An approach is provided for adiabatic quantum annealing (computing, AQC). There is disclosed a method for finding a solution by using adiabatic quantum annealing. In an embodiment of the method an initial state to an adiabatic quantum computing element is provided and an adiabatic quantum annealing is performed by the adiabatic quantum computing element. The result of the adiabatic quantum annealing is examined to determine whether one or more terminating criteria have been met. If the examining reveals that one or more terminating criteria have been met, returning a candidate solution with the lowest energy. If the examining reveals that one or more terminating criteria have not been met, the method further comprises adjusting the state of the adiabatic quantum computing element; and repeating the adiabatic quantum annealing. The present invention also relates to apparatuses and computer program products for implementing the method and circuitry relating to the adiabatic quantum annealing.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method comprising: providing an initial state to an adiabatic quantum computing element; performing an adiabatic quantum annealing by the adiabatic quantum computing element; examining the result of the adiabatic quantum annealing to determine whether one or more terminating criteria have been met; if the examining reveals that one or more terminating criteria have been met, returning a candidate solution with the lowest energy; if the examining reveals that one or more terminating criteria have not been met, the method further comprises: adjusting the state of the adiabatic quantum computing element by adding candidates to a set of penalized states; forming a penalty Hamiltonian; and adjusting an outer product couplings; and repeating the adiabatic quantum annealing. 2. The method of claim 1, wherein the examining comprises: sampling distribution of solutions of the adiabatic quantum annealing; calculating corresponding energies of the distribution of solutions; 3. The method of claim 1, wherein the penalty Hamiltonian is Hpen=−½Σj,k=1NJpen,jkσzj σzk. with J pen , jk = - M k , loop  M l , loop L loop  I j  I k with the persistent current in qubit j given by Ij. 4. The method according to claim 1, wherein the providing an initial state comprises: providing an initial Hamiltonian by H1=ΔΣjNσxj, where σxj is the Pauli x-matrix and Δ is an energy scale. 5. The method according to claim 1, wherein at each repetition the method comprises setting J pen = - C N 2  ( ∑ P  s J )  ( ∑ P  s J ) T , where {{right arrow over (s)}J, J=0, . . . , Ns−1} are the solutions in the penalised set. 6. An apparatus comprising: at least one processor; and at least one memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause an adiabatic quantum computing element to perform at least the following: provide an initial state to an adiabatic quantum computing element; perform an adiabatic quantum annealing by the adiabatic quantum computing element; examine the result of the adiabatic quantum annealing to determine whether one or more terminating criteria have been met; if the examining reveals that one or more terminating criteria have been met, returning a candidate solution with the lowest energy; if the examining reveals that one or more terminating criteria have not been met, the at least one memory and the computer program code are further configured to, with the at least one processor, cause the adiabatic quantum computing element to perform at least the following: adjust the state of the adiabatic quantum computing element by adding candidates to a set of penalized states; forming a penalty Hamiltonian; and adjusting an outer product couplings; and repeat the adiabatic quantum annealing. 7. The apparatus of claim 6, said at least one memory comprising computer program code configured to, with the at least one processor, cause the adiabatic quantum computing element to: sample distribution of solutions of the adiabatic quantum annealing; and calculate corresponding energies of the distribution of solutions. 8. The apparatus of claim 6, wherein the penalty Hamiltonian is Hpen=−½Σj,k=1NJpen,jkσzjσzk. with J pen , jk = - M k , loop  M l , loop L loop  I j  I k with the persistent current in qubit j given by Ij. 9. The apparatus according to claim 6, said at least one memory comprising computer program code configured to, with the at least one processor, cause the adiabatic quantum computing element to provide an initial state comprises: provide an initial Hamiltonian by H1=ΔΣjNσxj, where σxj is the Pauli x-matrix and Δ is an energy scale. 10. The apparatus according to claim 6, said at least one memory comprising computer program code configured to, with the at least one processor, cause the adiabatic quantum computing element to set J pen = - C N 2  ( ∑ P  s J → )  ( ∑ P  s J → ) T , where {{right arrow over (s)}J, J=0, . . . , Ns−1} are the solutions in the penalised set. 11. A computer-readable storage medium carrying one or more sequences of one or more instructions which, when executed by one or more processors, cause an adiabatic quantum computing element to at least perform the following steps: provide an initial state to an adiabatic quantum computing element; perform an adiabatic quantum annealing by the adiabatic quantum computing element; examine the result of the adiabatic quantum annealing to determine whether one or more terminating criteria have been met; if the examining reveals that one or more terminating criteria have been met, returning a candidate solution with the lowest energy; if the examining reveals that one or more terminating criteria have not been met, the computer-readable storage medium carrying one or more sequences of one or more instructions which, when executed by one or more processors, cause the adiabatic quantum computing element to perform at least the following: adjust the state of the adiabatic quantum computing element by adding candidates to a set of penalized states; forming a penalty Hamiltonian; and adjusting an outer product couplings; and repeat the adiabatic quantum annealing. 12. The computer-readable storage medium of claim 11 carrying one or more sequences of one or more instructions which, when executed by one or more processors, cause an adiabatic quantum computing element to: sample distribution of solutions of the adiabatic quantum annealing; and calculate corresponding energies of the distribution of solutions. 13. The computer-readable storage medium of claim 11, wherein the penalty Hamiltonian is Hpen=−½Σj,k=1NJpen,jkσzjσzk. with J pen , jk = - M k , loop  M l , loop L loop  I j  I k with the persistent current in qubit j given by Ij. 14. The computer-readable storage medium according to claim 11 carrying one or more sequences of one or more instructions which, when executed by one or more processors, cause an adiabatic quantum computing element to provide an initial state by: providing an initial Hamiltonian by H1=ΔΣjNσxj, where σxj is the Pauli x-matrix and Δ is an energy scale. 15. The computer-readable storage medium according to claim 11 carrying one or more sequences of one or more instructions which, when executed by one or more processors, cause an adiabatic quantum computing element to set J pen = - C N 2  ( ∑ P  s J → )  ( ∑ P  s J → ) T , where {{right arrow over (s)}J, J=0, . . . , Ns−1} are the solutions in the penalised set.