We have shown that the Born rule $(ρ=|ψ|^{2})$ is inconsistent with Lorentz symmetry of the Salpeter equation (square root Klein-Gordon equation). So we find relativistic modification of the Born rule as $ρ=\frac{1}{2mc^{2}}(|\sqrt{\widehat{H}-mc^{2}}ψ|^{2}+|\sqrt{\widehat{H}+mc^{2}}ψ|^{2})$ , which is consistent with Lorentz symmetry of this equationWe have shown that the Born rule $(ρ=|ψ|^{2})$ is inconsistent with Lorentz symmetry of the Salpeter equation (square root Klein-Gordon equation). So we find relativistic modification of the Born rule as $ρ=\frac{1}{2mc^{2}}(|\sqrt{\widehat{H}-mc^{2}}ψ|^{2}+|\sqrt{\widehat{H}+mc^{2}}ψ|^{2})$ , which is consistent with Lorentz symmetry of this equation

arXiv:1504.07582Apr 28, 20150 citations

Simulation of the Burgers equation by NMR quantum-information processing

Zhiying Chen, Jeffrey Yepez, David G. Cory

We report on the implementation of Burgers equation as a type-II quantum computation on a NMR quantum-information processor. Since the flow field evolving under the Burgers equation develops sharp features over time, this is a better test of liquid-state NMR implementations of type-II quantum computers than the previous examples using the diffusion equation. In particular, we show that Fourier approximations used in the encoding step are not the dominant error. Small systematic errors in the collision operator accumulate and swamp all other errors. We propose, and demonstrate, that the accumulation of this error can be avoided to a large extent by replacing the single collision operator with a set of operators with random errors and similar fidelities. Experiments have been implemented on 16 two-qubit sites for eight successive time steps for the Burgers equation.We report on the implementation of Burgers equation as a type-II quantum computation on a NMR quantum-information processor. Since the flow field evolving under the Burgers equation develops sharp features over time, this is a better test of liquid-state NMR implementations of type-II quantum computers than the previous examples using the diffusion equation. In particular, we show that Fourier approximations used in the encoding step are not the dominant error. Small systematic errors in the collision operator accumulate and swamp all other errors. We propose, and demonstrate, that the accumulation of this error can be avoided to a large extent by replacing the single collision operator with a set of operators with random errors and similar fidelities. Experiments have been implemented on 16 two-qubit sites for eight successive time steps for the Burgers equation.

arXiv:quant-ph/0410198Physical Review AOct 23, 200622 citations

The Born Approximation

K. T. Hecht

Graduate texts in contemporary physicsJan 1, 20002 citations

On solving for shocks and travelling waves using a quantum algorithm

Biswajit Basu, Andrea Staino, Frank Gaitan

In this paper, we solve for shocks and travelling waves in advection , inviscid Burgers’ and Burgers’ equations by implementing a recently established quantum algorithm in the literature. The quantum algorithm has been successful in solving Navier–Stokes, flow generated by Burgers’ and submarine tephra flow equations under certain initial and boundary conditions . Here, we further study the efficacy of the quantum algorithm by extending the application to advection , inviscid Burgers’ and Burgers’ equations under different kinds of initial and boundary conditions. In addition to central differencing and upwinding, Lax–Wendroff discretization scheme has also been introduced in the quantum algorithm to observe how numerical dissipation and dispersion are affected. We recover known travelling waves, and shocks with rarefaction and expansion.In this paper, we solve for shocks and travelling waves in advection , inviscid Burgers’ and Burgers’ equations by implementing a recently established quantum algorithm in the literature. The quantum algorithm has been successful in solving Navier–Stokes, flow generated by Burgers’ and submarine tephra flow equations under certain initial and boundary conditions . Here, we further study the efficacy of the quantum algorithm by extending the application to advection , inviscid Burgers’ and Burgers’ equations under different kinds of initial and boundary conditions. In addition to central differencing and upwinding, Lax–Wendroff discretization scheme has also been introduced in the quantum algorithm to observe how numerical dissipation and dispersion are affected. We recover known travelling waves, and shocks with rarefaction and expansion.

Computers & FluidsJan 30, 20254 citations

The Two Postulates

WORLD SCIENTIFIC eBooksJan 12, 20140 citations

We have shown that the Born rule

(ρ=|ψ|^{2})

is inconsistent with Lorentz symmetry of the Salpeter equation (square root Klein-Gordon equation). So we find relativistic modification of the Born rule as

ρ=\frac{1}{2mc^{2}}(|\sqrt{\widehat{H}-mc^{2}}ψ|^{2}+|\sqrt{\widehat{H}+mc^{2}}ψ|^{2})

, which is consistent with Lorentz symmetry of this equation