Quantum Simulation of the Majorana Equation and Unphysical Operations

TL;DR

This paper presents a method to simulate the Majorana equation, a non-Hamiltonian relativistic wave equation, using trapped ions, including the implementation of unphysical operations like charge conjugation.

Contribution

It introduces a novel quantum simulation approach for the Majorana equation and unphysical operations, expanding the capabilities of quantum simulators beyond Hamiltonian systems.

Findings

Successfully designed a quantum simulator for the Majorana equation

Implemented charge conjugation and related unphysical operations

Demonstrated the method in trapped ion systems

Abstract

A quantum simulator is a device engineered to reproduce the properties of an ideal quantum model. It allows the study of quantum systems that cannot be efficiently simulated on classical computers. While a universal quantum computer is also a quantum simulator, only particular systems have been simulated up to now. Still, there is a wealth of successful cases, such as spin models, quantum chemistry, relativistic quantum physics and quantum phase transitions. Here, we show how to design a quantum simulator for the Majorana equation, a non-Hamiltonian relativistic wave equation that might describe neutrinos and other exotic particles beyond the standard model. The simulation demands the implementation of charge conjugation, an unphysical operation that opens a new front in quantum simulations, including the discrete symmetries associated with complex conjugation and time reversal. Finally, we show how to implement this general method in trapped ions.