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Ground-state selection via nonlinear quantum dissipation

Alireza Ataei, Olle Eriksson, Vahid Azimi Mousolou

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.

Ground-state selection via nonlinear quantum dissipation

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 -qubit Hilbert space of dimension , convergence occurs in times scaling linearly with system size, , 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.

Paper Structure

This paper contains 13 sections, 26 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Results
  3. Discussion
  4. Acknowledgements

Figures (4)

  • Figure 1: Overlaps of the exact ground and first excited states with the corresponding initial random states as a function of $h$.
  • Figure 2: Exact and QLLG simulated energies for ground and first excited states.
  • Figure 3: The blue curve shows the energy error, defined as the absolute difference between the exact and QLLG-simulated ground-state energies for different values of $h$. The orange curve shows the infidelity of the ground-state overlaps between the exact and QLLG-simulated states as a function of $h$.
  • Figure 4: Spectral gap $\Delta E$ (blue curve) and convergence time $\tau$ given in Eq. \ref{['eq:stabletime']} (orange curve) as functions of $h$.