Operating a layered quantum networking environment with entanglement swap operations

One or more non-transitory computer readable media storing a program for managing entangled quantum states in a network of nodes, the program comprising instructions operable to cause one or more processors to perform steps comprising:

• for each of two or more pairs of nodes on a path over a set of N nodes in the network, establishing entanglement between pairs of quantum elements in the respective nodes of that pair of nodes based at least in part on one or more quantum signals transmitted over one or more quantum communication channels, where N>3;
• performing a plurality of entanglement swap operations among different respective subsets of nodes in the set of N nodes using the pairs of entangled quantum elements, where each entanglement swap operation comprises:
• performing a joint measurement on a non-entangled pair of quantum elements in a node that is a member of two different pairs of nodes of the two or more pairs of nodes, resulting in a measurement result;
• and
• managing the plurality of entanglement swap operations during establishment of end-to-end entanglement between respective quantum elements in the nodes at the respective ends of the path over the set of N nodes using a set of classical messages transmitted over one or more classical communication channels, where each of at least two classical messages in the set of classical messages comprises one or both of:
• information indicating success or failure of a particular entanglement swap operation, and
• information indicating the measurement result of the joint measurement performed for the particular entanglement swap operation;
• where one or more of the classical messages in the set of classical messages are sent in a first direction between nodes on the path, and one or more of the classical messages in the set of classical messages are sent a second direction opposite to the first direction between nodes on the path;
• and
• where none of the classical messages in the set of classical messages or messages acknowledging success or failure of one or more of the plurality of entanglement swap operations are transmitted from one of the nodes at the ends of the path with a destination of the other of the nodes at the ends of the path.

A system comprising:

• a network of nodes in which each of a plurality of nodes in the network of nodes includes at least one quantum element and is connected to at least one other node in the network of nodes by a quantum communication channel coupled to the quantum element;
• where network of nodes is configured to:
• for each of two or more pairs of nodes on a path over a set of N nodes in the network, establish entanglement between pairs of quantum elements in the respective nodes of that pair of nodes based at least in part on one or more quantum signals transmitted over one or more quantum communication channels, where N>3;
• perform a plurality of entanglement swap operations among different respective subsets of nodes in the set of N nodes using the pairs of entangled quantum elements, where each entanglement swap operation comprises:
• performing a joint measurement on a non-entangled pair of quantum elements in a node that is a member of two different pairs of nodes of the two or more pairs of nodes, resulting in a measurement result;
• and
• manage the plurality of entanglement swap operations during establishment of end-to-end entanglement between respective quantum elements in the nodes at respective ends of the path over the set of N nodes using a set of classical messages transmitted over one or more classical communication channels, where each of at least two classical messages in the set of classical messages comprises one or both of:
• information indicating success or failure of a particular entanglement swap operation, and
• information indicating the measurement result of the joint measurement performed for the particular entanglement swap operation;
• where one or more of the classical messages in the set of classical messages are sent in a first direction between nodes on the path, and one or more of the classical messages in the set of classical messages are sent a second direction opposite to the first direction between nodes on the path;
• and
• where none of the classical messages in the set of classical messages or messages acknowledging success or failure of one or more of the plurality of entanglement swap operations are transmitted from one of the nodes at the ends of the path with a destination of the other of the nodes at the ends of the path.