Workflow Steps: Formulation and Sampling

The two main steps of solving problems on quantum computers are:

1. Formulate your problem as an objective function

   Objective (cost) functions are mathematical expressions of the problem to be optimized; for quantum computing, these are models (e.g., quadratic models[1]) that have lowest values (energy) for good solutions to the problems they represent.

2. Find good solutions by sampling

   Samplers are processes that sample from low-energy states of objective functions. Find good solutions by submitting your model to one of a variety of Ocean’s quantum, classical, and hybrid quantum-classical samplers.

Solution steps: (1) a problem known in “problem space” (a circuit of Boolean gates, a graph, a network, etc) is formulated as a model, mathematically or using Ocean functionality, and (2) the model is sampled for solutions.

[1]

Quadratic models have one or two variables per term. A simple example of a quadratic model is,

\[Ax + By + Cxy\]

where \(A\), \(B\), and \(C\) are constants. Single-variable terms—\(Ax\) and \(By\) here—are linear with the constant biasing the term’s variable. Two-variable terms—\(Cxy\) here—are quadratic with a relationship between the variables.