Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains

Abstract

We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The dependence of the residual energy on this length scale and the velocity at which the magnetic field sweeps out the chain is shown to be nonmonotonic. We determine the conditions for an optimal suppression of the residual energy of the final state and show that inhomogeneous driving can outperform conventional adiabatic schemes based on homogeneous control fields by several orders of magnitude.

10 pages, 7 figures, published version

References in corpus (19)

• Universal adiabatic dynamics across a quantum critical point
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Defect production in non-linear quench across a quantum critical point
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Adiabatic tracking of quantum many-body dynamics
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
• Optimal non-linear passage through a quantum critical point
• Defect formation beyond Kibble-Zurek mechanism and holography
• Universal far-from-equilibrium Dynamics of a Holographic Superconductor
• Adiabatic dynamics in open quantum critical many-body systems
• Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field
• Counterdiabatic driving of the quantum Ising model
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• Controlling quantum critical dynamics of isolated systems
• Gradient critical phenomena in the Ising quantum chain
• Adiabatic preparation without Quantum Phase Transitions
• Gradient critical phenomena in the Ising quantum chain: surface behaviour

Cited by in corpus (26)

• Focus on Shortcuts to Adiabaticity
• Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
• Full Counting Statistics of Topological Defects After Crossing a Phase Transition
• Quantum annealing of the $p$-spin model under inhomogeneous transverse field driving
• Fast quantum state engineering via universal SU(2) transformation
• Universal dynamics of inhomogeneous quantum phase transitions: suppressing defect formation
• Sonic horizons and causality in the phase transition dynamics
• Hybrid quantum annealing for larger-than-QPU lattice-structured problems
• Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism
• Steering random spin systems to speed up the quantum adiabatic algorithm
• Shortcuts to Adiabatic Classical Spin Dynamics Mimicking Quantum Annealing
• Greedy parameter optimization for diabatic quantum annealing
• Quantum phase transition with inhomogeneous driving in the Lechner-Hauke-Zoller model
• Exact thermal properties of free-fermionic spin chains
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Quantum optimization within lattice gauge theory model on a quantum simulator
• Sampling diverse near-optimal solutions via algorithmic quantum annealing
• Quantum annealing speedup of embedded problems via suppression of Griffiths singularities
• Quantum annealing sampling with a bias field
• Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions
• Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields
• Accelerating adiabatic quantum transfer for three-level $\Lambda$-type structure systems via picture transformation
• Exact bounds on the energy gap of transverse-field Ising chains by mapping to random walks
• The anomalously slow dynamics of inhomogeneous quantum annealing
• Mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain
• Preparation of Many-body Ground States by Time Evolution with Variational Microscopic Magnetic Fields and Incomplete Interactions