A method for finding a solution to a computational problem, the computational problem comprising a system of linear binary relations, with a hybrid quantum computation system comprising a quantum computational network including a set of quantum gates, the set of quantum gates comprising a plurality of variational quantum gates with variable actions acting on a plurality of computation qubits of the quantum computational network, the variable actions forming a set of variational parameters θ, wherein the method comprises: initializing the plurality of computation qubits, comprising a plurality of ancilla qubits and a plurality of register qubits; applying the set of quantum gates to the computation qubits and measuring an outcome state; 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; iteratively improving the solution to the system of linear binary relations 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, 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 - updating the variational parameters θ based on the gradient. initializing the plurality of computation qubits, comprising a plurality of ancilla qubits and a plurality of register qubits; applying the set of quantum gates to the computation qubits and measuring an outcome state; 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; iteratively improving the solution to the system of linear binary relations 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, - 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, - updating the variational parameters θ based on the gradient.