Hybrid Quantum Computation Architecture for Solving Quadratic Unconstrained Binary Optimization Problems

The method according to claim 10, wherein

• m
• t
• =
• β
• 1
• ⁢
• m
• t
• -
• 1
• +
• (
• 1
• -
• β
• 1
• )
• ⁢
• ∇
• C
• ⁢
• |
• θ
• →
• =
• θ
• →
• t
• 1
• -
• β
• 1
• t
• ⁢
• ⁢
• and
• v
• t
• =
• β
• 2
• ⁢
• v
• t
• -
• 1
• +
• (
• 1
• -
• β
• 2
• )
• ⁢
• (
• ∇
• C
• ⁢
• |
• θ
• →
• =
• θ
• →
• t
• )
• 2
• 1
• -
• β
• 2
• t
• ,
• with β1 and β2 being real values between 0 and 1, ∇C|{right arrow over (θ)}={right arrow over (θ)}t being a gradient determined at iterative step t based on the output state for the shifted variational parameters {right arrow over (θ)}*, and (∇C|{right arrow over (θ)}={right arrow over (θ)}t)2 being the element square of the gradient determined at iterative step t, while mt−1 and vt−1 are the previously determined values at time step t−1 of mt and vt, respectively, and m0 and v0 are zero.

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 quantum computational network comprising a plurality of qubits and further comprises a plurality of layers of quantum gates acting on the qubits, the method comprising:

• initializing the qubits;
• sequentially applying 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 G with variable actions onto the qubits, wherein the variable actions θj of the variational quantum gates of the layers of quantum gates form a set of variational parameters {right arrow over (θ)};
• and
• determining an output state of the quantum computational network for obtaining a solution associated with the set of variational parameters {right arrow over (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 the conditional probabilities of measuring the computational basis states corresponding to the binary variables;
• and wherein the solution is iteratively improved by:
• applying the layers of quantum gates and additional quantum gates Ak conditionally applied based on the state of an ancilla qubit, the additional quantum gates fulfilling the equation ∂θjG=Σk=1K αkAk, with K being a real positive value, and determining the output state to evaluate a partial derivative of the layers of quantum gates with respect to the variable action θj of the variational parameters {right arrow over (θ)};
• determining a gradient of the cost function based on the partial derivative of the layers of quantum gates;
• and
• updating the variational parameters {right arrow over (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.

A hybrid quantum computation system for determining an extremal value of a cost function for solutions of a quadratic unconstrained binary optimization problem, the system comprising:

• a quantum computational network comprising
• a qubit register comprising a plurality of register qubits,
• a plurality of quantum gates selectively acting on the qubits of the qubit register including multi-quantum gates acting on multiple qubits of the qubit register, wherein the quantum gates comprise a plurality of variational quantum gates with respective variable actions onto the qubits of the qubit register, wherein the variable actions form a set of variational parameters {right arrow over (θ)};
• and
• a controller configured to
• initialize the qubits of the qubit register;
• apply the quantum gates to the qubit register in a sequence of layers with the variational parameters {right arrow over (θ)}, wherein each layer comprises variational quantum gates for determining an output state;
• apply the sequence with shifted variational parameters {right arrow over (θ)}*, the shifted variational parameters {right arrow over (θ)}* comprising a subset of the variational parameters {right arrow over (θ)}shifted by a shift and determine the associated output state for the shifted variational parameters {right arrow over (θ)}* and determining the output state for the shifted variational parameters {right arrow over (θ)}* to evaluate a partial derivative with respect to the subset of the variational parameters {right arrow over (θ)};
• and/or
• conditionally apply the layers of quantum gates and additional quantum gates Ak based on the state of an ancilla qubit, the additional quantum gates fulfilling the equation ∂θjG=Σk=1K αkAk, with K being a real positive value, and determine the output state to evaluate a partial derivative of the layers of quantum gates with respect to the variable action θj of the variational parameters {right arrow over (θ)};
• determine a gradient of a cost function based on the partial derivative, wherein the cost function associates a cost to a solution encoded in the output state, 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 the conditional probabilities of measuring the computational basis states corresponding to the binary variables;
• and
• update the variational parameters {right arrow over (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.