HYBRID QUANTUM COMPUTATION ARCHITECTURE FOR SOLVING A SYSTEM OF LINEAR BINARY RELATIONS

A method of driving a quantum computational network for finding a solution to a computational problem comprising a system of linear binary relations is provided, the method comprising: initializing computation qubits, applying a set of quantum gates to the computation qubits and measuring an outcome state, and determining a solution for the system of linear binary relations associated with the variational parameters θ based on a plurality of solution candidates for the individual relations of the system of linear binary relations encoded in the outcome state, wherein a state of the register qubits is associated with a select one of the binary relations and a state of the ancilla qubits is associated with a solution candidate for the select one of the binary relations, and wherein the solution is iteratively improved by, determining a plurality of partial derivatives of the set of quantum gates with respect to the variational parameters θ with the quantum computational network, determining a gradient of a cost function for the system of linear binary relations based on the plurality of partial derivatives of the set of quantum gates, wherein the cost function associates a cost to a solution candidate for the system of linear binary relations encoded in the outcome state of the computation qubits, and wherein the cost comprises an individual relation penalty associated with a mismatch between the sides of each of the relations and an inconsistency penalty associated with a clash of the value of the same variable in different linear binary relations after repeatedly measuring the computation qubits, and by updating the variational parameters θ based on an update function of a moving average over the gradient of the cost function and of a moving average over the squared gradient of the cost function.