Optimizing Timing of High-Success-Probability Quantum Repeaters

TL;DR

This paper analyzes how to optimize timing in quantum repeater networks to maximize success probability and minimize qubit storage, especially for different quantum computing tasks and link configurations.

Contribution

It introduces a comprehensive analysis of timing patterns and buffering strategies for high-success-probability quantum repeaters, highlighting conditions for zero-path-buffering solutions.

Findings

Zero path buffering exists for certain configurations and Bell inequality experiments.

Full teleportation computations often require non-zero path buffering.

Counter-propagating photon states can reduce storage time by half.

Abstract

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 application's 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.