Faster-than-Clifford Simulations of Entanglement Purification Circuits and Their Full-stack Optimization

TL;DR

This paper introduces a novel, faster simulation algorithm for entanglement purification circuits that enables efficient optimization and design of high-performance quantum repeaters, significantly advancing practical quantum communication.

Contribution

The authors develop a simulation method with constant complexity for modeling purification circuits, allowing for practical optimization and improved quantum repeater design.

Findings

New simulation algorithm with $ ext{O}(1)$ complexity for purification circuits

Optimized purification circuits outperform existing designs on noisy hardware

Enhanced error correlation shaping improves quantum error correction performance

Abstract

Quantum Entanglement is a fundamentally important resource in Quantum Information Science; however, generating it in practice is plagued by noise and decoherence, limiting its utility. Entanglement distillation and forward error correction are the tools we employ to combat this noise, but designing the best distillation and error correction circuits that function well, especially on today's imperfect hardware, is still challenging. Here, we develop a simulation algorithm for distillation circuits with gate-simulation complexity of $\mathcal{O}(1)$ steps, providing for drastically faster modeling compared to $\mathcal{O}(n)$ Clifford simulators or $\mathcal{O}(2^n)$ wavefunction simulators over $n$ qubits. This new simulator made it possible to not only model but also optimize practically interesting purification circuits. It enabled us to use a simple discrete optimization algorithm to design purification circuits from $n$ raw Bell pairs to $k$ purified pairs and study the use of these circuits in the teleportation of logical qubits in second-generation quantum repeaters. The resulting purification circuits are the best-known purification circuits for finite-size noisy hardware and can be fine-tuned for specific hardware error models. Furthermore, we design purification circuits that shape the correlations of errors in the purified pairs such that the performance of the error-correcting code used in teleportation or other higher-level protocols is greatly improved. Our approach of optimizing multiple layers of the networking stack, both the low-level entanglement purification, and the forward error correction on top of it, are shown to be indispensable for the design of high-performance second-generation quantum repeaters.