Counterdiabatic driving of the quantum Ising model

Abstract

The system undergoes adiabatic evolution when its population in the instantaneous eigenbasis of its time-dependent Hamiltonian changes only negligibly. Realization of such dynamics requires slow-enough changes of the parameters of the Hamiltonian, a task that can be hard to achieve near quantum critical points. A powerful alternative is provided by the counterdiabatic modification of the Hamiltonian allowing for an arbitrarily quick implementation of the adiabatic dynamics. Such a counterdiabatic driving protocol has been recently proposed for the quantum Ising model [A. del Campo et al., Phys. Rev. Lett. 109, 115703 (2012)]. We derive an exact closed-form expression for all the coefficients of the counterdiabatic Ising Hamiltonian. We also discuss two approximations to the exact counterdiabatic Ising Hamiltonian quantifying their efficiency of the dynamical preparation of the desired ground state. In particular, these studies show how quantum criticality enhances finite-size effects in the counterdiabatic dynamics.

11 pages, version accepted in JSTAT

References in corpus (5)

• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum Criticality
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Adiabatic tracking of quantum many-body dynamics
• Spectral function and fidelity susceptibility in quantum critical phenomena

Cited by in corpus (26)

• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Quantum Dynamics in Krylov Space: Methods and Applications
• Focus on Shortcuts to Adiabaticity
• Shortcuts to adiabaticity for quantum annealing
• Shortcuts to Adiabaticity in Krylov Space
• Controlling quantum critical dynamics of isolated systems
• Two-parameter counter-diabatic driving in quantum annealing
• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Optimal suppression of defect generation during a passage across a quantum critical point
• Counterdiabatic control in the impulse regime
• Variational counterdiabatic driving of the Hubbard model for ground-state preparation
• Shortcuts to adiabaticity in the infinite-range Ising model by mean-field counter-diabatic driving
• Multi-spin counter-diabatic driving in many-body quantum Otto refrigerators
• Efficient Paths for Local Counterdiabatic Driving
• Fast-forward approach to adiabatic quantum dynamics of regular spin clusters: nature of geometry-dependent driving interactions
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions
• Scaling of errors in digitized counterdiabatic driving
• Minimal action control method in quantum critical models
• A numerical approach for calculating exact non-adiabatic terms in quantum dynamics
• Quantum Shortcut to Adiabaticity for State Preparation in a Finite-Sized Jaynes-Cummings Lattice
• Machine-learning-inspired quantum control in many-body dynamics
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Spatiotemporal Quenches in Long-Range Hamiltonians
• Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes