Iterative quantumassisted eigensolver
Abstract
The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solidstate physics to combinatorial optimization. We provide a hybrid quantumclassical algorithm for approximating the ground state of a Hamiltonian that builds on the powerful Krylov subspace method in a way that is suitable for current quantum computers. Our algorithm systematically constructs the ansatz by using any given choice of the initial state and the unitaries describing the Hamiltonian. The only task of the quantum computer is to measure overlaps and no feedback loops are required. The measurements can be performed efficiently on current quantum hardware without requiring any complicated measurements such as the Hadamard test. Finally, a classical computer solves a wellcharacterized quadratically constrained optimization program. Our algorithm can reuse previous measurements to calculate the ground state of a wide range of Hamiltonians without requiring additional quantum resources. Further, we demonstrate our algorithm for solving a class of problems with thousands of qubits. The algorithm works for almost every random choice of the initial state and circumvents the barren plateau problem.
 Publication:

Physical Review A
 Pub Date:
 November 2021
 DOI:
 10.1103/PhysRevA.104.L050401
 arXiv:
 arXiv:2010.05638
 Bibcode:
 2021PhRvA.104e0401B
 Keywords:

 Quantum Physics
 EPrint:
 11 pages, 7 figures