Iterative Quantum Optimization with Adaptive Problem Hamiltonian
arXiv:2204.13432 · doi:10.1103/PhysRevA.106.022435
Abstract
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of qubits, however, poses the risk of finding only the optimum within the restricted space supported by this Hamiltonian. We describe an iterative algorithm in which a solution obtained with such a restricted problem Hamiltonian is used to define a new problem Hamiltonian that is better suited than the previous one. In numerical examples of the shortest vector problem, we show that the algorithm with a sequence of improved problem Hamiltonians converges to the desired solution.
arXiv comment6 pages, 4 figures
References in corpus (10)
- Quantum Computing in the NISQ era and beyond
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- A variational eigenvalue solver on a quantum processor
- The theory of variational hybrid quantum-classical algorithms
- Noisy intermediate-scale quantum (NISQ) algorithms
- Towards Practical Quantum Variational Algorithms
- Training variational quantum algorithms is NP-hard
- Two quantum Ising algorithms for the Shortest Vector Problem: one for now and one for later
- Not-so-adiabatic quantum computation for the shortest vector problem
- Quantum mean value approximator for hard integer value problems