Ground-state selection via nonlinear quantum dissipation

TL;DR

This paper introduces a physically realizable nonlinear quantum dissipation method using quantum Landau--Lifshitz-Gilbert dynamics to efficiently find ground states in large quantum systems, outperforming traditional numerical approaches.

Contribution

The authors demonstrate that QLLG dynamics can selectively suppress excited states and drive systems toward ground states in linear time, offering a new experimental approach for quantum ground-state preparation.

Findings

Convergence time scales linearly with system size N.

Method effectively suppresses excited states in random initial states.

Numerical simulations confirm analytical predictions for spin chain Hamiltonians.

Abstract

Finding the ground state of complex quantum systems remains a central challenge in many-body physics, quantum chemistry, and combinatorial optimization, due to the exponential growth of the Hilbert-space dimension and the entangled structure of ground states. We show that quantum Landau--Lifshitz-Gilbert (QLLG) dynamics, proposed in [Phys. Rev. Lett. 133, 266704 (2024)], provides a physically realizable, real-time nonlinear mechanism that selectively suppresses excited-state components and drives the system toward the lowest-energy eigenstate contained in the initial state. Unlike purely numerical methods such as the imaginary-time projection method, QLLG combines coherent precession with dissipative suppression, enabling experimentally accessible ground-state preparation. For random initial states in the $N$-qubit Hilbert space of dimension $2^N$, convergence occurs in times scaling linearly with system size, $N$, and inversely with the spectral gap. We provide numerical simulations of our analytical results with a Hamiltonian describing an interacting spin chain with Heisenberg exchange and a Zeeman term. Our results identify nonlinear quantum dissipation as a powerful tool for real-time ground-state preparation in large quantum systems and quantum optimization.