Preparing general mixed quantum states on quantum computers

Abstract: The preparation of quantum states serves as a pivotal subroutine across various domains, including quantum communication protocols, quantum computing, and the exploration of quantum correlations and other resources within physical systems. Building upon the protocols introduced in previous works [M. B. Pozzobom and J. Maziero, Quantum Inf. Process. 18, 142 (2019)] and [E. R. G\aa rding et al., Entropy 23, 797 (2021)], the authors of [F. Shahbeigi, M. Karimi and V. Karimipour, Phys. Scr. 97, 025101 (2022)] demonstrated the capability to prepare mixed two-qubit X-real states on quantum computers by extending the methodology initially devised for mixed two-qubit Bell-diagonal states. In this article, we delve into an overlooked pattern within these quantum circuits, allowing us to generalize the approach to encompass a broader scope. Presenting an algorithm tailored for the preparation of $d$-dimensional mixed quantum states using quantum information processors, we offer a significant advancement in mixed state preparation methodologies. To validate the efficacy of our algorithm, we conducted comprehensive tests utilizing both X and non-X mixed two-qubit states, as well as arbitrary random density matrices spanning one, two, and three qubits.