Grover Energy Transfer at Relativistic Speeds

TL;DR

This paper explores how relativistic effects can enhance the efficiency of energy transfer algorithms inspired by Grover's quantum search, achieving near-perfect transfer with fewer steps at high velocities.

Contribution

It introduces a relativistic extension of Grover's energy transfer algorithm, demonstrating improved efficiency through non-linear effects at speeds close to light.

Findings

Efficiency approaches 100% as velocities near light speed

Number of steps reduces to approximately 1 at relativistic speeds

Maximum transfer efficiency depends on speed and number of objects

Abstract

Grover's algorithm for quantum search can also be applied to classical energy transfer. The procedure takes a system in which the total energy is equally distributed among $N$ subsystems and transfers most of the it to one marked subsystem. We show that in a relativistic setting the efficiency of this procedure can be improved. We will consider the transfer of relativistic kinetic energy in a series of elastic collisions. In this case, the number of steps of the energy transfer procedure approaches 1 as the initial velocities of the objects become closer to the speed of light. This is a consequence of introducing non-linearities in the procedure. However, the maximum attainable transfer will depend on the particular combination of speed and number of objects. In the procedure, we will use $N$ elements, like in the classical case, instead of the $log_2(N)$ states of the quantum algorithm.