High-fidelity tracking of the evolution of multilevel quantum states

Yu. I. Bogdanov; N. A. Bogdanova; Yu. A. Kuznetsov; V. F. Lukichev

doi:10.1117/12.2624232

30 January 2022 High-fidelity tracking of the evolution of multilevel quantum states

Yu. I. Bogdanov, N. A. Bogdanova, Yu. A. Kuznetsov, V. F. Lukichev

Proceedings Volume 12157, International Conference on Micro- and Nano-Electronics 2021; 1215729 (2022) https://doi.org/10.1117/12.2624232
Event: International Conference on Micro- and Nano-Electronics 2021, 2021, Zvenigorod, Russian Federation

Abstract

The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based on the use of the spinor representation of the Lorentz transformation group. In the simplest case of one-qubit states, it turns out that, in addition to three-dimensional rotations on the Bloch sphere, one can introduce four-dimensional Lorentz pseudorotations, similar to the transformations of the special theory of relativity. We show that feedback through weakly perturbing adaptive quantum measurements turns out to be capable of providing high-precision control of the quantum system, while introducing only weak perturbations into the initial quantum state. It turns out that, together with the control of a quantum system through its weak perturbation, the developed algorithms for controlling the evolution of the state of a quantum system can be super-efficient, providing a higher measurement accuracy than any standard POVM (PositiveOperator Valued Measure) protocols. The results of the study are important for the development of optimal adaptive methods for quantum states and operations controlling.

Citation Download Citation

Yu. I. Bogdanov, N. A. Bogdanova, Yu. A. Kuznetsov, and V. F. Lukichev "High-fidelity tracking of the evolution of multilevel quantum states", Proc. SPIE 12157, International Conference on Micro- and Nano-Electronics 2021, 1215729 (30 January 2022); https://doi.org/10.1117/12.2624232

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available