As Accurate as Needed, as Efficient as Possible: Approximations in DD-based Quantum Circuit Simulation

TL;DR

This paper introduces two new approximation strategies for decision diagram-based quantum circuit simulation that significantly reduce memory usage and computational time while allowing user-controlled accuracy trade-offs.

Contribution

It presents novel DD-based approximation methods that exploit quantum probabilistic nature to achieve more compact representations and faster simulations.

Findings

Speed-ups up to several orders of magnitude

Controlled accuracy degradation

Enhanced memory reduction in quantum simulations

Abstract

Quantum computers promise to solve important problems faster than conventional computers. However, unleashing this power has been challenging. In particular, design automation runs into (1) the probabilistic nature of quantum computation and (2) exponential requirements for computational resources on non-quantum hardware. In quantum circuit simulation, Decision Diagrams (DDs) have previously shown to reduce the required memory in many important cases by exploiting redundancies in the quantum state. In this paper, we show that this reduction can be amplified by exploiting the probabilistic nature of quantum computers to achieve even more compact representations. Specifically, we propose two new DD-based simulation strategies that approximate the quantum states to attain more compact representations, while, at the same time, allowing the user to control the resulting degradation in accuracy. We also analytically prove the effect of multiple approximations on the attained accuracy and empirically show that the resulting simulation scheme enables speed-ups up to several orders of magnitudes.