Abstract: Method and system are provided for efficiently populating a phase diagram for modeling of multiple substances. The method may include defining an n-way phase diagram with data points each being an n-tuple describing the n substance inputs, wherein the n-way phase diagram is defined at a user-configured resolution. The method may select an initial subset of data points and calculate their contribution to the phase diagram. The method may then generate a Bayesian model based on the initial subset of calculated data points and predicting the resultant phase and an associated uncertainty of all the uncalculated data points in the defined phase diagram. The method may select a sample subset of the data points using maximum entropy sampling and calculating a resultant phase for each of the selected data points, and incorporate the calculated phases into the Bayesian model.

Abstract: Systems and methods that facilitate motion formalism utilizing quantum computing, to compute matrix operators in terms of commutators between qubit operators and measurements on the quantum hardware, wherein the commutators are computed utilizing symbolic calculus. Embodiments reduce computational cost of generalized eigenvalue synthesis relying on symbolic calculus and parallelization. Embodiments disclosed herein can also develop estimators of excited-states properties, considering constants of motion (e.g. spin) and non-constants of motions (e.g. dipoles, density matrices).

Abstract: Systems and methods that facilitate motion formalism utilizing quantum computing, to compute matrix operators in terms of commutators between qubit operators and measurements on the quantum hardware, wherein the commutators are computed utilizing symbolic calculus. Embodiments reduce computational cost of generalized eigenvalue synthesis relying on symbolic calculus and parallelization. Embodiments disclosed herein can also develop estimators of excited-states properties, considering constants of motion (e.g. spin) and non-constants of motions (e.g. dipoles, density matrices).

Abstract: Method and system are provided for efficiently populating a phase diagram for modeling of multiple substances. The method may include defining an n-way phase diagram with data points each being an n-tuple describing the n substance inputs, wherein the n-way phase diagram is defined at a user-configured resolution. The method may select an initial subset of data points and calculate their contribution to the phase diagram. The method may then generate a Bayesian model based on the initial subset of calculated data points and predicting the resultant phase and an associated uncertainty of all the uncalculated data points in the defined phase diagram. The method may select a sample subset of the data points using maximum entropy sampling and calculating a resultant phase for each of the selected data points, and incorporate the calculated phases into the Bayesian model.