Quantum mean-value approximator for hard integer-value problems

Iterative Quantum Optimization with Adaptive Problem Hamiltonian

“…The ability to update the problem Hamiltonian during the progress of the algorithm opens up a new avenue of combining classical and quantum mechanical elements in an algorithm. Whereas many current hybrid algorithms such as VQE [8][9][10][11] have quantum and classical components -the quantum mechanical evaluation of a function and its classical minimization -that are independent of each other, the classical and quantum mechanical aspects in IQOAP are closely intertwined in that extracting classical information from QAOA [12,13] (or a similar algorithm) and classically updating the basis and corresponding problem Hamiltonian creates a modified problem to be solved by quantum mechanical means. The updated problem in turn gives access to classical information of increased relevance, and this interplay of quantum and classical elements then results in the algorithm's convergence.…”

“…of lowest depth [16] can realise a state |Ψ that results in high probabilities to project onto a low-lying eigenstate of H P upon measurement of the observables Qi if initial state |Ψ 0 , Rabi-angles β and γ and driver Hamiltonian H D are chosen suitably [13,17].…”

“…Since this expectation value can be classically evaluated without explicit construction of the state |Ψ in Eq. ( 4) [13,20], this minimization can be performed classically without using quantum mechanical computational resources.…”

“…Since the shortest-vector problem can be mapped onto a quantum Ising Hamiltonian [5], such that its eigenvectors and eigenvalues correspond to lattice vectors and their squared lengths, it can readily be formulated as a quantum mechanical algorithm such as an adiabatic algorithm [6,7], variational quantum eigensolver [8][9][10][11] or a quantum approximate optimization algorithm (QAOA) [12,13].…”