Classical circuits can simulate quantum aspects

TL;DR

This paper presents a classical circuit-based method for simulating quantum systems by using a generalized similarity transformation to connect Hamiltonians, enabling accessible and accurate quantum simulations without quantum hardware.

Contribution

It introduces a novel classical circuit approach for quantum simulation using a generalized similarity transformation, broadening practical quantum modeling capabilities.

Findings

Successfully simulates quantum systems from 2-state to n-state.

Provides a classical alternative to quantum computers for simulation.

Offers a reinterpretation of Born's rule in electrical circuits.

Abstract

This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system simulation using classical circuits. By synthesizing interaction networks, we accurately simulate quantum systems of varying complexity, from $2-$state to $n-$state systems. Unlike quantum computers, classical approaches do not require stringent conditions, making them more accessible for practical implementation. Our reinterpretation of Born's rule in the context of electrical circuit simulations offers a perspective on quantum phenomena.