0034] In some embodiments, the high-level quantum systems each include a T center.

[0035] In some embodiments, each of the first and second nodes includes at least five of the high-level quantum systems, and the method attempts to establish quantum entanglement between each of at least five of the high-level quantum systems of the first node and a respective corresponding one of the quantum states of the plurality of high-level quantum systems of the second node in parallel.

[0036] In some embodiments, each of the first and second nodes includes at least 10 of the high-level quantum systems, and the method attempts to establish quantum entanglement between each of at least 10 of the beta quantum systems of the first node and a corresponding one of the plurality of high-level quantum systems of the second node in parallel.

[0037] In some embodiments, the method includes teleporting a quantum gate or a quantum state from the first node to the second node using the entanglement of a selected one of the quantum states of each of the alpha quantum systems.

[0038] In some embodiments, the method includes configuring an intra-node network of the first node to provide an optical connection between a high-level quantum system and a selected one of the alpha quantum systems or a beta quantum system associated with a selected one of the alpha quantum systems.

[0039] In some embodiments, the first node includes N high-level quantum systems, each of the N high-level quantum systems being connected to a corresponding port of a first optical switch operable to selectively couple the high-level quantum system to either an intra-node optical network or an inter-node optical network of the node, and configuring the intra-node network of the first node includes operating the first optical switch to connect an entangled one of the high-level quantum systems of a pair of high-level quantum systems to the intra-node optical network of the first node.

[0040] In some embodiments, the first node includes M alpha quantum systems, each of the M alpha quantum systems being 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 a selected one of the alpha quantum systems to a high-level quantum system belonging to an entangled one of a pair of high-level quantum systems.

[0041] In some embodiments, the method includes extending one entangled entanglement of a pair of high-level quantum systems to provide three or more multi-particle entangled states of the high-level quantum systems.

[0042] In some embodiments, three or more high-level quantum systems in the multi-particle entangled quantum state include high-level quantum systems at least at a first node, a second node, and a third node.

[0043] In some embodiments, the intra-node optical network is characterized by a loss less than 3 dB.

[0044] In some embodiments, the inter-node optical network is characterized by a loss greater than 3 dB.

[0045] In some embodiments, the method continues an attempt to establish quantum entanglement of the quantum states of pairs of high-level quantum systems by the inter-node optical net at a rate sufficient to replace the entangled pairs of high-level quantum systems that are consumed by quantum decoherence or whose entanglement is broken, thereby maintaining the resources of at least one entangled pair of the high-level quantum systems.

[0046] In some embodiments, the method includes providing a third node including one or more alpha quantum systems and a plurality of high-level quantum systems, and attempting to establish quantum entanglement of the quantum states of each of a second plurality of pairs of high-level quantum systems by the inter-node optical network, each of the second plurality of pairs including one of the plurality of high-level quantum systems of the first node and a respective corresponding one of the plurality of high-level quantum systems of the third node.

[0047] Another aspect of the present invention provides a quantum network including a plurality of nodes or cells. Each node or cell includes at least one alpha quantum system, a plurality of high-level quantum systems, and an intra-node optical network optically coupled to the at least one alpha quantum system and the plurality of high-level quantum systems. The inter-node optical network is configurable to provide a plurality of optical paths, each of which optically connects a corresponding pair of high-level quantum systems. Each pair includes one of the high-level quantum systems of a first one of the nodes and one of the corresponding high-level quantum systems of a second one of the nodes. The controller attempts to simultaneously entangle each of the high-level quantum systems of the pairs of beta quantum systems via the inter-node optical network, and when one of the entangled high-level quantum systems of the pairs of high-level quantum systems detects entanglement, transfers the entangled state of the one of the entangled high-level quantum systems of the pairs of high-level quantum systems to one or more selected alpha quantum systems of the first one of the nodes and / or one or more selected alpha quantum systems of the second one of the nodes via the intra-node optical network.

[0048] In some embodiments, the alpha and high-level quantum systems each include a broker element having a broker state and at least one client element having a client state.

[0049] In some embodiments, the controller executes a protocol for entangling the broker states of a pair of high-level quantum systems, and when one of the entangled broker states of the pair of high-level quantum systems is entangled, executes a protocol for transferring the entanglement to the client state of one of the entangled high-level quantum systems of the pair of high-level quantum systems, executes a protocol for entangling the broker state of one of the entangled high-level quantum systems of the pair of high-level quantum systems of the first node with a selected one of the broker states of the alpha quantum systems of the first node, and executes a protocol for transferring the entanglement of the client state of one of the entangled high-level quantum systems of the pair of high-level quantum systems of the first node to a selected one of the client states of the alpha quantum systems of the first node, and is further configured to do so.

[0050] In some embodiments, the broker state and the client state each include a first spin state and a second spin state.

[0051] In some embodiments, the first spin state includes an electron spin state.

[0052] In some embodiments, the second spin state includes a nuclear spin state.

[0053] In some embodiments, the broker element and the client element have a fixed spatial relationship in each of the alpha quantum systems.

[0054] In some embodiments, the strength of the hyperfine coupling between the broker element and the client element is the same for each of the alpha quantum systems.

[0055] In some embodiments, each of the alpha quantum systems and / or each of the high-level quantum systems is embedded in a crystal substrate.

[0056] In some embodiments, the quantum system includes a light-emitting center.

[0057] In some embodiments, the high-level quantum systems each include a T center.

[0058] In some embodiments, the inter-node optical network has greater loss than the intra-node optical networks of the first and second nodes.

[0059] In some embodiments, the intra-node optical network is characterized by a loss less than 3 dB.

[0060] In some embodiments, the inter-node optical network is characterized by a loss greater than 3 dB.

[0061] In some embodiments, each of the nodes includes at least five of the high-level quantum systems.

[0062] In some embodiments, for each of the plurality of nodes, the intra-node network includes an optical mixer having a first and second input port and a first output port, and a single-photon detector at each of the output ports, and the controller is configured to optically couple a selected alpha quantum system to the first input port of the optical mixer and to configure the intra-node network to optically connect an entangled pair of high-level quantum systems to the second input port of the optical mixer.

[0063] In some embodiments, each of the plurality of nodes includes a first optical switch having a plurality of input ports, each of the plurality of input ports being optically connected to one of the one or more alpha quantum systems of the node, and the output port being optically connected to the first input port of the optical mixer.

[0064] In some embodiments, for each of a plurality of nodes, the intra-node network includes an optical mixer having first and second input ports and first and second output ports, and a single-photon detector at each of the output ports, and the controller optically couples a quantum system intermediate between a selected alpha quantum system and a high-level quantum system of an entangled pair to the first input port of the optical mixer and configures the intra-node network to optically connect the high-level quantum system of the entangled pair to the second input port of the optical mixer.

[0065] In some embodiments, each of the plurality of nodes includes a first optical switch having a plurality of input ports, each of the plurality of input ports being optically connected to one of the respective plurality of quantum systems of the node, and the output port being optically connected to the first input port of the optical mixer.

[0066] In some embodiments, each of the plurality of nodes includes a second optical switch having a plurality of input ports, each of the plurality of input ports being optically connected to one of the respective plurality of high-level quantum systems of the node, and the output port being optically connected to the second input port of the optical mixer.

[0067] Another aspect of the present invention provides a method for distributing entanglement, the method comprising providing a plurality of cells, each cell including a plurality of quantum systems, the plurality of quantum systems including a plurality of high-level quantum systems each selectively connectable to either 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, connecting, pair by pair, a plurality of pairs of high-level quantum systems, each pair including two of the high-level quantum systems and the two high-level quantum systems being in different ones of the cells, configuring an inter-cell optical network to connect the plurality of pairs of high-level quantum systems, and attempting to establish quantum entanglement of the quantum states of each of the plurality of pairs of high-level quantum systems by the inter-cell optical network.

[0068] In some embodiments, the plurality of cells includes three or more of the cells, and for at least one cell, the plurality of high-level quantum systems includes one or more high-level quantum systems paired with one corresponding high-level quantum system of the first other one of the cells and one or more high-level quantum systems paired with one corresponding high-level quantum system of the second other one of the cells.

[0069] In some embodiments, attempting to establish quantum entanglement of the quantum states of each of the plurality of pairs of high-level quantum systems is performed simultaneously for at least five of the pairs.

[0070] In some embodiments, the method includes maintaining at least a predetermined number of pairs of high-level quantum systems in an entangled state and automatically replenishing the entangled pairs as the entanglement of the pairs is consumed.

[0071] In some embodiments, the method includes automatically replenishing the entangled pairs in response to a predetermined time having elapsed since the entanglement of one of the entangled pairs.

[0072] In some embodiments, the method includes detecting success in the entanglement of the quantum states of the entangled pairs among the pairs of high-level quantum systems, and in each of the first cell and the second cell among the plurality of cells, using the respective intra-cell optical network to transfer the entanglement of each of the high-level quantum systems of the entangled pairs of high-level quantum systems to a selected one of the quantum states of the alpha quantum system of each cell.

[0073] In some embodiments, the alpha quantum system and the high-level quantum system each include a broker element having a broker state and a client element having a client state, and the method includes entangling the broker state of one of the high-level quantum systems of a pair of high-level quantum systems and transferring the entanglement of the broker state to the client state of one of the high-level quantum systems of the pair of high-level quantum systems.

[0074] Another aspect of the present invention provides a system for distributing quantum entanglement. The system includes a plurality of cells. Each cell includes a plurality of quantum systems and a plurality of high-level quantum systems that are each selectively connectable to either an inter-cell optical network or an intra-cell optical network, and one or more low-level quantum systems that are connectable to the intra-cell optical network. The system is operable to configure an inter-cell optical network that connects each of a plurality of pairs of high-level quantum systems, where each pair includes two of the high-level quantum systems and the two high-level quantum systems of each of the plurality of pairs are in different ones of the cells, and to execute a non-deterministic quantum entanglement protocol for each of the high-level quantum systems of the plurality of pairs of high-level quantum systems using the inter-cell optical network, and includes a controller.

[0075] In some embodiments, the inter-cell optical network includes a plurality of optical mixers, each optical mixer having first and second input ports, and configuring the inter-cell optical network includes coupling the high-level quantum systems of each pair to the corresponding first and second input ports of one of the plurality of optical mixers for each pair.

[0076] In some embodiments, each cell includes a first optical switch operable to selectively couple each of the high-level quantum systems of the cell to either the inter-cell optical network or the intra-cell optical network.

