Southwest Quantum Information and Technology

Band-limited quantum optimal control

Presenting Author: Adrian Orozco, Center for Quantum Information and Control (CQuIC), University of New Mexico
Contributing Author(s): Grant Biedermann, Mike Martin and Ivan Deutsch

Control of quantum systems is important for the development of quantum technology. Many researchers have explored a variety of functional analytic methods for synthesizing optimal control waveforms that evolve a quantum system from an initial state to a final target state. In particular, the GRadient Ascent Pulse Engineering (GRAPE) method has proven to be a powerful platform for synthesizing these controls. However, in the standard GRAPE algorithm controls are designed in the time domain and there is no direct way of limiting its bandwidth, which is important in practical applications. In addition, for higher dimensional Hilbert spaces GRAPE requires more time steps to completely specify the system’s state. As the total coherence time is limited, the bandwidth will increase when augmenting the number of time steps. These concerns are greatly important when implementing these designed controls in the laboratory. We circumvent these problems by expanding the control via a truncated Fourier series constraining the bandwidth through its Fourier coefficients. A gradient ascent method is used to numerically optimize the Fourier coefficients of a piecewise constant control that lead to the desired evolution of our quantum state. A weakly dressed symmetric Rydberg ensemble model is used to investigate the effect of expanding the control in this way [1]. We find that the control waveform can be designed to have two important characteristics for practical applications; a band-limited power spectrum and constrained control amplitudes during the entire evolution. Furthermore, we find that the total number of time steps (total evolution time) can be restricted for a particular range of Hilbert space dimensions without imparting additional constraints to experimental apparatus. 1. T. Keating, C. H. Baldwin, Y.-Y. Jau, J. Lee, G. W. Biedermann, and I. H. Deutsch, Phys. Rev. Lett. 117, 213601 (2016).

(Session 5 : Thursday from 5:00pm - 7:00pm)