QuboGenerator

The QuboGenerator class is the main concept of the package. It provides methods for the automatic construction of QUBO formulations, including the computation of penalty factors for individual cost functions, the creation of auxiliary variables to reduce cost functions to quadratic order, and the translation into different output formats.

A QuboGenerator object represents a single problem instance and collects constraints and cost functions related to it. It is an abstract base class for specialized QUBO generators, such as the PathFindingQuboGenerator to extend.

It provides the following output formats:

Simplified QUBO formula

The QUBO formulation of the corresponding problem instance as a simplified formula, including sum expressions and additional functions if necessary, to provide a human-readable representation of the QUBO.

Expanded QUBO formula

The QUBO formulation of the corresponding problem expanded as a polynomial expression, without any sums or additional functions. This expression also includes additional auxiliary variables, if necessary, to reduce the order of the products to quadratic expressions.

QUBO matrix

The QUBO as a triangular matrix \(Q\), such that the QUBO problem can be represented as

\[\mathbf{x}^* = \text{argmin}_{\mathbf{x}} \mathbf{x}^T Q \mathbf{x}\]

Entry \(Q_{ij}\) of the matrix represents the coefficient of the quadratic term \(x_i * x_j\) in the expanded QUBO expression.

Quantum Operator

The QUBO as a hamiltonian operator whose minimum eigenstate encodes to the optimal assignment.

Quantum algorithms such as Grover adaptive search, QAOA, VQE, or QPE can be used to solve the eigenvalue problem.

Quantum Circuit

Qiskit’s QAOA implementation to solve the given QUBO problem. Returns an instance of the qiskit QAOA class that can be used to optimize the problem’s hamiltonian operator. This allows end users to run the quantum algorithms without needing to interact with any quantum computing concepts directly themselves.