Speaker
Description
Variational quantum eigensolvers (VQEs) are among the most widely studied hybrid quantum–classical algorithms for near-term devices. Yet, they are held back by three persistent obstacles: barren plateaus, convergence to spurious local optima, and the lack of an intrinsic certificate that the optimized state is the desired ground state.
We introduce and analyze an adiabatic VQE that addresses all three. Starting from the easily prepared ground state of a simple Hamiltonian, the variational parameters are optimized sequentially along a discretized path of Hamiltonians, each optimization warm-started from the solution of the previous one. We prove that, under explicit spectral and geometric conditions, gradient-based optimization tracks the instantaneous ground state along the entire path -- a concrete mechanism by which the algorithm avoids barren plateaus and local optima in the relevant region of parameter space.
A central feature is runtime verification: measurements of the energy standard deviation certify that the variational state is close to an eigenstate and, given a lower bound on the spectral gap, that it is the ground state. The algorithm is therefore not only variational and adiabatic but self-verifying. It can adapt its step size and reject unreliable updates using only quantities measurable during execution.
Together, these results give a rigorous foundation for scalable variational ground-state preparation and a route toward reliable hybrid quantum algorithms for optimization, simulation, and quantum machine learning.
| Topic | Quantum variational circuits and their applications |
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| Additional Topic | Hybrid quantum-classical approaches for learning and optimization |