Hybrid Schrödinger-Feynman Simulation of Quantum Circuits With Decision Diagrams

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 Schrödinger-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 simulationallowing to simulate certain hard circuits within minutes that could not be simulated in a whole day thus far.

Tensor Networks or Decision Diagrams? Guidelines for Classical Quantum Circuit Simulation

“…The overall contraction then reduces to the sum of several independent contractions of simpler tensor networks. Promising initial investigations towards realizing such schemes for decision diagrams have been conducted in [27].…”

The basis of design tools for quantum computing

“…The MQT offers the classical quantum circuit simulator DDSIM that can be used to perform various quantum circuit simulation tasks based on using decision diagrams as a data structure. This includes strong and weak simulation [12,13,14], approximation techniques [15,16], noise-aware simulation [17,18,19], hybrid Schrödinger-Feynman techniques [20], support for dynamic circuits, the computation of expectation values [21], the simulation of mixeddimensional systems [22], and more [23,24,25,26]. Example 1.…”

“…Our overarching objective is to provide solutions for design tasks across the entire quantum software stack. This entails high-level support for end users in realizing their applications [6,7,8,9,10,11], efficient methods for the classical simulation [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], compilation [11,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46], and verification [47,48,49,50,51,52,53,54,…”