ECAMP 15

Reconstruction of Quantum Gates using Quantum Process Tomography

Arash Dezhang Fard$^{1,2}$, Yujie Sun$^{1}$, Marek Kopciuch$^{4}$, Adam Miranowicz$^{4}$, Szymon Pustelny$^{1,3}$
$^1$Marian Smoluchowski Institute of Physics, Jagiellonian University in Krakow, 30-348 Krakow, Poland
$^2$Doctoral School of Exact and Natural Sciences, Jagiellonian University in Krakow, 30-348 Krakow, Poland
$^3$Department of Physics, Harvard University, Cambridge, MA 02138, USA
$^4$Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznan, Poland

Quantum gate reconstruction plays a crucial role in quantum computing by enabling the verification and characterization of quantum operations. Quantum Process Tomography (QPT) is a powerful technique that is used to fully reconstruct the process matrix of a quantum gate, providing a comprehensive understanding of its behavior. By utilizing QPT, one can identify imperfections in quantum gates, making it an essential tool for the development of reliable quantum computing systems.

In this study, we present our experimental investigations on the reconstruction of quantum gates using the QPT technique in the qutrit system. The core of our experimental setup is a room-temperature $^{87}$Rb atomic vapor cell, which contains two hyperfine ground states with $F=1$ and $F=2$ ($F$ is the total angular momentum). To achieve a qutrit system, the $F=2$ state is depleted using a laser beam. To perform the QPT, a set of initial states corresponding to the Gell-Mann matrices is chosen. By comparing initial states with their evolved counterparts, we gain insight into the quantum process. For more insightful characterization of the measured process, we reconstructed the minimal set of Kraus maps that describe measured process. We demonstrate the reconstruction of some fundamental quantum gates, showcasing the high precision of the gate reconstruction using the QPT technique [1,2,3].

1. A. D. Fard, M. Kopciuch, and Y. Sun, P. Wlodarczyk, and S. Pustelny, Isolating Pure Quadratic Zeeman Splitting, arXiv, 2412.07610, 2024.
2. Y. Sun, M. Kopciuch, A. D. Fard, A. Miranowicz, and S. Pustelny Quantum Process Tomography of Room-Temperature Alkali-Metal Vapor, In preparation.
3. A. D. Fard, Y. Sun, M. Kopciuch, A. Miranowicz, and S. Pustelny Reconstruction of Quantum Gates via Quantum Process Tomography, In preparation.