[0077] In some embodiments, each cell includes a second optical switch operable to selectively connect one of the low-level quantum systems of the cell to any one of the plurality of high-level quantum systems of the cell.

[0078] In some embodiments, one of the high-level quantum systems is a beta quantum system, and the cell includes an alpha quantum system connectable to the beta quantum system by an intra-cell optical network.

[0079] In some embodiments, the alpha quantum system and the beta quantum system each include a broker element having a broker state and a client element having a client state.

[0080] In some embodiments, the broker state and the client state each include a first spin state and a second spin state.

[0081] In some embodiments, the first spin state includes an electron spin state.

[0082] In some embodiments, the second spin state includes a nuclear spin state.

[0083] In some embodiments, the quantum system is embedded in a crystalline substrate.

[0084] In some embodiments, the quantum system includes a luminescent center.

[0085] In some embodiments, the high-level quantum systems each include a T center.

[0086] Another aspect of the present invention provides a layered quantum network that includes a plurality of quantum systems. Each of the quantum systems includes a broker element and a client element. The plurality of quantum systems is associated with an optical network and provides a layered topology in which a first plurality of quantum systems designated as alpha quantum systems are each associated with one of a plurality of corresponding nodes, and a second plurality of quantum systems designated as beta quantum systems are each associated with a corresponding one of the nodes. Each of the nodes has an intra-node optical network. The beta quantum system is selectively connectable to a corresponding one of the plurality of intra-node optical networks or to one of the at least one inter-node optical networks. A controller is configured to entangle the quantum states of a pair of beta quantum systems, the pair including one of a first and a second of the pair of beta quantum systems, and the first and second beta quantum systems of the pair are associated with different ones of a first and a second of each of the nodes, and to apply the resulting entangled state of the pair of beta quantum systems to teleport an alpha quantum state of a first node or a quantum gate involving an alpha quantum system of the first node to a second node by executing a probabilistic entanglement protocol.

[0087] In some embodiments, the intra-node optical network is characterized by a probability of single-photon loss that is lower than the probability of single-photon loss of at least one of the inter-node optical networks.

[0088] In some embodiments, the intra-node optical network includes a third plurality of quantum systems each designated as a gamma quantum system respectively associated with one of the corresponding nodes, the intra-node network is configurable to provide an optical link connecting a pair of gamma quantum systems, each pair of gamma quantum systems including a first gamma quantum system and a second gamma quantum system, and the first and second gamma quantum systems of each pair being respectively associated with one of different nodes, and the inter-node optical network is further configurable to provide an optical link connecting the first and second gamma quantum systems of each pair to at least one beta quantum system of each respective node.

[0089] In some embodiments, the intra-node optical network is 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 optical connection including an interaction unit having first and second inputs respectively arranged to receive photon states generated from the connected alpha and beta quantum systems, and first and second outputs respectively arranged to supply photons to first and second single-photon detectors, the interaction unit being configured to enable interference between the photon states generated from the connected alpha and beta quantum systems.

[0090] Another aspect of the present invention provides a layered quantum network including a quantum system disposed in at least three layers. The layered quantum network includes a top layer including a plurality of quantum systems designated as top layer quantum systems, a bottom layer including a plurality of quantum systems designated as bottom layer quantum systems distributed among a plurality of cells, one or more intermediate layers each including a respective plurality of quantum systems designated as intermediate layer quantum systems, and an optical network configurable to provide a chain of optical links extending from a first one of a first bottom layer quantum system of a cell to a second one of a second bottom layer quantum system of the cell by the intermediate layer quantum systems and the top layer quantum systems. The optical network includes 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 an optical link connecting a quantum system associated with a cell to another one of the quantum systems external to the cell. The chain of optical links includes an optical link connecting the first bottom layer quantum system to a first one of the intermediate layer quantum systems, an optical link connecting the second bottom layer quantum system to a second one of the intermediate layer quantum systems, a top layer optical link connecting a pair composed of the first and second ones of the top layer quantum systems, one or more optical links directly or indirectly connecting the first intermediate layer quantum system to the first top layer quantum system, and one or more optical links directly or indirectly connecting the second intermediate layer quantum system to the second top layer quantum system. The controller is configured to distribute quantum entanglement to the first and second intermediate quantum systems by executing a pre-announced entanglement protocol to entangle the quantum states of the first and second top layer quantum systems and extending that entanglement to the first and second intermediate layer quantum systems.

[0091] In some embodiments, the controller is further configured to entangle the quantum states of each of a plurality of pairs of top-layer quantum systems, extend the entanglement of each of the plurality of pairs of top-layer quantum systems to respective pairs of middle-layer quantum systems, and purify the entanglement of the entangled pairs of middle-layer quantum systems.

[0092] In some embodiments, the controller is configured to cause teleportation of the quantum state of a first bottom-layer quantum system to a second bottom-layer quantum system using entanglement of the quantum states of a first and a second middle-layer quantum systems.

[0093] In some embodiments, the controller is configured to cause teleportation of a quantum gate controlled by a first bottom-layer quantum system to apply the quantum gate to a second bottom-layer quantum system using entanglement of the quantum states of a first and a second middle-layer quantum systems.

[0094] Further aspects and exemplary embodiments are shown in the accompanying drawings and / or described in the following description.

[0095] It is emphasized that the present invention relates to combinations of all the above features even if these features are described in different claims.

[0096] The accompanying drawings illustrate non-limiting exemplary embodiments of the present invention.

Brief Description of the Drawings

[0097]

Figure 1

Figure 1A

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 8A

Figure 8B-9A

Figure 10

Figure 10A-10C

Figure 11

Figure 12

DETAILED DESCRIPTION OF THE INVENTION

[0098] Definition In a quantum system, "connected" means connected by an optical path, an optical link, an optical waveguide, or an optical network extending between quantum systems. "Connected" includes cases where an optical path, an optical link, an optical waveguide, or an optical network is operable to carry photons or photon states emitted by each of the quantum systems to a location where the photons or photon states can interact with each other (such as interference) (e.g., an optical mixer, an optical beam splitter, an optical coupling waveguide, etc.). For example, when an optical network is configured such that photons generated from each of the optical systems are supplied to an interaction unit having first and second inputs respectively arranged to receive photon states generated from the connected quantum systems, and first and second outputs arranged to supply photons to first and second single-photon detectors, the two quantum systems are "connected", and the interaction unit is configured to enable interference between photon states generated from the connected quantum systems.

[0099] "Entanglement" means a situation where the quantum states of individual quantum systems in a group of two or more quantum systems cannot be described independently of another quantum state of the quantum systems in that group. An equivalent definition of "entanglement" is that the state of a plurality of quantum systems is a state that cannot be decomposed into the states of the individual quantum systems that make it up. For example, two entangled particles can each have a quantum state that is a superposition of spin-up and spin-down states, while the combined spin of the two particles is restricted to zero. Quantum entanglement can exist even between quantum systems separated by very large distances.

[0100] "Highly entangled state" means a maximally entangled state or a state close to a maximally entangled state. A Bell pair is an example of a highly entangled state.

[0101] "Quantum bit" means a quantum system having first and second quantum states that can be used to represent quantum information and can exist in a quantum superposition. Examples of quantum systems that can be used as quantum bits include particles having spin (e.g., electrons, atomic nuclei, holes) where different spin states can represent information, particles having exciton states where the presence or absence of excitons can represent information, such as electrons having different orbital states where the orbital state occupied by the particle can represent information, and the like.

[0102] "Qutrit" means a quantum system having three or more quantum states that can be used to represent quantum information and can exist in a quantum superposition. Particles having a spin greater than 1 / 2 can be applied as, for example, qutrits.

[0103] "Broker quantum system" means a quantum system applied as a path for deterministically transferring a quantum state to another quantum system (client quantum system).

[0104] "Client quantum system" means a quantum system that receives the transfer of a quantum state from a broker quantum system.

[0105] "Quantum system" means a system having practical applications for the storage and / or manipulation of quantum information. A quantum system supports a plurality of quantum states and superpositions of at least two supported quantum states. Examples of quantum systems include spin (e.g., electron spin, nuclear spin), quantum bits, qutrits, quantum dots, damage centers such as T, I, M centers, NV centers, impurity atoms in silicon or other substrates, and aggregates of two or more of these. In some embodiments, the quantum system is used as a quantum bit. For example, the quantum system can be composed of or include a spin having two spin states, and the spin can be used as a quantum bit for storing and manipulating information represented by either one or a superposition of the two individual spin states.

[0106] 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 specific details. In other instances, well-known elements have not been shown or described in detail in order not to unnecessarily obscure the invention. Accordingly, the specification and drawings are to be interpreted in an illustrative rather than a restrictive sense.

[0107] One application of the present technology is to establish entanglement between quantum systems connected by an optical path (e.g., an optical waveguide, an optical fiber, free space, etc.). In some embodiments, the optical path is non-deterministic, which means that the same photon or photon state emitted into the optical path can 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, and some photons or photon states may experience different changes in phase / polarization or other properties when propagating along the optical path.

[0108] In some embodiments, the optical path has high loss (i.e., the probability that a photon sent to one end of the optical path reaches the other end of the optical path is less than about 50% (which corresponds to 3 dB loss)). In some embodiments, the optical path has a loss in the range of about 3 dB to about 40 dB (which corresponds to the possibility that a single photon crosses the optical path without being lost in the range of about 50% to about 0.01%).

[0109] A probabilistic entanglement protocol can be applied to establish quantum entanglement of quantum systems connected by an optical path. The probability of success of quantum entanglement from one execution of the probabilistic entanglement protocol varies depending on the details of the protocol and the probability that a single photon generated during the execution of 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 on an optical link with high loss in the range of about 10 -7 % to about 20% probability of success of entanglement from one iteration of entanglement.

[0110] The present technology provides an approach that can be applied to mitigate the problems as described in the background section. This approach involves providing a plurality of quantum systems connected by an optical path and simultaneously executing a quantum entanglement protocol for each pair of quantum systems, where each pair includes quantum systems connected by an optical path.

[0111] As soon as any one of the quantum systems in the pair is successfully entangled, the goal of obtaining entanglement of the quantum systems at either end of the optical path is achieved. The entangled pair can then be applied as a resource, for example, to teleport a quantum state or a quantum gate from one end of the optical path to the other, for use in quantum cryptography, or for any other application of entanglement.

