Complexity of Quantum Charged Particle in External Magnetic Field

TL;DR

This paper studies the circuit complexity of a quantum charged particle in a magnetic field, analyzing its time evolution, oscillations, and bounds, revealing novel behaviors not reducible to harmonic oscillator models.

Contribution

It introduces a detailed analysis of complexity for a charged particle in a magnetic field using Nielsen approach, highlighting unique features and bounds.

Findings

Complexity depends on time, temperature, and cyclotron frequency.

Oscillation amplitude of complexity varies with parameters.

Rate of complexity obeys Lloyd bound.

Abstract

In this paper, we investigate the circuit complexity of a quantum charged particle in an external magnetic field. Utilizing the Nielsen approach, we determine the complexity of thermofield double states as functions of time, temperature, and cyclotron frequency. We analyze both the complexity and the amplitude of its oscillations across various parameter values, and reveal that these results cannot be derived as a limit of the harmonic oscillator case. Finally, we calculate the rate of complexity and show that it obeys the Lloyd bound.