Quantum and classical annealing in a continuous space with multiple local minima

• URL: http://arxiv.org/abs/2203.11417v1
• Date: Tue, 22 Mar 2022 02:02:23 GMT
• Title: Quantum and classical annealing in a continuous space with multiple local minima
• Authors: Yang Wei Koh and Hidetoshi Nishimori
• Abstract summary: We show that quantum annealing yields a power law convergence, thus an exponential improvement over simulated annealing. We also reveal how diabatic quantum dynamics, quantum tunneling in particular, steers the systems toward the global minimum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima, and the classical approach of simulated annealing is predicted to have a logarithmically slow convergence to the global minimum. We show by extensive numerical analyses that quantum annealing yields a power law convergence, thus an exponential improvement over simulated annealing. The power is larger, and thus the convergence is faster, than a prediction by an existing phenomenological theory for this problem. Performance of simulated annealing is shown to be enhanced by introducing quasi-global searches across energy barriers, leading to a power-law convergence but with a smaller power than in the quantum case and thus a slower convergence classically even with quasi-global search processes. We also reveal how diabatic quantum dynamics, quantum tunneling in particular, steers the systems toward the global minimum by a meticulous choice of annealing schedule. This latter result explicitly contrasts the role of tunneling in quantum annealing against the classical counterpart of stochastic optimization by simulated annealing.

Related papers

• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model [0.0]
  We investigate various aspects of the quantum annealing dynamics using different approaches. We observe qualitative differences between the quantum and classical methods, in particular at intermediate times. At short times, however, the methods are similar again, which can be explained by relating the short-time expansion of quantum annealing to a high-temperature expansion.
  arXiv  Detail & Related papers  (2022-12-16T18:23:05Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Convergence condition of simulated quantum annealing for closed and open systems [0.0]
  We derive a generic condition for simulated quantum annealing to converge to thermal equilibrium at a given, typically low, temperature. Both closed and open systems are treated.
  arXiv  Detail & Related papers  (2022-09-30T15:14:15Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• The quantum annealing gap and quench dynamics in the exact cover problem [0.0]
  Annealing explores equilibrium phases of a Hamiltonian with slowly changing parameters. Quenches are sudden changes of the Hamiltonian, producing a non-equilibrium situation.
  arXiv  Detail & Related papers  (2021-06-15T12:43:23Z)
• Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics [0.0]
  We study the problem numerically through the generalized Kibble-Zurek mechanism of defect distribution. When the system is open (coupled to the environment), the average number of defects does not follow the theoretical prediction. The distribution of defects in the open system turns out to be not far from the theoretical prediction.
  arXiv  Detail & Related papers  (2021-06-02T04:17:07Z)
• Dynamical replica analysis of quantum annealing [0.0]
  An interesting alternative approach to the dynamics of quantum spin systems was proposed about a decade ago. It involves creating a proxy dynamics via the Suzuki-Trotter mapping of the quantum ensemble to a classical one. In this chapter we give an introduction to this approach, focusing on the ideas and assumptions behind the derivations.
  arXiv  Detail & Related papers  (2020-10-23T12:17:38Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.