Quantum Algorithms of Solving the Backtracking of One-dimensional Cellular Automata

TL;DR

This paper introduces a quantum algorithm that efficiently finds the initial configuration of one-dimensional cellular automata leading to a specific state, leveraging polynomial quantum resources and achieving success probabilities comparable to Shor's algorithm.

Contribution

It presents a novel quantum algorithm for backtracking cellular automata, improving the efficiency of identifying initial states with polynomial quantum resources.

Findings

The quantum algorithm operates with polynomial quantum gates and qubits.

It achieves success probability similar to Shor's order-finding algorithm.

The method offers a potentially efficient solution for cellular automata backtracking.

Abstract

In [Wolfram 1982; Wolfram 1983; Wolfram 2002], the backtracking of one-dimensional cellular automata is to find out which of the 2n possible initial configurations of width n evolve to a specific configuration. In this paper, in one-dimensional cellular automata for a specific configuration of width n, its unique initial configuration can be found by mean of the proposed quantum algorithm with polynomial quantum gates, polynomial quantum bits and the successful probability that is the same as that of Shor's quantum order-finding algorithm in [Shor 1994].