[0112] In a preferred embodiment, the execution of the quantum entanglement protocol is automated. The computer system can adjust the execution of the steps of the quantum entanglement protocol for different pairs of the quantum system and determine the timing at which quantum entanglement of any pair of the quantum systems is established. In some embodiments, entanglement attempts are made essentially continuously, such that at any given time, one or more pairs of qubits are entangled and available for use as resources. In some embodiments, the entanglement attempts are performed on demand, and any practical number of entanglement attempts can be made simultaneously, so that the time required to establish an entangled pair of the quantum system is significantly reduced compared to the case where entanglement attempts are sequentially repeated for a single pair of the quantum system until quantum entanglement is achieved.

[0113] Without loss of generality, the quantum systems located at both ends of the optical path can be considered to belong to "nodes" or "cells". The present technology can be applied to establishing quantum entanglement between quantum systems in different nodes and / or distributing quantum entanglement to one or more other quantum systems within a node. The nodes need not be physically separated by a specific distance, but can be separated by any distance, including ranges from very large distances to very small distances.

[0114] FIG. 1 shows an exemplary system 100 according to an exemplary implementation of the present technology. The system 100 can be applied to efficiently construct an entangled state. The system 100 includes a plurality of nodes 102. FIG. 1 shows a simple example where the system 100 includes quantum systems associated with three nodes 102. However, the system 100 can have any practical number of nodes 102 from two upwards.

[0115] Each node 102 includes a plurality of quantum systems. FIG. 1 includes quantum systems 20A and 20B (collectively or generally referred to as quantum system 20). System 100 can be operated as described herein to generate entanglement between two or more of the quantum systems 20B in two or more of the nodes 102.

[0116] To explain the operation of system 100, it is convenient to consider the case where each quantum system 20 is a qubit. The quantum system 20 is not limited to qubits (for example, it can include systems that combine two or more qubits and / or qutrits, as in other examples described herein). As described below (e.g., see FIG. 7), in some embodiments, each quantum system 20 can include an element that can function as a broker and an element that can function as a client. By way of example only, the broker element can include an electron spin, and the client element can include a nuclear spin.

[0117] The quantum system 20 can be realized, for example, by particles having an essential spin. Different spin states can correspond to different computed values. Since the quantum system 20 is a quantum system, it is not limited to a specific spin state. For example, a particle having spin 1 / 2 may be observed to be spin-up or spin-down with respect to an arbitrarily selected axis. However, the particle can have a quantum state that is a specific superposition of spin-up and spin-down.

[0118] System 100 includes an optical path connecting different nodes 102. In the illustrated embodiment, the optical path is provided by a reconfigurable inter-node optical communication network 110. Network 110 is highly connected and can be configured to provide a plurality of optical links simultaneously between any two nodes 102 within system 100, such that each of the optical links provides an optical path that optically couples one of the first quantum systems 20B of node 102 to the other quantum system 20B of node 102.

[0119] Entanglement can be generated between pairs of quantum systems 20B at different nodes 102, for example as described above. Such entanglement can optionally be extended to multi-particle entanglement of groups of three or more quantum systems 20B for applications where multi-particle entanglement is desired.

[0120] In the illustrated embodiment, each node 102 includes one or more additional quantum systems 20A. Specifically, each node 102 includes a group 104 composed of a plurality of quantum systems 20B and a group 106 composed of one or more other quantum systems 20A.

[0121] The quantum system 20A may be referred to as an "alpha" quantum system, and the quantum system 20B may be referred to as a "beta" quantum system. This nomenclature reflects the idea that the quantum systems 20 of the system 100 can be logically arranged in "layers" (e.g., alpha and beta layers) where the quantum systems 20 belonging to each layer can play different roles. For example, the beta quantum system 20B can be applied to establish entanglement between different nodes 102, and the alpha quantum system 20A can be used in operations that consume the entanglement provided by the beta quantum system 20B. This nested layer structure can be extended to three or more layers (e.g., alpha, beta, gamma layers).

[0122] At 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 low-loss optical paths 113 that connect each one of the beta quantum systems 20B to each one of the alpha quantum systems 20A. The low-loss optical paths 113 facilitate applying deterministic quantum operations between the quantum systems 20A, 20B of any node 102.

[0123] The quantum systems 20 of nodes 102 need not be in any particular spatial relationship to each other. The quantum systems 20 of nodes 102 are interconnected by a low-loss optical network 112, and the beta quantum systems 20B of nodes 102 can be connected to quantum systems external to nodes 102 by an optical communication network 110. The optical links provided by networks 110 and 112 can have any practical length, from small to very large.

[0124] Nodes 102 can be spatially separated from each other, but this is not essential in all implementations. Implementations are also possible where the quantum systems of two or more different nodes 102 are co-located (e.g., distributed in the same area of a substrate). In another implementation, it is also possible for quantum systems 20 remote from different nodes 102 to be more widely separated (e.g., located on different substrates, in different refrigerators, in different buildings, etc.). The quantum systems 20 belonging to the same node 102 can be close to each other and / or widely dispersed and separated.

[0125] Figure 1A shows a very simple example of a node 102-1. 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), as well as 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 the inter-node network 110 (a portion of waveguides 111-1 and 111-2 is shown). Each alpha quantum system 20A and each beta quantum system 20B are optically connected or connectable to a waveguide 113 of the low-loss optical network 112.

[0126] System 100 includes a controller 118 that adjusts the operation of system 100 and additional elements described elsewhere in this specification. The controller 118 can be configured to, for example, set and / or manipulate the quantum state of the quantum system 20 and / or control the optical networks 110 and / or 112 to provide a desired optical connection between the quantum systems 20.

[0127] The mechanism for setting and manipulating the quantum state of the quantum system 20 depends on the nature of the quantum system 20 and can include, for example, a mechanism for generating a bias and / or a local magnetic field, a radiation source (e.g., optical radiation, such as high-frequency radiation like microwave radiation) that can be supplied to the quantum system 20 individually and / or in groups, and a mechanism for applying an electric field to the individual quantum systems 20. The controller 118 can be configured to initialize any of the quantum systems 20 to a desired quantum state, for example, by applying a combination of optical pulses and / or radio frequency pulses known in the art to the quantum system 20. Examples of adjustment tasks that the controller 118 can be configured to perform include performing single qubit control operations, processing the results of single qubit measurements, and dynamically reconfiguring the optical network 110 and / or the optical network 112 as needed to optimize the network connection for generating and distributing entangled states.

[0128] FIG. 2 is a flowchart showing an overview of a method 200 for generating entanglement between a first selected alpha quantum system 20A of node 102 and a second selected alpha quantum system 20A of node 102.

[0129] In block 202, the network 110 is configured to 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 way that facilitates entangling each pair of beta quantum systems 20B.

[0130] In block 204, each beta quantum system 20B of two nodes (e.g., nodes 102A and 102B, see FIG. 2A) is initialized to a quantum state suitable for a probabilistic entanglement protocol that is applied in an attempt to entangle the pair of quantum states of quantum system 102B.

[0131] In block 206, method 200 attempts to entangle each pair of beta quantum systems 20B. These attempts can be made in parallel (e.g., simultaneously or at overlapping times). Attempts to entangle different ones of the pairs of beta quantum systems 20B can be made asynchronously or synchronously. Each attempt at entanglement can include applying a sequence of operations of a protocol for entanglement of the corresponding pair of beta quantum systems 20B. The protocol can be a probabilistic protocol. For example, each attempt at entanglement can include applying the steps of an entanglement protocol as described in S.D. Barrett, et al, PRA 71, 060310R (2005).

[0132] Block 206 is repeated until it is confirmed that at least one of the pairs of beta qubits has been successfully entangled, as determined in block 206A. In some embodiments, success in block 206A is detected by detecting a precursor pattern of photon detection events at a photodetector corresponding to one of the pairs of beta quantum systems 20B.

[0133] FIG. 2A shows an exemplary optical path 111 of network 110 optically connected between two quantum systems 20B by a suitable optical coupler 117. Optical path 111 includes an optical mixer 116 where single photon states associated with quantum systems 20B can interfere. Single photon detectors 118A and 118B are operable to detect photons in a pattern that heralds entanglement (or indicates that an attempt at entanglement has not been successful).

[0134] Any attempt at entanglement initiated in block 206 may fail. The failure may be due to any cause, such as loss of photons in network 110, improper initialization of quantum system 20B, etc. Network 110 may suffer from significant optical losses (e.g., distance between nodes 102, optical losses associated with switches used to configure network 110 to provide the desired connections, efficiency less than 100% of single-photon detectors, etc.). The failure of an entanglement attempt can be detected, for example, by observing the pattern of photon detections at corresponding photodetectors 118A and 118B that do not correspond to a successful entanglement, and / or by not observing the pattern of photon detections at detector 116 that corresponds to a successful entanglement.

[0135] If an attempt to entangle a pair of beta quantum systems 20B fails, block 206 may re-initialize each of the pairs of beta quantum systems 20B and attempt to entangle the pairs of beta quantum systems again. At the end of block 206, at least one pair of beta quantum systems 20B, including the beta quantum system 20B within node 102A and the beta quantum system 20B within node 102B, is entangled. For example, if it is predicted that at least one pair of beta quantum systems 20B is successfully entangled, block 206 may be completed.

[0136] Since many entanglement attempts can be executed in parallel, the amount of time expected to obtain at least one pair of beta quantum systems 20B that is entangled can be significantly reduced compared to the case where attempts to entangle one pair of beta quantum systems 20B are made sequentially.

[0137] As discussed elsewhere in this specification, in some embodiments, beta quantum system 20B may include two or more elements each having a different quantum state (e.g., one or more electron spins and / or one or more nuclear spins). In such cases, the steps of method 200 may be applied to individual ones of these elements. For example, when the quantum state of an electron spin (or nuclear spin) element of one beta quantum system 20B becomes entangled with the quantum state of a corresponding electron spin (or nuclear spin) of one of the paired beta quantum systems 20B, block 206 may be completed.

[0138] FIG. 3 is a block diagram showing an exemplary implementation of a single node 102 having N alpha quantum systems 20A and M beta quantum systems 20B. In this exemplary embodiment, switch 128 can be operated to connect beta quantum system 20B to either the inter-node network 110 or the intra-node network 112. Switch 128 can be operated to connect some or all of beta quantum systems 20B to the inter-node network 110 for the purpose of generating entanglement with beta quantum systems of other nodes 102. Switch 128 can be set to connect one or more beta quantum systems 20B to the intra-node network 112 for the purpose of transferring quantum entanglement to a selected one of alpha quantum systems 20A.

