Hybrid Schr\"odinger-Feynman Simulation of Quantum Circuits With Decision Diagrams

TL;DR

This paper introduces a hybrid Schrödinger-Feynman approach using decision diagrams to improve classical quantum circuit simulation, enabling faster simulation of complex circuits by leveraging parallel processing.

Contribution

It demonstrates the feasibility of combining Schrödinger and Feynman methods with decision diagrams, addressing previous limitations in scalability and parallelization.

Findings

Simulates hard quantum circuits within minutes, previously taking hours.

Advances decision diagram-based simulation techniques.

Shows potential for handling larger quantum circuits efficiently.

Abstract

Classical simulations of quantum computations are vital for the future development of this emerging technology. To this end, decision diagrams have been proposed as a complementary technique which frequently allows to tackle the inherent exponential complexity of these simulations. In the worst case, however, they still cannot escape this complexity. Additionally, while other techniques make use of all the available processing power, decision diagram-based simulation to date cannot exploit the many processing units of today's systems. In this work, we show that both problems can be tackled together by employing a hybrid Schr\"odinger-Feynman scheme for the simulation. More precisely, we show that realizing such a scheme with decision diagrams is indeed possible, we discuss the resulting problems in its realization, and propose solutions how they can be handled. Experimental evaluations confirm that this significantly advances the state of the art in decision diagram-based simulation -- allowing to simulate certain hard circuits within minutes that could not be simulated in a whole day thus far.