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Accurate modeling of quantum systems interacting with environments requires addressing non-unitary dynamics, which significantly complicates computational approaches. In this work, we enhance an open quantum system (OQS) theory using density-matrix purification, enabling a unitary description of dynamics by entangling the system with an environment of equal dimension. We first establish the connection between density-matrix purification and conventional OQS methods. We then demonstrate the standalone applicability of purification theory by deriving system-environment interactions from fundamental design principles. Using model systems, we show that the purification approach extends beyond the complete positivity condition and effectively models both Markovian and non-Markovian dynamics. Finally, we implement density-matrix purification on a quantum simulator, illustrating its capability to map non-unitary OQS dynamics onto a unitary framework suitable for quantum computers.

We present an exact ansatz for the eigenstate problem of mixed fermion-boson systems that can be implemented on quantum devices. Based on a generalization of the electronic contracted Schr\"odinger equation (CSE), our approach guides a trial wave function to the ground state of any arbitrary mixed Hamiltonian by directly measuring residuals of the mixed CSE on a quantum device. Unlike density-functional and coupled-cluster theories applied to electron-phonon or electron-photon systems, the accuracy of our approach is not limited by the unknown exchange-correlation functional or the uncontrolled form of the exponential ansatz. To test the performance of the method, we study the Tavis-Cummings model, commonly used in polaritonic quantum chemistry. Our results demonstrate that the CSE is a powerful tool in the development of quantum algorithms for solving general fermion-boson many-body problems.

Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schr\"odinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh-Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.

Quantum states of a novel Bose-Einstein condensate, in which both fermion-pair and exciton condensations are simultaneously present, have recently been realized theoretically in a model Hamiltonian system. Here we identify quantum phase transitions in that model between fermion-pair and exciton condensations based on a geometric analysis of the convex set of ground-state 2-particle reduced density matrices (2-RDMs). The 2-RDM set provides a finite representation of the infinite parameter space of Hamiltonians that readily reveals a fermion-pair condensate phase and two distinct exciton condensate phases, as well as the emergence of first- and second-order phase transitions as the particle number of the system is increased. The set, furthermore, shows that the fermion-exciton condensate (FEC) lies along the second-order phase transition between the exciton and fermion-pair condensate phases. The detailed information about the exciton and fermion-pair phases, the forces behind these phase, as well as their associated transitions provides additional insight into the formation of the FEC condensate, which we anticipate will prove useful in its experimental realization.

Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general quantum-computing approach to quantum phase transitions that exploits the geometric structure of reduced density matrices. While typical approaches to quantum phase transitions examine discontinuities in the order parameters, the origin of phase transitions -- their order parameters and symmetry breaking -- can be understood geometrically in terms of the set of two-particle reduced density matrices (2-RDMs). The convex set of 2-RDMs provides a comprehensive map of the quantum system including its distinct phases as well as the transitions connecting these phases. Because 2-RDMs can potentially be computed on quantum computers at non-exponential cost, even when the quantum system is strongly correlated, they are ideally suited for a quantum-computing approach to quantum phase transitions. We compute the convex set of 2-RDMs for a Lipkin-Meshkov-Glick spin model on IBM superconducting-qubit quantum processors. Even though computations are limited to few-particle models due to device noise, comparisons with a classically solvable 1000-particle model reveal that the finite-particle quantum solutions capture the key features of the phase transitions including the strong correlation and the symmetry breaking.

We introduce the Unity Perception package which aims to simplify and accelerate the process of generating synthetic datasets for computer vision tasks by offering an easy-to-use and highly customizable toolset. This open-source package extends the Unity Editor and engine components to generate perfectly annotated examples for several common computer vision tasks. Additionally, it offers an extensible Randomization framework that lets the user quickly construct and configure randomized simulation parameters in order to introduce variation into the generated datasets. We provide an overview of the provided tools and how they work, and demonstrate the value of the generated synthetic datasets by training a 2D object detection model. The model trained with mostly synthetic data outperforms the model trained using only real data., Comment: We corrected tasks supported by NVISII platform. For the Unity perception package, see https://github.com/Unity-Technologies/com.unity.perception