[0139] The intra-node network 112 enables any pair composed of one of the beta quantum systems 20B and one of the alpha quantum systems 20A to be connected to an optical mixer 130 (which may include, for example, a beam splitter). The optical mixer 130 has two outputs, each connected to a corresponding single photon detector (140-1 and 140-2).

[0140] In the embodiment of FIG. 3, the in-node network 112 includes an M×1 optical switch 132 that enables connecting any one of the beta quantum systems 20B1-1 to 20B-M to one input of the optical mixer 130, and an N×1 optical switch 134 that enables connecting any one of the alpha quantum systems 20A-1 to 20A-N to the second input of the optical mixer 130. The optical switches 128, 130, 132 can be controlled by the controller 118.

[0141] In some embodiments, some or all of the switches 128 are initially configured to connect the corresponding beta quantum system 20B to the corresponding optical link of the inter-node network 110. An attempt is made to entangle the beta quantum system 20B with a corresponding external quantum system external to the node 102. When entanglement between one of the beta quantum systems 20B and the corresponding external quantum system is detected, the corresponding switch 128 can be configured to connect the entangled beta quantum system 20B to the in-node network 112, and the switch 132 can be configured to provide an optical connection between the entangled beta quantum system 20B and the optical mixer 130.

[0142] If it is desirable 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 can be configured to provide an optical connection from the selected alpha quantum system 20A to the optical mixer 130. This entanglement can then be transferred to the selected alpha quantum system 20A as described elsewhere in this specification.

[0143] FIG. 4 is a block diagram showing an exemplary configuration of the inter-node network 110. In this example, P nodes 102-1 to 102-P each have M ports each corresponding to a beta quantum system 20B. These ports are each connected to corresponding ports of an MP×MP optical switch 150. The optical switch 150 is also connected to a plurality of optical mixers 152 each having two input ports and two output ports. Each output port of each mixer 152 is connected to a corresponding single-photon detector 140. The switch 150 can be operable to connect one beta quantum system 20B of a node 102 to a first input port of one of the optical mixers 152 and another second beta quantum system 20B of the node 102 to a second input port of one of the optical mixers 152. Photons detected by the corresponding detector 140 can herald entanglement of the beta quantum systems 20B of the first and second nodes optically coupled to the mixer 152.

[0144] In some operating modes, the optical switch 150 can be configured to connect a plurality (e.g., 2 to M) of ports of a first one of the M ports of the nodes 102 to the first input ports of the corresponding plurality of mixers 152 and the same number of ports of a second one of the ports of the nodes 102 to the second input ports of the corresponding plurality of mixers 152.

[0145] In some operating modes, the optical switch 150 can be configured to connect a first plurality (e.g., 2 to M) of ports of a first one of the M ports of the nodes 102 to the first input ports of the corresponding plurality of mixers 152 and to connect each of the second input ports of the corresponding plurality of mixers 152 to a port of one of a plurality of other nodes 102. Such a mode can be used to simultaneously generate entanglement of the beta quantum systems of a plurality of other nodes 102 with the beta quantum system 20B of the first one of the nodes 102.

[0146] The beta quantum system 20B and the alpha quantum system 20A may include, for example, material qubits (as opposed to "flying" qubits (photons)). In a preferred embodiment, the beta quantum system 20B and the alpha quantum system 20A include luminescent centers within a substrate such as silicon. For example, the alpha quantum system and the beta quantum systems 20B and 20A may each be provided by a luminescent center or an ensemble of luminescent centers within the substrate.

[0147] For example, the luminescent centers may include defects such as T centers, I centers, or M centers, nitrogen-carbon centers, Al1 or Ga1 centers, or radiation damage centers having unpaired ground state spins, or luminescent centers selected from impurities such as selenium, or tellurium, or sulfur, or atoms of other double donor impurities.

[0148] In any embodiment, some or all of the quantum systems may be identical. For example, all of the alpha quantum system, all of the beta quantum system, all of the gamma quantum system, all of the quantum systems within a cell or node, all of the quantum systems that may be connected by a particular optical link or network, or all of the quantum systems may have the same structure (e.g., provided by the same type of luminescent center).

[0149] FIG. 5 schematically shows a structure 50 that provides an environment for an exemplary quantum system 20 that may be the alpha quantum system 20A or the beta quantum system 20B. In some embodiments, the quantum system 20 includes a luminescent center 52 within a substrate 54. The substrate 54 may include, for example, a silicon or diamond substrate.

[0150] The substrate 54 is preferably a material composed of atoms having no net nuclear spin. For example, the substrate 54 may include purified silicon 28 (i.e., silicon that is more than 92.23% silicon 28). In some embodiments, the material of the substrate 42 is at least 96%, or 99%, or 99.5%, or 99.9% (by atom number) silicon 28.

[0151] FIG. 5 shows a magnet 56 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 and spin-down states of the spin, such as the electron spin or 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) in the vicinity of the quantum system 20 may enhance the magnetic field from the adjustable magnet 56. The magnet 56B may be deposited, for example, on, in, or near the substrate 54.

[0152] FIG. 5 also shows an antenna 57 (which may include one or more coils) that can be driven by an RF signal source 57A to manipulate the quantum state of the quantum system 20 by a resonance effect (such as electron spin resonance (“ESR”)), as is known to those skilled in the art. The RF signal source 57A can be controlled to generate pulses of radiation, such as π-pulses or π / 2-pulses, and when such pulses are supplied, they manipulate the quantum state of the quantum system 20. The antenna 57 can be incorporated, for example, within or deposited on the substrate on which the quantum system 20 is located, or placed in close proximity to the quantum system 20 sufficient to supply RF radiation to the quantum system 20 to manipulate the quantum state of the quantum system 20 in a desired manner.

[0153] FIG. 5 also shows a narrowband light source 58 arranged to illuminate the location of the quantum system 20. The light source 58 can emit light having a wavelength corresponding to, for example, an optical transition of the quantum system 20. The transition can include, for example, raising an electron from a ground state to an excited state, generation of an exciton, a spin-flip transition. The light source 58 can include, for example, a laser. The laser can be adjustable to emit light having wavelengths corresponding to different optical transitions of the quantum system 20.

[0154] FIG. 5 also shows a variable potential circuit 59B configured to apply a controllable potential difference between the electrodes 59A and the electrodes 59A. The circuit 59B can be controlled to vary the electric field at the location of the quantum system 20. The electric field can shift the energy levels of the quantum system 20 (e.g., by the Stark effect).

[0155] The structure 50 includes an optical structure 60 including a waveguide 60A and a resonant cavity 60B. The cavity 60B enhances the optical coupling between the quantum system 20 and the waveguide 60A. The waveguide 60A can optically couple the quantum system 20 to the in-node network 112 and / or the between-node network 110, for example.

[0156] The substrate 54 is housed in a refrigerator 59 that can cool the substrate 54 to cryogenic temperatures. In some embodiments, the operating temperature of the structure 44 can be very low (e.g., a few mK or a few Kelvin).

[0157] The controllable elements of the system 50 (e.g., the magnet control circuit 56A, the RF signal source 57A, the light source 58, and / or the variable potential circuit 59B) can be controlled by the controller 118.

[0158] FIG. 6 is a non-limiting and exemplary energy level diagram of the qubit 50. The ground state levels 61H and 61L can correspond to the spin-up and spin-down states of an unpaired spin (e.g., of an electron, a nucleus, or a hole), for example. For example, the levels 61H and 61L can be the result of hyperfine splitting caused by the interaction between the nuclear spin and the electron spin at the location of the quantum system 20, or splitting caused by another magnetic field at the location of the quantum system 20.

[0159] States 62H and 62L can respectively correspond to, for example, the spin-up and spin-down states of unpaired spins (such as electrons, nuclear spins, or holes). States 62H and 62L can be respectively related to states 61H and 61L by orbital or exciton transitions. The energy difference between state 62H and 61H, or between state 62L and 61L, can correspond to the energy of a photon at the optical wavelength.

[0160] As shown in FIG. 6, the energy difference ΔE1 between state 61H and 62H is different from the energy difference ΔE2 between state 61L and 62L. In some embodiments, the difference between ΔE1 and ΔE2 corresponds to a frequency difference sufficient to spin-selectively couple the spins of the quantum system 20 to the optical structure 60 (for example, when the Q factor of the 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 do not couple well to the resonator 60B, by giving the resonator 60B a resonance frequency corresponding to either of ΔE1 and ΔE2). For example, the difference between ΔE1 and ΔE2 is 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).

[0161] For example, when photons 66 having a wavelength (or equivalent frequency or energy) corresponding to ΔE1 are provided, the quantum system 20 can absorb one of the photons 66 and transition from state 61H to state 62H. The quantum system 20 can then transition from state 61H to state 62H and emit photons 66 having the same energy ΔE1.

[0162] Since the quantum system 20 is a quantum system, the quantum system 20 is not necessarily in a definite quantum state. Instead, the quantum system 20 can be in a superposition of different states (e.g., a superposition of states 61H and 61L). Also, both the state of the quantum system 20 and the state of the photon 66 can be in a superposition of a state in which the quantum system 20 emits or interacts with the photon and a state in which it does not. In general, the quantum state of the quantum system consisting of the quantum system 20 and the photon 66 includes various possible interactions between the quantum system 20 and the photon 66. As a result, the quantum states of the quantum system 20 and the photon 66 can be entangled.

[0163] Here, a more detailed example of the method according to the present technology will 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 a quantum state that can be independently controlled, and quantum information can be selectively transferred between the elements of each quantum system 20. For example, each of the quantum systems 20 can include at least one electron spin and at least one nuclear spin that can each be applied to store quantum information.

[0164] In some embodiments, part or all of the quantum system is provided by a structure in which the blocker element and one or more client elements have a fixed spatial relationship. For example, the quantum system can be provided by a luminescent center including an atom having a set of spatial arrangements in which an electron spin associated with one of the atoms is applied as a blocker element and nuclear spins associated with one or more of the atoms are applied as one or more client elements. In some embodiments, for part or all of the quantum system, the hyperfine interaction between the blocker element and the client element of the quantum system has the same strength. This is the case, for example, when each of a group of quantum systems includes a substantially identical atomic arrangement such that the distance between the blocker element and the client element is substantially the same.

[0165] This notation

Number

Number

[0166] In some embodiments, one of the elements of the quantum system 20 can be used as a broker and another element of the quantum system 20 can be used as a client. The broker element can be used to exchange quantum information with other quantum systems 20. The client element can be used to store quantum information in the quantum system 20. The client element can have a longer decoherence time than the broker element.

