A method of driving a quantum computational network for determining an extremal value of a cost function for solutions of a quadratic unconstrained binary optimization problem, the method being performed by a hybrid quantum computation system comprising the quantum computational network, a measurement sensor, and a controller, wherein the quantum computational network comprises a qubit register which comprises a plurality of qubits implemented in controllable quantum mechanical systems including a plurality of register qubits and at least one ancilla qubit, and wherein the quantum computational network further comprises a plurality of layers of quantum gates acting on the qubits, the method comprising: - initializing, by the controller, the qubits in the controllable quantum mechanical systems; - sequentially applying, by the controller, the layers of quantum gates to the qubits, wherein each layer comprises multi-qubit quantum gates acting on a plurality of qubits and a plurality of variational quantum gates with two eigenvalues and variable actions onto the qubits, wherein the variable actions of the variational quantum gates of the layers of quantum gates form a set of variational parameters θ; and - determining, with the measurement sensor, an output state of the quantum computational network for obtaining a solution associated with the set of variational parameters θ, wherein each binary variable of the quadratic unconstrained binary optimization problem is associated with a computational basis state of the register qubits, and the solution is obtained by evaluating, by the controller, the probabilities of measuring the computational basis states corresponding to the binary variables; and wherein the method is characterized in that the solution is iteratively improved by: - sequentially applying, by the controller, the layers of quantum gates with shifted variational parameters θ * twice for each variational gate, the shifted variational parameters θ * comprising a subset of the variational parameters θ shifted by symmetric shifts for each variational gate; - determining, with the measurement sensor, the output states for the shifted variational parameters θ * to evaluate a partial derivative with respect to each variable action θ j of the variational parameters θ; - determining, by the controller, a gradient of the cost function based on the output states for the shifted variational parameters; and - updating, by the controller, 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. - initializing, by the controller, the qubits in the controllable quantum mechanical systems; - sequentially applying, by the controller, the layers of quantum gates to the qubits, wherein each layer comprises multi-qubit quantum gates acting on a plurality of qubits and a plurality of variational quantum gates with two eigenvalues and variable actions onto the qubits, wherein the variable actions of the variational quantum gates of the layers of quantum gates form a set of variational parameters θ; and - determining, with the measurement sensor, an output state of the quantum computational network for obtaining a solution associated with the set of variational parameters θ, wherein each binary variable of the quadratic unconstrained binary optimization problem is associated with a computational basis state of the register qubits, and the solution is obtained by evaluating, by the controller, the probabilities of measuring the computational basis states corresponding to the binary variables; - sequentially applying, by the controller, the layers of quantum gates with shifted variational parameters θ * twice for each variational gate, the shifted variational parameters θ * comprising a subset of the variational parameters θ shifted by symmetric shifts for each variational gate; - determining, with the measurement sensor, the output states for the shifted variational parameters θ * to evaluate a partial derivative with respect to each variable action θ j of the variational parameters θ; - determining, by the controller, a gradient of the cost function based on the output states for the shifted variational parameters; and - updating, by the controller, 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.