Iterative Quantum Assisted Eigensolver

TL;DR

This paper introduces a hybrid quantum-classical algorithm for estimating Hamiltonian ground states, leveraging Krylov subspace methods suitable for current quantum hardware, and demonstrating scalability to thousands of qubits.

Contribution

It presents a novel iterative algorithm that constructs the Ansatz without feedback, uses simple measurements, and reuses data, advancing quantum ground state estimation methods.

Findings

Efficient on current quantum hardware with no complex measurements.

Capable of handling thousands of qubits.

Works for most initial states, avoiding barren plateau issues.

Abstract

The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical 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 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 well characterized 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 problems consisting of thousands of qubits. The algorithm works for almost every random choice of the initial state and circumvents the barren plateau problem.