[0167] With this arrangement, the quantum states of the broker elements of pairs of beta quantum systems 20B within different nodes 102 (the "broker quantum states") can be entangled as described above. The entangled broker quantum states can then be transferred to the client elements of the beta quantum systems 20B. Thereby, the broker element of each beta quantum system 20B becomes available for use in transferring entanglement to the alpha quantum system 20A.

[0168] Transferring entanglement from the beta quantum system 20B to the alpha quantum system 20A can involve generating entanglement between the broker element of the beta quantum system 20B and the alpha quantum system 20A to which the entanglement is being transferred.

[0169] FIG. 7 is a flowchart of an exemplary method 250 that generates entanglement between a pair of broker elements of a beta quantum system 20B and then distributes that entanglement to the client element of a selected alpha quantum system 20A.

[0170] The resulting entanglement (e.g., an entangled Bell pair state) can then be consumed for any purpose. This consumption can take the form of, for example, a remote quantum gate operating on a client element of one or more alpha quantum systems 22. Such a remote quantum gate can be used, for example, to extend an existing entangled state to a multi-particle entangled state of three or more qubits.

[0171] In block 252 of method 250, network 110 is configured to 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 entangling each pair of beta quantum systems 20B.

[0172] In block 254, the broker elements (e.g., electron spins) of the beta quantum systems 20B of each of the two nodes (e.g., nodes 102A and 102B, see FIG. 2A) are initialized to a quantum state suitable for a probabilistic entanglement protocol that is applied in an attempt to entangle the quantum states of the broker elements of the pair of quantum systems 102B.

[0173] In block 256, attempts are made to entangle the broker elements of each pair of beta quantum systems 20B. These attempts can be made in parallel for different pairs (e.g., simultaneously or at overlapping times). The attempts to entangle the broker elements of different pairs of beta quantum systems 20B can be made asynchronously or synchronously. Block 256 can apply any suitable entanglement protocol (e.g., a probabilistic one and / or a protocol heralded as described elsewhere in this specification).

[0174] Block 256 is repeated until it is confirmed that at least one broker element of a pair of the beta quantum system 20B has been successfully entangled, as determined in block 256A. In some embodiments, success in block 256A is detected by detecting a precursor pattern of photon detection events in a photodetector corresponding to one of the pairs of the beta quantum system 20B.

[0175] In block 257, the entanglement established in block 256 is transferred to the client elements (e.g., nuclear spins) of the entangled beta quantum system 20B. After block 257, the client qubit states of at least one pair of the beta quantum system 20B are entangled.

[0176] In block 258, network 112 is configured to optically couple each of the beta quantum systems 20B entangled with a selected alpha quantum system 20A within the same node 102.

[0177] In block 259, the quantum state of the broker element of the entangled beta quantum system 20B is entangled with the broker element of the corresponding selected alpha quantum system 20A using the optical connection of block 258.

[0178] The quantum entanglement protocol used to implement block 259 can operate probabilistically. However, since network 112 can be a low-loss optical network, a successful entanglement can be heralded much more quickly than would be expected in a lossy optical network 110. In block 259, attempts at entanglement can be repeated until a successful coupling is heralded.

[0179] In block 260, using the entanglement generated in block 259, the entanglement of the client elements of the entangled beta quantum system 20B is transferred to the broker elements of the corresponding alpha quantum system 20A (e.g., by quantum teleportation). After block 260, at least one pair of the broker qubit states of the alpha quantum system 20A (where the paired alpha quantum systems 20A are at different nodes 102) are entangled.

[0180] In block 261, the entanglement of the selected broker elements of the alpha quantum system 20A is transferred to the client elements of the selected alpha quantum system 20A. After block 261, the client qubit states of the selected alpha quantum system 20A (where the paired selected alpha quantum systems 20A are at different nodes 102) are entangled. The resulting entanglement of the client elements of the alpha quantum system 20A at different nodes 102 can then be consumed.

[0181] In some embodiments, the alpha quantum system 20A functions as a computing resource. For example, the controller 118 can be configured to cause the system 100 to execute a quantum computing algorithm by initializing the alpha quantum system 20A to 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 entangling the alpha quantum system 20A with each other and / or with alpha quantum systems 20A within other nodes 102 (as described above). In method 250, electron spins can be used in the role of the broker (i.e., the broker elements can include electron spins), and nuclear spins can be used in the role of the client (i.e., the client elements can include nuclear spins).

[0182] For example, the quantum system 20 may each include a T center. Within the T center, quantum information can be transferred between the electron spin of the T center and one or more nuclear spins of the T center. In some embodiments, the electron spin functions as a broker qubit, and the nuclear spin functions as a client qubit.

[0183] FIG. 8 shows a simple system 80 including two nodes 102-1 and 102-2. Each beta quantum system 20B of the nodes 102 is shown. Each alpha quantum system 20A of the nodes 102 is shown. Each beta quantum system 20B includes a broker element 81B and a client element 82B. Each alpha quantum system 20A includes a broker element 81A and a client element 82A.

[0184] In this example, the broker 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 broker elements 81A, 81B may be provided by the electron spins of the T center. The present technology is not limited to these selections of the broker element and the client element. The quantum system 20 may take any of a variety of forms including elements suitable for applications as the broker element and the client element.

[0185] The system 80 may include additional elements. For example, the system 80 may include additional nodes, additional quantum systems, additional electron spins, and / or additional nuclear spins (not shown). For example, each of the nodes 102-1 and 102-2 of the system 80 may each include a plurality of beta quantum systems 20B.

[0186] It is assumed that it is desired to entangle the quantum state of the client element 82A of the selected alpha quantum system 20A of node 102-1 with the quantum state of the corresponding client element 82A of the selected alpha quantum system 20A of node 102-2. Exemplary methods for achieving such entanglement include several main steps involving interactions 84-1 to 84-5. FIG. 8B is a diagram symbolically showing these interactions.

[0187] In FIG. 8B, the quantum states are represented by symbols Ψ with subscripts that identify specific elements of the individual quantum systems 20. In the beta quantum system 20B, the subscript includes "20B". In the alpha quantum system 20A, the subscript includes "20A". In the broker element, the subscript includes "e". In the client element, the subscript includes "n". In the quantum circuit diagrams of FIGS. 8B, 9, and 9A, the symbol E represents the entanglement process, the symbol M represents a measurement, the symbol H represents a Hadamard gate, the symbol X represents an X measurement, the symbol Z represents a Z measurement, and the symbol + represents a CNOT gate.

[0188] For the purposes of this example, the quantum systems 20A, 20B have energy levels in the ground state as shown in FIG. 8A. FIG. 8 is annotated with a schematic showing the interactions 84 (interactions 84-1 to 84-5) that run in parallel with the blocks of method 250. Before interaction 84-1, the beta quantum system 20B is initialized. Initialization may include, for example, placing each of the quantum systems 20B in the same ground state.

[0189] FIG. 8A shows an example where the initialization involves placing the broker element 81B of the beta quantum system 20B

Number

Number

[0190] This initialization may include optically exciting each of the beta quantum systems 20B using light having a wavelength corresponding to the transition 85-1 from either of the states 86A and 86B to the excited state 75. The transition 85-1 may include, for example, an electronic orbital transition.

[0191] The light may be supplied, for example, from an appropriately adjusted laser. From the excited state 75, the quantum state of the blocker element 81B may transition, by the transition 85-2, to the state 86C (which may be the desired state for initialization) or the state 86D (an undesired state).

[0192] The RF drive may be applied to stimulate the transition 85-3 from the state 86D back to the state 86A or 86B. The RF drive may have a frequency corresponding to the energy difference between the state 86D and the state 86A or 86B. Once the quantum system 20B falls into the state 86C, it remains in the state 86C because transitions to other states are not possible.

[0193] The light and the RF drive may be applied, for example, for a period sufficient to initialize the beta quantum system 20B. The required period may be determined by simulation or experiment. Usually, it is sufficient to supply the light and the RF drive for a period of about 10 microseconds or less.

[0194] Then, each blocker element (electron spin) of the quantum system 20B, by applying the Sqrt(X) gate, is in a superposition state of electron spin-up and downward electron spin-down (e.g., the state:

Number

[0195] Interaction 84-1 entangles the quantum states of the blocker elements 81B (electron spins) of the beta quantum system 20B. In some embodiments, a plurality of quantum systems 20B in each of nodes 102-1 and 102-2 are initialized, and an attempt is made to concurrently entangle the quantum states of pairs of the blocker elements of these quantum systems as described above.

[0196] For example, quantum entanglement can be achieved by applying an optical pulse having a wavelength (e.g., 75) selected to correspond to a spin-selective optical transition to an excited state to each beta quantum system 20B. "Spin-selective" means that the transition occurs in only one electron spin state. When the transition occurs, a photon is emitted when the excited state decays. For example, the light can have a wavelength corresponding to transition 85-1. The length of the optical pulse can be selected such that only a single photon is emitted. For example, the optical pulse can have a duration of about 1 ns.

[0197] One of ordinary skill in the art will recognize that there is a possibility of relaxation from the excited state 75 to one of states 86A or 86B, and relaxation to one of states 86C or 86D. The likelihood of each of these outcomes is determined by the "branching ratio". Typically, the branching ratio is such that the probability of relaxation to one of states 86A or 86B is in the range of about 0% to about 10%, while the probability of relaxation to one of states 86C and 86D is in the range of about 90% to about 100%.

[0198] During the initialization of the quantum system 20 as described above, transition 85-1 can be triggered multiple times, and as a result, relaxation occurs multiple times. As a result, even if the probability of relaxation to state 86C or 86D is low, if a sufficient number of cycles are given, the probability that the state of the quantum system 20 will be initialized to state 86C is high (approaching 100%).

[0199] However, the entanglement protocol may involve calling transition 85-1 only once. Therefore, there is a finite probability, determined by the branching ratio (which may be small), that executing the entanglement protocol (e.g., by reversing the electron spin) can cause a random change in the quantum state of the quantum system 20.

[0200] Since each of the beta quantum systems 20B is initialized to a quantum state involving a superposition of electron spin-up and electron spin-down, the desired combined state of the electron spin and any emitted photons is a superposition of the state where the electron is spin-up and one photon is emitted and the state where the electron is spin-down and no photon is emitted.

[0201] Any emitted photon state is routed by the network 110 to an optical mixer (e.g., 152) that enables interference of the photon states emitted from the paired beta quantum systems 20B. The optical mixer may include, for example, free-space optics and / or integrated optics. The supply of optical pulses to the quantum system 20B is timed so that the emitted photon states have an opportunity to interact with each other within the optical mixer. A single-photon detector at the output port of the optical mixer is monitored to detect the case where exactly one photon is detected.

