Quantum Simulation of Noncausal Kinematic Transformations

TL;DR

This paper introduces a quantum simulation framework for implementing noncausal kinematic transformations, such as Galilean boosts and parity operations, enabling exploration of phenomena beyond special relativity.

Contribution

It presents a novel method to encode and realize linear coordinate transformations in quantum simulators, expanding the capabilities of quantum simulation for studying advanced kinematic effects.

Findings

Demonstrates implementation of Galilean boosts in quantum systems

Enables direct measurement of dynamical quantities without full tomography

Allows exploration of noncausal phenomena beyond special relativity

Abstract

We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations, in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system.