A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics

TL;DR

This paper introduces a unified formalism for quantum dynamics that encompasses various quantum algorithms and reveals their connection to natural quantum phenomena, exemplified by proton behavior in water systems.

Contribution

It presents a general framework linking quantum algorithms with quantum chemical dynamics and natural phenomena, highlighting underlying structural similarities.

Findings

Unified formalism for quantum dynamics and algorithms

Connection between quantum algorithms and biological quantum phenomena

Illustration of Shor's algorithm structure in water proton behavior

Abstract

We describe a general formalism for quantum dynamics and show how this formalism subsumes several quantum algorithms including the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor algorithms as well as the conventional approach to quantum dynamics based on tensor networks. The common framework exposes similarities among quantum algorithms and natural quantum phenomena: we illustrate this connection by showing how the correlated behavior of protons in water wire systems that are common in many biological and materials systems parallels the structure of Shor's algorithm.