[0202] Next, πRF pulses are supplied to each of the beta quantum systems 20B. The π pulse rotates the quantum state of the electrons in the quantum systems 71A and 71B by 180 degrees about the X-axis in the Bloch sphere representation. Then, the step of applying an optical pulse having a wavelength selected to correspond to a spin-selective optical transition and detecting the emitted photons is repeated.

[0203] The single photon detected after each optical pulse heralds that the quantum states of the paired electrons of the beta quantum system 20B are in an entangled state. If photons are detected in any other combination (e.g., zero or two photons are detected at any stage), the entanglement process is restarted.

[0204] In interaction 84-2, quantum entanglement is transferred to the client element 82B (nuclear spin) of the beta quantum system 20B. Interaction 84-2 can transfer the entanglement of the electron spins in the paired beta quantum system 20B to the nuclear spins of the quantum system 20B, for example, by applying a SWAP gate between the electron spin and the nuclear spin. Applying the SWAP gate can include applying, for a time sufficient to promote the transition from state

Number

Number

[0205] The advantage of transferring entanglement to the nuclear spins of the quantum system 71 is that the decoherence time of the nuclear spins can be significantly longer than that of the electron spins because the nuclear spins are usually more isolated from the environment than the electron spins. Also, transferring entanglement to the nuclear spins of the beta quantum system 20B frees up the electron spins of the quantum system 20B for the next step.

[0206] In interactions 84-3 and 84-4, the entanglement is transferred to the blocker elements (e.g., electron spins) 81A of the alpha quantum system 20A at each of nodes 102-1 and 102-2. In interaction 84-3, the electron spin quantum state of the beta quantum system 20B is entangled with the selected electron spin quantum state of the alpha quantum system 20A. These entanglements can be brought about by the same procedure as described above for entangling the quantum state of the electron spins of the beta quantum system 20B, except that photon collection and detection are performed on the in-node optical network 112 in each case and the above-described initialization procedure is modified so that only the blocker elements (electron spins) of the beta quantum system 20B and the corresponding selected alpha quantum system 20A are initialized. In this modified initialization procedure, the quantum system 20B can be excited with light having a wavelength equal to that of the transition 85-1 from either of states 86A and 86B to the excited state 75. The non-zero probability of relaxation to states 86C and 86D via transition 85-2 holds the blocker spin in the state |↑> as transition 85-2 is cycled. Thus, this procedure initializes the blocker element 82B to a known state while minimally disturbing the quantum state of the corresponding client element (e.g., nuclear spin) 82B. Usually, it is sufficient to supply light for a period of about 1 microsecond or less.

[0207] 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 broker element 81A (e.g., electron spin) of the corresponding selected alpha quantum system 20A at each of nodes 102-1 and 102-2. This can be done independently at nodes 102-1 and 102-2. Teleportation consumes the entanglement of the broker elements 81A, 81B of the alpha and beta quantum systems 20A, 20B.

[0208] Teleportation at each node may include, for example, performing local Bell state measurements on the electron spin and nuclear spin of the beta quantum system 20B.

[0209] The Bell state measurement can be performed, for example, by the following sequence of operations, namely, 1. Apply a CNOT gate to the electron spin of the beta quantum system 20B, using the nuclear spin of the beta quantum system 20B as the control, 2. Perform a Z measurement on the electron spin of the beta quantum system 20B, 3. If the result of the Z measurement is in an even parity state, apply a π rotation to the electron spin of the corresponding alpha quantum system 20A, 4. Perform an X measurement (i.e., a projective measurement onto the X basis) on the nuclear spin of the beta quantum system 20B, 5. Apply feedforward to the electron spin of the beta quantum system 20B.

[0210] When the nuclear spin is upward, the CNOT gate flips the electron spin. Otherwise, the CNOT gate does not operate. From FIG. 8A, it can be seen that the CNOT gate represents the transition from state 86C to state 86A. For example, the CNOT gate can be implemented 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 swap states 86A and 86C. The duration can be determined through simulation and / or experimental calibration. The duration can be, for example, on the order of 10 μs (e.g., in the period of 100 ns to 100 μs).

[0211] Performing a Z measurement on the electron spin of the beta quantum system 20B can include resonant spin-selective photon cycling and photon detection. If a photon is detected, the result of the measurement is that the electron spin has a state corresponding to the spin-selective transition. This measurement can include applying light having a wavelength resonant with the spin-selective transition for a time sufficient to generate and detect photons. Preferably, in the measurement, multiple photons are generated and detected to perform a more faithful measurement. For example, the measurement can involve applying light for a time sufficient to generate and detect a sufficient number of photons to verify the spin with at least a threshold fidelity (e.g., a fidelity of 90% or more). In some exemplary embodiments, the light is applied for a period of about 10 ns (e.g., in the range of 1 ns to 50 ns). The pulse duration can be determined based on simulation and / or experiment.

[0212] Performing an X measurement (e.g., nuclear spin) of the client element 81B may include, for example, applying a π / 2 pulse to a nuclear transition to rotate the projection of the X Bloch sphere on the Z axis, and then measuring the spin-up ensemble of the nuclear spins of the beta quantum system 20B while applying an RF drive at a frequency equal to the separation between states 86C and 86A. The π / 2 pulse may have a duration of, for example, about 10 μs (e.g., in the range of 1 to 100 μs). The resonant spin-selective optical cycling may have a duration of, for example, about 10 μs (e.g., in the range of 5 to 50 μs).

[0213] For feedforward, for example, if it is determined that the X measurement (nuclear spin) of the client element 82B of the beta quantum system 20B has even parity (e.g., the |-> state, i.e., the state [Number] ), it may include applying a [z] gate to the electron spin of the beta quantum system to rotate it by π about the Z axis of the Bloch sphere. Otherwise, if it is determined that the X measurement has odd parity (e.g., the |+> state, i.e., the state [Number] ), do nothing. Applying the [z] gate may include, for example, varying the energy of the broker element 81B (e.g., electron spin) of the beta quantum system 20B by applying an electric field or changing a magnetic field for a period sufficient to accumulate a π radian phase shift, or advancing the phase of the state in the phase tracking software.

[0214] In interaction 84-5, quantum entanglement is transferred to the client element (nuclear spin) 82A of the alpha quantum system 20A. After the quantum state of the nuclear spin of the beta quantum system 20B is transferred to the electron spin of the alpha quantum system 20A (as described above, for example), entanglement can be transferred to the nuclear spin of the alpha quantum system 84-5 as shown. This can be performed in the same manner as described above for interaction 84-2.

[0215] 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 cases where the nodes 102A and 102B have available alpha and beta quantum systems that can function to transfer quantum information as described above. Also, those skilled in the art will recognize that the described methods can be modified by using other combinations of quantum gates and operations that produce equivalent results.

[0216] Generation of multi-particle entangled states FIG. 9 shows a method for generating a multi-particle entangled state involving three or more qubits that can be located at different nodes. The horizontal lines in FIG. 9 represent individual qubits, and initially, the quantum state is |Ψ i >(where i ε {1,..., 6}). In FIG. 9, H represents a Hadamard gate. The CNOT gates 90 are applied sequentially to add additional qubits to the entangled state. Each CNOT gate 90 is controlled by the topmost qubit to which the gate is connected.

[0217] Since the individual qubits can be in different nodes, the CNOT gates can be implemented as teleportated non-local CNOT gates as described, for example, in J. Eisen, Phys. Rev. A 62, 052317 2000. By teleporting a gate between two nodes, a pair of entangled qubits that can be entangled as a resource using, for example, the techniques described above can be applied.

[0218] Figure 9A schematically shows an implementation form of a CNOT gate teleported between quantum states |Ψ A > and |Ψ B > using entangled states |Ψ 1 > and |Ψ 2 >.

[0219] Segmented Architecture - Exemplary Features and Variations It can be understood that segmenting a distributed quantum network (e.g., a quantum computer) into a nested network having multiple layers (e.g., an alpha layer and a beta layer, or an alpha layer, a beta layer, and a gamma layer, etc.) can advantageously increase the rate of achieving entanglement between high-level (e.g., "beta" and / or "gamma") quantum states by performing an attempt to simultaneously entangle multiple pairs of entangled high-level quantum states.

[0220] Figure 10 shows an exemplary quantum network 200 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 between gamma quantum systems 20C and an optical network 110B that can be applied to establish entanglement between quantum systems 20B.

[0221] The network 110 also includes a node 202 that includes both a gamma quantum system 20C and a beta quantum system 20B, and an optical network 212 that can be applied to an entanglement extension from the quantum system 20C to the quantum system 20B (e.g., in a similar manner to the in-node network 112 of the node 102). The optical network 212 can be, for example, a low-loss optical network similar to the network 112.

[0222] In some embodiments, the optical network 110C has significantly greater losses than the optical network 110B or 112. In some embodiments, the time required to establish entanglement of pairs of the gamma quantum system 20C is reduced by simultaneously attempting entanglement of a relatively larger number of pairs of the quantum system 20C compared to the number of pairs of the beta quantum system 20B for which entanglement attempts are made simultaneously using the optical network 110B.

[0223] In a network having three or more layers (e.g., alpha, beta, gamma layers), each layer may have a different function. The quantum system of the lowest layer (e.g., alpha layer) can be used for storage and manipulation of quantum information (e.g., performing quantum computing). The quantum system of one or more top layers (e.g., gamma quantum system) can be used to establish entanglement between different cells. The quantum system of the intermediate (e.g., beta) layer can serve to separate the quantum system of the lowest layer from the quantum system of the top layer and can serve to distill and / or purify the quantum entanglement generated between the quantum systems of the top layer.

[0224] For example, in an "entanglement layer" (e.g., gamma layer), entanglement can be established between multiple pairs of quantum systems. The entanglement is transferred to a "distillation / purification layer" (e.g., beta layer), where multiple pairs of entangled quantum systems are transformed to obtain a smaller number of maximally entangled pairs. This purification or distillation can be performed using any suitable purification / distillation procedure. Subsequently, the maximally entangled pairs of the beta quantum system can be consumed to perform processing in the "computation" layer of the lowest layer (e.g., by teleporting quantum states and / or quantum gates between cells).

