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Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term. 

Abstract Topological data analysis (TDA) methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially complex and high dimensional data sets. The space of persistence diagrams can be endowed with various metrics, which admit a statistical structure and allow to use these summaries for machine learning algorithms, e.g. the Wasserstein distance. However, computing the distance between two persistence diagrams involves finding an optimal way to match the points of the two diagrams and may not always be an easy task for classical computers. Recently, quantum algorithms have shown the potential to speedup the process of obtaining the persistence information displayed on persistence diagrams by estimating the spectra of persistent Dirac operators. So, in this work we explore the potential of quantum computers to estimate the distance between persistence diagrams as the next step in the design of a fully quantum framework for TDA. In particular we propose variational quantum algorithms for the Wasserstein distance as well as the $d_p^c$distance. Our implementation is a weighted version of the quantum approximate optimization Algorithm that relies on control clauses to encode the constraints of the optimization problem. 

In recent years, applications of quantum simulation have been developed to study the properties of strongly interacting theories. This has been driven by two factors: on the one hand, needs from theorists to have access to physical observables that are prohibitively difficult to study using classical computing; on the other hand, quantum hardware becoming increasingly reliable and scalable to larger systems. In this work, we discuss the feasibility of using quantum optical simulation for studying scattering observables that are presently inaccessible via lattice QCD and are at the core of the experimental program at Jefferson Laboratory, the future Electron-Ion Collider, and other accelerator facilities. We show that recent progress in measurement-based photonic quantum computing can be leveraged to provide deterministic generation of required exotic gates and implementation in a single photonic quantum processor. Published by the American Physical Society2024