Quantum Annealing and Thermalization: Insights from Integrability.

@article{Li2018QuantumAA,
title={Quantum Annealing and Thermalization: Insights from Integrability.},
author={Fuxiang Li and Vladimir Y. Chernyak and Nikolai A. Sinitsyn},
journal={Physical review letters},
year={2018},
volume={121 19},
pages={
190601
}
}
• Published 2 April 2018
• Physics, Medicine
• Physical review letters
We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap during the whole evolution, and a programmable computational problem that is encoded by parameters of the Ising part of the spin Hamiltonian. Our solution enables exact nonperturbative characterization of final nonadiabatic excitations, including a scaling of their number with the annealing rate and…
10 Citations
Analytical solution for low energy state estimation by quantum annealing to arbitrary Ising spin Hamiltonian
• Bin Yan
• Physics
• 2021
We point to the existence of an analytical solution to a general quantum annealing (QA) problem of finding low energy states of an arbitrary Ising spin Hamiltonian HI by implementing time evolution
Quantum neural networks to simulate many-body quantum systems
• Physics, Mathematics
Physical Review B
• 2018
We conduct experimental simulations of many body quantum systems using a \emph{hybrid} classical-quantum algorithm. In our setup, the wave function of the transverse field quantum Ising model is
Counterdiabatic Hamiltonians for multistate Landau-Zener problem
• Physics
SciPost Physics
• 2018
We study the Landau–Zener transitions generalized to multistate systems. Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we introduce the auxiliary Hamiltonians that are
Dynamic spin localization and γ -magnets
• Physics, Mathematics
• 2019
We construct an explicitly solvable model of interacting quantum spins under the action of linearly time-dependent magnetic field. The Hamiltonian, which we call the gamma-magnet, does not conserve
Dynamics and control of entangled electron-photon states in nanophotonic systems with time-variable parameters
• Physics
• 2021
We study the dynamics of strongly coupled nanophotonic systems with time-variable parameters. The approximate analytic solutions are obtained for a broad class of open quantum systems including a
Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory
• Physics
• 2021
We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting
Emergent topology under slow nonadiabatic quantum dynamics
• Physics
• 2020
The authors study the nonadiabatic dynamics of topologically nontrivial, noninteracting systems in arbitrary dimensions under slow, rather than the usual sudden, quenches. They find that, in this
Integrability in the multistate Landau-Zener model with time-quadratic commuting operators
• Physics, Mathematics
• 2020
All currently known exactly solvable multistate Landau–Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also
Integrable multistate Landau–Zener models with parallel energy levels
• Physics, Mathematics
• 2020
We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/\tau$-time-dependent parameters. Many already known solvable MLZ models
Phase diagram of the dynamics of a precessing qubit under a quantum measurement
• Physics
• 2020
We study the phase transitions induced by sequentially measuring a single qubit precessing under an external transverse magnetic field. Under projective quantum measurement, the probability

References

SHOWING 1-10 OF 56 REFERENCES
Colloquium : Quantum annealing and analog quantum computation
• Physics
• 2008
The recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations is reviewed here. The concept is introduced in successive
Theory of Quantum Annealing of an Ising Spin Glass
• Physics, Medicine
Science
• 2002
By comparing classical and quantum Monte Carlo annealing protocols on the two-dimensional random Ising model (a prototype spin glass), this work confirms the superiority of quantumAnnealing relative to classical annealed and proposes a theory of quantum annealer based on a cascade of Landau-Zener tunneling events.
Zero-temperature quantum annealing bottlenecks in the spin-glass phase
• S. Knysh
• Physics, Medicine
Nature communications
• 2016
Here it is shown how for large problems the complexity becomes dominated by O(log N) bottlenecks inside the spin-glass phase, where the gap scales as a stretched exponential.
Quantum annealing for the number-partitioning problem using a tunable spin glass of ions
• Physics, Medicine
Nature communications
• 2016
This work demonstrates that in a trapped ion setup, with present day technology, it is possible to realize a spin model of the Mattis-type that exhibits spin glass phases by controlling the detuning of the spin-phonon coupling.
Defects in Quantum Computers
• Mathematics, Medicine
Scientific Reports
• 2018
A test based on an exactly solvable many body system–the quantum Ising chain in transverse field–and implement it on the D-Wave machine to assess how quantum or adiabatic is a specific hardware.
Digitized adiabatic quantum computing with a superconducting circuit.
The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems.
Dynamics of a quantum phase transition: exact solution of the quantum Ising model.
The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The
Thermalization and its mechanism for generic isolated quantum systems
• Physics, Medicine
Nature
• 2008
It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki.
A quantum annealing architecture with all-to-all connectivity from local interactions
• Physics, Medicine