[0225] Figures 10A - 10C are additional non - limiting examples of possible topologies of the systems described herein. Figure 10A schematically shows a system 200 - 1 in which nodes or cells 102 each include an alpha quantum system 20A and a plurality of beta quantum systems 20B. The inter - node network 110 is configurable to provide an optical link associating one beta quantum system of one of the nodes 102 with one of a plurality of corresponding beta quantum systems within two or more other nodes 102. This architecture facilitates establishing entanglement between any pair of beta quantum systems 20B of the nodes 102 of system 200 - 1.

[0226] Figure 10B schematically shows an exemplary node 102 of system 200 - 2. System 200 - 2 can have any number of nodes 102. The nodes 102 include a quantum system 20A and corresponding beta quantum systems 20B interconnected by an optical network 112. In this example, the beta quantum systems 20B function as intermediaries between the alpha quantum system 20A and a plurality of gamma quantum systems 20C. This configuration may improve the isolation of the quantum state of the alpha quantum system 20A from noise resulting from the operation of the gamma quantum systems 20C (e.g., for executing an entanglement protocol involving the gamma quantum systems 20C).

[0227] Figure 10C schematically shows an exemplary node 102 of system 200 - 3. The nodes of Figure 10C are similar to the nodes of Figure 10B except that the nodes include a plurality of beta quantum systems 20B, each associated with a corresponding alpha quantum system 20A, and the optical network of the nodes enables each of the beta quantum systems 20B to be selectively connected to any one of a plurality of gamma quantum systems 20C. The nodes of Figure 10C can be scaled to include any number of corresponding alpha / beta quantum system pairs, and each of the beta quantum systems can be selectively connected by the optical network 110B to any two, three, or more gamma quantum systems 20C.

[0228] In a system where network 112 connects each alpha quantum system 20A to a corresponding beta quantum system 20B, as illustrated in FIGS. 10B and 10C, the connectivity of network 112 is low, and the probability of photon loss can be relatively very low.

[0229] The rate of entanglement between two beta-beta quantum bit banks or two gamma-gamma quantum bit banks increases as (1-(1-p)^N), where p is the probability of a single channel succeeding in any given trial and N is the number of beta-beta channels attempting entanglement in parallel. FIG. 11 is an example of a plot of this function when the probability of achieving entanglement in any given trial is 10%. This rate of increase in entanglement can lead to a faster operating speed for distributed quantum information processing.

[0230] In some embodiments, entanglement of the beta quantum systems can be generated continuously, or periodically, or otherwise stochastically. This can be particularly useful when the entangled beta quantum systems have a long coherence time (e.g., a coherence time of 100 microseconds or more). In such cases, pairs of entangled beta quantum systems can be instantaneously available as resources that can be used, for example, to teleport quantum states between nodes, teleport gates between nodes, and extend entanglement to existing nodes.

[0231] Also, an nested structure network can be designed and provided as a protection layer against noise and interference between a beta quantum system and an alpha quantum system. Computational qubits (e.g., represented by the quantum state of the alpha quantum system) can be separated from noise with probabilistic entanglement gates (such as can be used to generate entanglement of remote quantum systems), especially when probabilistic gates are applied across a highly connected map. This problem still exists when a quantum system incorporating a broker qubit and a client qubit is used and the broker qubits of different quantum systems are entangled using probabilistic entanglement gates. Even in such a configuration, due to the coupling between the broker qubit and the client qubit, the client qubit will inevitably be disturbed by attempts at probabilistic entanglement involving the corresponding broker qubit. Since these disturbances are constructively added with each attempt at a probabilistic entanglement protocol, as the lossiness of the links used in attempts to entangle the broker qubit increases, the overall magnitude of the disturbances increases.

[0232] Links tend to increase in lossiness as connectivity increases. The quantum state of the client qubit, which is constantly exposed to these disturbances, will deteriorate rapidly. Thus, such client qubits are not ideal for use as computational qubits. In an architecture with a nested structure as described herein, when the alpha quantum system can host computational qubits, these computational qubits are separated from the disturbances associated with multiple attempts at entanglement across a relatively lossy inter-node network (e.g., network 110).

[0233] The alpha quantum system may instead be exposed to a relatively lossless optical link of an in-node network (e.g., network 112). This reduces the number of cycles of entanglement attempts experienced by the alpha quantum system. The beta quantum system is not necessarily used for computing. Thus, the quantum states of the beta quantum system (broker and client) can be freely reset at any time when damaged. Further, since the client of the beta quantum system need not contain computing information and can exist in an eigenstate, it is less susceptible to the effects of noise associated with entanglement attempts.

[0234] Figure 12 is a plot showing the effect of this separation. The curve in Figure 11 is based on a simulation of the remaining fidelity of the states of two entangled client qubits as a function of photon loss after the network has gone through the probabilistically entangled quantum state stage required for addition to the entangled state of an additional quantum system. Since high connectivity usually means high photon loss, by operating with low loss in the alpha network (e.g., 112) and allowing high photon loss in the beta network (e.g., 110), a highly connected, substantially low-loss quantum entanglement network is generated.

[0235] Exemplary Applications The foregoing description has illustrated the principles and building blocks that enable the construction of a wide range of systems. Some such systems may have a fixed configuration. Some such systems may have a dynamically variable configuration.

[0236] The systems described herein may be made operable in a range of alternative operating modes (which may be determined, for example, by the configuration of controller 118). For example, · Attempts at beta-beta entanglement between multiple beta quantum systems of one node and multiple beta quantum systems of another node may be executed in parallel. Attempts at beta-beta entanglement between a beta quantum system of one node and two or more other nodes can be performed in parallel (it is not essential that the parallel entanglement attempts occur between the same two nodes). · Multiple quantum systems configured for use as beta quantum systems at one or more specific nodes can be varied. For example, individual quantum systems within a node can be used as alpha quantum systems and then reconfigured for use as beta quantum systems, and vice versa. · The system can be operated to maintain an entanglement resource such that a supply of a desired number of entangled quantum systems is generated and maintained available. For example, the system can be configured to generate entanglement groups of two or more quantum systems, each group including quantum systems belonging to two or more nodes. The number and configuration of quantum systems provided to different nodes can be varied to meet demand. This entanglement can be utilized, for example, for gates between nodes or teleportation of quantum states, generation of entangled states of alpha quantum states at different nodes, etc. The system can be configured to keep the entanglement resource available (e.g., by automatically generating alternative groups of entangled quantum systems before the entangled states of existing groups of entangled quantum systems are expected to be lost due to decoherence or other effects). · The system can be extended or connected to other systems as described herein by establishing entanglement between high-level quantum systems (e.g., gamma optical systems) interconnected by additional optical links. · The system can change its operation based on the performance of the optical link. For example, the performance (e.g., lossiness) of the network 110 between nodes can change over time. The system can monitor the performance of one or more optical links and configure to change its operation according to the performance, for example, by attempting to entangle more pairs of a beta quantum system in parallel, and / or holding an entangled beta quantum system with more resources, and / or using a different quantum entanglement protocol when the performance of the optical link is poor.

[0237] As described herein, the difference between an "alpha" quantum system and a "beta" quantum system is their connectivity. The alpha quantum system is connected to the network 112 between nodes with relatively less loss, while the beta quantum system can be selectively connected to either the network 110 between nodes (which may have greater loss compared to the network 112 between nodes) or the network 112 within the node.

[0238] In some embodiments, all quantum systems that host qubits (or the number of quantum systems that host more qubits than the number of quantum systems typically used as beta quantum systems at one time) can be selectively connected to either the network 110 between nodes or the network 112 within the node (e.g., by the switch 128). In such embodiments, any of the selectively connectable quantum systems can be used as a beta quantum system (e.g., by controlling to selectively connect the quantum system to the network 110 between nodes at some times and to the network 112 within the node at other times), or as an alpha quantum system (e.g., by always, or at selected times, connecting the quantum system only to the network 112 within the node). In such embodiments, a particular quantum system can be used as an alpha quantum system at some times and as a beta quantum system at other times.

[0239] In some embodiments, one or more qubits of one or more beta quantum systems are configured as an alpha quantum system temporarily (e.g., by disconnecting from the inter-node network 110). For example, such qubits can be applied as auxiliary qubits for quantum computing executed using the qubits of the alpha quantum system.

[0240] 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 pairs of beta quantum systems can be performed using a protocol that generates high-fidelity entanglement at the expense of entanglement bandwidth (e.g., a beta-beta connection can be executed 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 executed using a single-photon heralded protocol (such a protocol sacrifices fidelity for a very high entanglement bandwidth, thereby minimizing the number of attempts at entanglement to achieve entanglement). In some embodiments, other entanglement protocols are used to establish entanglement by particularly lossy connections (e.g., connections of the inter-node network that extend between cryostats or over long distances, or connections of a "gamma" network layer that connects multiple beta networks to form a larger system).

[0241] The technology can change. For example, it is not essential for the entanglement of the beta quantum system 21 to be generated on demand. In some embodiments, the controller 118 operates to continuously attempt to generate an entangled state between the beta quantum systems 21 of different nodes 102. In this mode of operation, entangled pairs of beta quantum systems can be available almost continuously as a resource.

[0242] The systems described in this specification have a wide range of applications, such as, for example, encryption key distribution, distributed quantum computing, quantum information transmission, quantum information storage, and retrieval.

[0243] Exemplary Implementations of the Controller A control system (e.g., controller 118) for implementing the techniques described herein can be implemented using a programmable data processor configured by the provision of specially designed hardware, configurable hardware, software (which may optionally include "firmware") executable on a data processor, a special purpose dedicated computer or data processor programmed, configured, or constructed to perform one or more steps in a method as detailed herein, and / or a combination of two or more of these. Examples of specially designed hardware include logic circuits, application specific integrated circuits ("ASICs"), large scale integrated circuits ("LSIs"), very large scale integrated circuits ("VLSIs"), etc. Examples of configurable hardware include one or more programmable logic devices such as programmable array logic ("PAL"), programmable logic array ("PLA"), field programmable gate array ("FPGA"), etc. Examples of programmable data processors include microprocessors, digital signal processors (DSPs), embedded processors, graphics processors, math coprocessors, general purpose computers, server computers, cloud computers, mainframe computers, computer workstations, etc. For example, one or more data processors within the control circuit of a device can implement the methods described herein (e.g., methods for establishing entanglement of qubits at different nodes) by executing software instructions in a program memory accessible to the processor.

