Quantum Simulation of the Majorana Equation and Unphysical Operations

Casanova, Jorge; Sabín, Carlos; León, Juan; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; García-Ripoll, Juan José; Solano, E.

doi:10.1103/physrevx.1.021018

Cited by 84 publications

(141 citation statements)

References 140 publications

(336 reference statements)

Supporting

Mentioning

140

Contrasting

Unclassified

Order By: Relevance

“…In Ref. [31], we gave a first example showing how to implement quantum simulations of phenomena beyond quantum physics. Consequently, a natural question arises: is it possible to simulate processes violating special relativity in a quantum device respecting it?…”

mentioning

confidence: 99%

Quantum Simulation of Noncausal Kinematic Transformations

Alvarez-Rodriguez

Casanova²,

Lamata³

et al. 2013

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

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. [27,28], the quantum Rabi model in superconducting qubits [29], and relativistic quantum mechanics in circuit QED [30]. It is known that the computational power of a quantum simulator may overcome that of classical computers. However, the set of operations that we can apply in the former is restricted compared with the versatility of the latter. For example, a wide set of unphysical but computable operations, while formally implementable with universal quantum computers, are not accessible to current quantum simulators.A quantum simulation can be seen as a process in which a quantum system is forced to behave according to a given mathematical model, closely reproducing its dynamics. At the same time, the simulator has a dynamics governed by the fundamental laws of nature. In this sense, we wonder whether quantum simulators may encode processes violating their internal operating rules. In Ref.[31], we gave a first example showing how to implement quantum simulations of phenomena beyond quantum physics. Consequently, a natural question arises: is it possible to simulate processes violating special relativity in a quantum device respecting it?In this Letter, we propose a formalism that allows the implementation of Galilean boosts and, in general, coordinate transformations, as spatial or time parity operations, at any evolution time of a quantum simulation. This is significant to increase the versatility of quantum simulators, enabling the change of reference frame in situ during an experiment. The ability of generating these computable operations allows us to obtain correlations between different reference frames. These correlations include, among others, relevant physical quantities as propagators and self-correlation functions, that would otherwise require full state tomography. Moreover, one could also test and analyze the ultimate limits of a quantum simulator, exploring the exciting possibility of implementing noncausal kinematics as, e.g., instantaneous translations or boosts in a controllable quantum platform. This kind of formalism may also give the capability to probe the boundary between physical and unphysical evolution. We will present the proposed method in the context of linear coordinate transformations, where the Galileo group is included. Moreover, this proposal also allows the implementation of nonlinear coordinate transformations, as is the case of...

show abstract

mentioning

confidence: 99%

Quantum Simulation of Noncausal Kinematic Transformations

Alvarez-Rodriguez

Casanova²,

Lamata³

et al. 2013

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Equation (20) is well suited to study the electromagnetic properties of neutrinos and Majorana particles [15,28,29] such as charge conjugation and time reversal, allowing for an experimental study of our Equations (16a) and (b).…”

Section: Chiral Electromagnetic Neutrinomentioning

confidence: 99%

Chiral Maxwell’s Equations as Two Spinor System: Dirac and Majorana Neutrino

Torres-Silva¹

2013

JEMAA

View full text Add to dashboard Cite

This work clarifies the relation between Maxwell, Dirac and Majorana neutrino equations presenting an original way to derive the Dirac and neutrino equation from the chiral electrodynamics leading, perhaps, to novel conception in the mass generation by electromagnetic fields. In the present article, it is shown that Maxwell equations can be written in the same form as the two components Dirac and neutrino equations, that is the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations. We propose a simple approach with the electric field E parallel to the magnetic field H . Our analysis is based on the chiral or Weyl form of the Maxwell equations in a chiral vacuum. This theory is a new quantum mechanics (QM) interpretation for Dirac and neutrino equation. The below research proves that the QM of particles represents the electrodynamics of the curvilinear closed chiral waves. Electromagnetic properties of neutrinos are discussed.

show abstract

“…Let us reiterate that though CTC's are problematic in Einstein's theory of relativity due to violation of principle of causality, the problem is circumvented in quantum framework. As demonstrated in [57][58][59][60] the affect of CTC's can be mimicked using classical and quantum simulation. For instance in Ref.…”

Section: Introductionmentioning

confidence: 99%