Optimizing Timing of High-Success-Probability Quantum Repeaters

Optimizing a connection through a quantum repeater network requires careful attention to the photon propagation direction of the individual links, the arrangement of those links into a path, the error management mechanism chosen, and the applications pattern of consuming the Bell pairs generated. We analyze combinations of these parameters, concentrating on one-way error correction schemes (1-EPP) and high success probability links (those averaging enough entanglement successes per round trip time interval to satisfy the error correction system). We divide the buffering time (defined as minimizing the time during which qubits are stored without being usable) into the link-level and path-level waits. With three basic link timing patterns, a path timing pattern with zero unnecessary path buffering exists for all $3^h$ combinations of $h$ hops, for Bell inequality violation experiments (B class) and Clifford group (C class) computations, but not for full teleportation (T class) computations. On most paths, T class computations have a range of Pareto optimal timing patterns with a non-zero amount of path buffering. They can have optimal zero path buffering only on a chain of links where the photonic quantum states propagate counter to the direction of teleportation. Such a path reduces the time that a quantum state must be stored by a factor of two compared to Pareto optimal timing on some other possible paths.