This paper introduces a novel approach to quantum computation by integrating temporal logic programming with quantum state transitions. The core idea is to extend the capabilities of temporal logic programming to directly control and reason about the evolution of quantum systems. Traditional quantum programming often relies on unitary transformations and circuit descriptions, which can be complex and difficult to verify, especially for complex quantum algorithms. We propose a programming language that allows programmers to define temporal logic constraints on the desired quantum state transitions. These constraints effectively act as a higher-level specification of the quantum computation, offering improved clarity, maintainability, and verification capabilities. The system allows for precise control over quantum computations by specifying state transitions over time. This approach leverages the expressiveness of temporal logic to handle complex quantum systems and algorithms, ultimately simplifying the process of quantum algorithm design and implementation. The theoretical framework and fundamental concepts are presented, laying the groundwork for further development and exploration of this new paradigm.
Polariton condensates provide a versatile platform for exploring non-equilibrium phase transitions and collective phenomena in open quantum systems. Near the condensation threshold, these systems are particularly sensitive to fluctuations and instabilities, which can strongly influence the condensate formation. Using optical trapping and homodyne detection, we directly access the photon statistics and second-order correlation function
g(2)(0) of the condensate. We show that polariton condensation near the threshold is not a purely static transition, but instead undergoes a dynamical regime characterized by stochastic hopping between condensed and non-condensed states. These intermittent dynamics are accompanied by a gradual reduction of
g(2)(0) towards unity, revealing the progressive build-up of coherence even in the presence of strong temporal fluctuations. Numerical simulations, based on a stochastic Truncated Wigner description of the driven-dissipative polariton field, reproduce these dynamics and capture the essential role of noise and reservoir interactions. This work demonstrates that the observed temporal hopping is an intrinsic feature of polariton condensation, providing a dynamical perspective that goes beyond static descriptions of the condensation phase transition.