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.
Highlights
A quantum simulator is a device engineered to reproduce the properties of an ideal quantum model
Driven by the need of the simulation, we devise a general method for implementing a number of mathematical operations that are unphysical, including charge conjugation, complex conjugation, and time reversal
Examples include black holes in Bose-Einstein condensates [9], quantum field theories [10,11], and recent quantum simulations of relativistic quantum effects such as Zitterbewegung and the Klein paradox [12,13,14,15,16] in trapped ions
Summary
We 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. We show how the Majorana equation [17] can be simulated in an analog quantum simulator, having the implementation of complex conjugation of the wave function as a key requirement. In this manner, we are able to propose a general scheme for implementing this and other unphysical operations, such as charge conjugation and time reversal.
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