Joint Cutting for Hybrid Schr\"odinger-Feynman Simulation of Quantum Circuits

TL;DR

This paper introduces a joint cutting technique for Hybrid Schr"odinger-Feynman quantum circuit simulation, significantly reducing simulation times and outperforming previous methods, thus advancing classical simulation capabilities for quantum algorithms.

Contribution

It proposes a novel joint cutting method that groups gates into blocks before cutting, reducing exponential overhead and improving simulation efficiency compared to existing approaches.

Findings

Joint cutting outperforms standard HSF by up to 4000x

Joint cutting outperforms Schr"odinger-style simulation by up to 200x

Experimental results demonstrate significant efficiency gains

Abstract

Despite the continuous advancements in size and robustness of real quantum devices, reliable large-scale quantum computers are not yet available. Hence, classical simulation of quantum algorithms remains crucial for testing new methods and estimating quantum advantage. Pushing classical simulation methods to their limit is essential, particularly due to their inherent exponential complexity. Besides the established Schr\"odinger-style full statevector simulation, so-called Hybrid Schr\"odinger-Feynman (HSF) approaches have shown promise to make simulations more efficient. HSF simulation employs the idea of "cutting" the circuit into smaller parts, reducing their execution times. This, however, comes at the cost of an exponential overhead in the number of cuts. Inspired by the domain of Quantum Circuit Cutting, we propose an HSF simulation method based on the idea of "joint cutting" to significantly reduce the aforementioned overhead. This means that, prior to the cutting procedure, gates are collected into "blocks" and all gates in a block are jointly cut instead of individually. We investigate how the proposed refinement can help decrease simulation times and highlight the remaining challenges. Experimental evaluations show that "joint cutting" can outperform the standard HSF simulation by up to a factor $\approx 4000\times$ and the Schr\"odinger-style simulation by a factor $\approx 200\times$ for suitable instances. The implementation is available at https://github.com/cda-tum/mqt-qsim-joint-cutting.