Digital Quantum Simulation of Reaction-Diffusion Systems on Lattice

TL;DR

This paper demonstrates how digital quantum computers can simulate complex stochastic reaction-diffusion systems directly at the probability distribution level, leveraging Trotterization and PITE techniques across diverse examples.

Contribution

It introduces a novel quantum simulation approach for stochastic reaction-diffusion systems using a spin representation and probabilistic methods, directly addressing the exponential complexity.

Findings

Successful simulation of reaction-diffusion processes on quantum hardware

Application to systems with active-absorbing phase transitions

Demonstration of the method's versatility across different examples

Abstract

The quantum computer offers significant advantages in simulating physical systems, particularly those with exponentially large state spaces, such as quantum systems. Stochastic reaction-diffusion systems, characterized by their stochastic nature, also exhibit exponential growth in the dimension of the state space, posing challenges for simulation at a probability distribution level. We explore the quantum simulation of stochastic reaction-diffusion systems on a digital quantum computer, directly simulating the system at the master equation level. Leveraging a spin representation of the system, we employ Trotterization and probabilistic imaginary time evolution (PITE) to simulate the probability distribution directly. We illustrate this approach through four diverse examples, ranging from simple single-lattice site generation-annihilation processes to a system featuring active-absorbing phase transition.