Abstract: Some embodiments include a process, including obtaining, with a classical computer system, a mathematical problem to be solved by a quantum computing system, wherein: the quantum computing system comprises one or more quantum computers, the mathematical problem involves more variables than any of the one or more quantum computers have logical qubits, and solving the mathematical problem entails determining values of the variables; decomposing, with the classical computer system, the mathematical problem into a plurality of sub-problems, wherein decomposing the mathematical problem into the plurality of sub-problems comprises decomposing the mathematical problem with machine learning into quantum circuits; causing, with the classical computer system, the quantum computing system to solve each of the sub-problems and aggregate solutions to the sub-problems to determine a solution to the mathematical problem; and storing, with the classical computer system, the solution to the mathematical problem in memory.

Abstract: Methods and systems for providing a digital cart management system for use by customers within a retail location. In use, a customer shops within a retail location and adds items to a digital cart as the customer is adding the items to a physical cart, e.g., at least in part by voice input. When the customer is finished shopping, the customer can checkout via a digital process, thereby bypassing point of sale devices at the retail location.

Abstract: Methods and systems for providing a digital cart management system for use by customers within a retail location. In use, a customer shops within a retail location and adds items to a digital cart as the customer is adding the items to a physical cart, e.g., at least in part by voice input. When the customer is finished shopping, the customer can checkout via a digital process, thereby bypassing point of sale devices at the retail location.

Abstract: Some embodiments include a process, including obtaining, with a classical computer system, a mathematical problem to be solved by a quantum computing system, wherein: the quantum computing system comprises one or more quantum computers, the mathematical problem involves more variables than any of the one or more quantum computers have logical qubits, and solving the mathematical problem entails determining values of the variables; decomposing, with the classical computer system, the mathematical problem into a plurality of sub-problems, wherein decomposing the mathematical problem into the plurality of sub-problems comprises decomposing the mathematical problem with machine learning into quantum circuits; causing, with the classical computer system, the quantum computing system to solve each of the sub-problems and aggregate solutions to the sub-problems to determine a solution to the mathematical problem; and storing, with the classical computer system, the solution to the mathematical problem in memory.

Abstract: Methods and systems for providing a digital cart management system for use by customers within a retail location. In use, a customer shops within a retail location and adds items to a digital cart as the customer is adding the items to a physical cart, e.g., at least in part by voice input. When the customer is finished shopping, the customer can checkout via a digital process, thereby bypassing point of sale devices at the retail location.

Abstract: Methods and systems for managing an item assortment from among a collection of heterogeneous items are disclosed. One method includes receiving item data associated with the collection of heterogeneous items that defines values for a plurality of item attributes, and calculating a score for a degree of substitutability between items. A community detection algorithm is applied to edge weights that are based on the scores between items, to identify substitution groups among the items. Preferred attributes common to items within the substitution groups are found, and an item assortment is updated based on a determination of substitutability among items in at least one of the substitution groups.