[0244] In addition, the present technology can be implemented in the form of a program product that, when executed, causes a data processor to execute software instructions for performing the methods described herein. The program product can include any non-transitory storage medium that, when executed by a data processor, bears a set of computer-readable instructions that cause the data processor to execute the methods described herein. The program product according to the present invention can take any of a wide variety of forms. The program product can include, for example, magnetic data storage media such as floppy disks, hard disk drives, optical data storage media such as CD-ROMs, DVDs, etc., electronic data storage media including ROMs, flash RAMs, EPROMs, magnetic data storage media including hard-wired or pre-programmed chips (e.g., EEPROM semiconductor chips), nanotechnology memories, etc. The computer-readable signals on the program product can optionally be compressed or encrypted.

[0245] Interpretation As used herein, when a component (e.g., a software module, a processor, an assembly, a device, a circuit, etc.) is referred to, unless otherwise specified, the reference to that component (including the reference to "means") shall be construed to include any equivalent component that performs the function of the recited component (i.e., that is functionally equivalent), including components that are not structurally equivalent to the disclosed structure that performs the function in the illustrated exemplary embodiments of the present invention.

[0246] Unless the context clearly requires otherwise, throughout the specification and the claims · "comprise", "comprising", and like expressions are to be construed in an inclusive sense rather than an exclusive or exhaustive sense; that is, in the sense of "including, but not limited to", · "Connected", "coupled", or variations thereof, mean any connection or coupling, either direct or indirect, between two or more elements, and the coupling or connection between elements can be physical, logical, or a combination thereof. · Terms such as "this specification", "above", "below", and similar terms, when used to describe this specification, refer to this specification as a whole and not to a particular part of this specification. · "Or", with respect to a list of two or more items, has the following interpretation of the term, namely, Covering any one of the items in the list, all of the items in the list, and all combinations of any of the items in the list. · The singular forms "a", "an", and "the" also include the appropriate plural meanings. These terms ("a", "an", and "the") mean one or more unless otherwise stated. · "And / or" is used to indicate that one or both of the stated cases may occur. For example, "A and / or B" includes both (A and B) and (A or B). · When "about" is applied to a numerical value, it means the numerical value ±10%. · When a feature is described as being "optional" or "optionally" present, or as being present "in some embodiments", the present disclosure is intended to encompass embodiments in which the function is present, other embodiments in which the function does not necessarily exist, and still other embodiments in which the function is excluded. Further, when a combination of functions is described in this application, this description is intended to serve as a precursor to the use of exclusive terms such as "only", "solely", etc. in relation to the combination of functions, and the use of "negative limitations" to exclude the existence of other functions. · "First" and "second" are used for illustrative purposes and should not be understood as indicating or implying relative importance or indicating the number of the technical features shown.

[0247] Terms indicating directions such as "vertical", "transverse", "horizontal", "upward", "downward", "front", "rear", "inner", "outer", "left", "right", "before", "after", "upper", "bottom", "lower", "upper", "down", etc. are used in this specification and the appended claims (if any), but these depend on the specific direction of the device being described and illustrated. The subject matter described in this specification can envision various alternative directions. Therefore, these terms regarding directions are not strictly defined and should not be construed narrowly.

[0248] When a range of values is recited, that recited range includes all sub-ranges within that range. A range description is intended to support not only the values at the endpoints of the range, but also any intermediate value to ten decimal places below the lower limit of the range, or any value within any sub-range or set of sub-ranges of the range, unless the context clearly indicates otherwise or a part of the recited range is explicitly excluded. Ranges that exclude one or both of the included endpoints of a recited range that includes one or both of its endpoints are also included in the present invention.

[0249] Specific numerical values described in this specification are preceded by "about". In this context, the phrase "about" literally supports the exact numerical value that precedes it, as well as all other numerical values that are close to or approximately equal to that numerical value. A specific numerical value is within "about" of a specifically recited numerical value if it provides a substantial equivalent of the specifically recited numerical value in the context in which the specifically recited numerical value is presented.

[0250] In this specification, for purposes of illustration, specific examples of systems, methods, and apparatuses are described. These are merely examples. The techniques provided herein may also be applied to systems other than the above-described exemplary systems. Many changes, modifications, additions, omissions, and permutations are possible within the practice of this invention. The present invention includes variations of the described embodiments that will be apparent to those skilled in the art, including replacing features, elements, and / or acts with equivalent features, elements, and / or acts, mixing and combining features, elements, and / or acts from different embodiments, combining features, elements, and / or acts from the embodiments described herein with features, elements, and / or acts of other technologies, and / or omitting combinations of features, elements, and / or acts described in the embodiments.

[0251] As will be apparent to those skilled in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein has individual 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 present invention.

[0252] Any of the above-described aspects regarding an apparatus also apply to a method, and vice versa.

[0253] Any of the described methods may be performed in the order of the described events or in any other logically possible order. For example, if a process or block is presented in a given order, in alternative examples, a routine having steps in a different order may be executed or a system having blocks may be employed, and some processes or blocks may be deleted, moved, added, subdivided, combined, and / or modified to provide alternatives or subcombinations. Each of these processes or blocks may be implemented in a variety of different ways. Also, although a process or block may be shown as being executed in a time series, these processes or blocks may be executed in parallel, simultaneously, or at different times.

[0254] In this specification, various features are described as being present within "some embodiments". Such features are not essential 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 such features. All possible combinations of such features are contemplated by this disclosure, even if such features are shown in different drawings and / or described in different sections or paragraphs. This is limited to the extent that a particular one of such features is not compatible with another one of such features in the sense that a person skilled in the art would not be able to construct a practical embodiment combining such incompatible features. Thus, the description that "some embodiments" have feature A and "some embodiments" have feature B should be construed as explicitly indicating that the inventor also contemplates embodiments combining feature A and feature B (except where the description states otherwise or where feature A and feature B are inherently incompatible).

[0255] Accordingly, the claims appended below and the claims introduced hereinafter are intended to be construed to include all such modifications, rearrangements, additions, omissions, and subcombinations that can reasonably be inferred. The claims should not be limited by the preferred embodiments described 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 present invention provides first and second nodes, each including one or more alpha quantum systems and a plurality of high-level quantum systems, wherein the alpha quantum systems and high-level quantum systems of each node are interconnected by an intra-node optical network, and the high-level quantum systems of the first node are connectable to at least corresponding high-level quantum systems of the second node by an inter-node optical network. An attempt to establish quantum entanglement of each quantum state of a first plurality of pairs of the high-level quantum systems by the internode optical network, wherein each of the pairs includes one of the plurality of high-level quantum systems of the first node and each corresponding one of the plurality of high-level quantum systems of the second node. To detect success in entanglement of the quantum states of the entangled pair among the pair of high-level quantum systems, In each of the first and second nodes, the entanglement of each high-level quantum system of the entangled pair of high-level quantum systems is transferred to a selected quantum state of the alpha quantum system in each node using the respective intra-node optical network. Methods that include...

2. The method according to claim 1, wherein the internode optical network has greater loss than the intranode optical networks of the first and second nodes.

3. The method according to claim 1, wherein attempts to establish quantum entanglement of one different quantum state among the plurality of pairs of the high-level quantum system are performed simultaneously.

4. The alpha quantum system and the high-level quantum system each include a broker element having a broker state and a client element having a client state, and the method is Entangle one of the Broker states of the pair of high-level quantum systems, Transferring the entanglement to the client state of one of the high-level quantum systems in the pair of high-level quantum systems, Transferring the entanglement to the selected client state of the alpha quantum system of the first node The method according to claim 1, including the method described in claim 1.

5. In the second node, one of the pair of high-level quantum systems of the second node is entangled with the selected one of the Broker states of the alpha quantum system of the second node, In the second node, the entanglement of the client state of one of the pair of high-level quantum systems in the second node is transferred to the selected client state of the alpha quantum system in the second node. The method according to claim 4, further comprising:

6. The method according to claim 1, wherein, for at least one of the first and second nodes, transferring the entanglement of each high-level quantum system of an entangled pair of high-level quantum systems to a selected quantum state of the alpha quantum system of each node using the respective intra-node optical network, includes transferring the entanglement to the selected one of the alpha quantum systems, and sequentially transferring the entanglement from each of the high-level quantum systems to one or more intermediate-level quantum systems, and from one of the one or more intermediate-level quantum systems to the selected alpha quantum system.

7. The method according to claim 6, wherein the one or more intermediate-level quantum systems are used to purify the entanglement.

8. It is a quantum network, There are multiple nodes, and each node is A node optical network optically coupled to at least one alpha quantum system and the plurality of high-level quantum systems, An internode optical network configurable to provide multiple optical paths, each of which optically connects corresponding pairs of high-level quantum systems, each of which includes an internode optical network comprising a first high-level quantum system of a node and a second corresponding high-level quantum system of a node, comprising a plurality of nodes, It is a controller, An attempt is made to entangle each of the high-level quantum systems in the pair of high-level quantum systems via the aforementioned internode optical network. A controller is configured to, when one of the pair of high-level quantum systems detects entanglement, transfer the entangled state of the one of the pair of high-level quantum systems to a selected alpha quantum system of the first one or more alpha quantum systems of the node, and / or to a selected alpha quantum system of the second one or more alpha quantum systems of the node, via the intranode optical network. A quantum network equipped with these features.

9. The quantum network according to claim 8, wherein the controller is configured to simultaneously attempt to entangle each of the high-level quantum systems of the pair of high-level quantum systems.

10. The quantum network according to claim 8, wherein the alpha quantum system and the high-level quantum system each include a broker element having a broker state and at least one client element having a client state.

11. The aforementioned controller A protocol is executed to entangle the Broker state of the pair of high-level quantum systems. When the entangled broker state of the pair of high-level quantum systems is entangled, a protocol is executed to transfer the entanglement to the client state of the entangled broker state of the pair of high-level quantum systems. A protocol is executed to entangle the Broker state of one of the entangled high-level quantum systems of the pair of high-level quantum systems of the first node with the selected Broker state of the alpha quantum system of the first node. Execute a protocol for transferring the entanglement of the client state of one of the pair of high-level quantum systems of the first node to the selected client state of the alpha quantum system of the first node. The quantum network according to claim 10, further configured as follows.

12. The quantum network according to claim 10, wherein the broker state and the client state each include a first spin state and a second spin state, the first spin state includes an electron spin state and the second spin state includes a nuclear spin state.

13. The quantum network according to claim 8, wherein each of the alpha quantum system and / or the high-level quantum system is embedded in a crystalline substrate, and the quantum system includes a light-emitting center.

14. The quantum network according to claim 13, wherein the high-level quantum system each includes a T-center.

15. The quantum network according to claim 8, wherein the internode optical network has greater losses than the intranode optical networks of the first and second nodes.

Images