Hamiltonian engineering for adiabatic quantum computation: Lessons from shortcuts to adiabaticity

Abstract

We discuss applications of shortcuts to adiabaticity (STA) to adiabatic quantum computation. After reviewing the fundamental properties and the present status of STA from the author's personal point of view, we apply the method to the adiabatic algorithm of the Grover's problem. We discuss two possible implementations of STA for the adiabatic quantum computations: the method of quantum adiabatic brachistochrone and the Lewis-Riesenfeld invariant-based inverse engineering.

10 pages, 8 figures, article for JPSJ Special Topics, minor changes for v2

References in corpus (25)

• Shortcut to adiabatic passage in two and three level atoms
• Bounds for the adiabatic approximation with applications to quantum computation
• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Shortcut to adiabaticity for an interacting Bose-Einstein condensate
• Fast optimal transition between two equilibrium states
• Quantum Adiabatic Brachistochrone
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Shortcuts to adiabaticity in three-level systems using Lie transforms
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Integrable time-dependent quantum Hamiltonians
• Shortcuts to adiabaticity for quantum annealing
• Fast adiabatic evolution by oscillating initial Hamiltonians
• Shortcut loading atoms into an optical lattice
• Counterdiabatic driving of the quantum Ising model
• Fast-forward scaling in a finite-dimensional Hilbert space
• Realistic Shortcuts to Adiabaticity in Optical Transfer
• Steering random spin systems to speed up the quantum adiabatic algorithm
• Shortcuts to Adiabatic Classical Spin Dynamics Mimicking Quantum Annealing
• Shortcuts to adiabaticity in the infinite-range Ising model by mean-field counter-diabatic driving
• Shortcuts to adiabaticity applied to nonequilibrium entropy production: An information geometry viewpoint
• Unitary deformations of counterdiabatic driving
• Quantum-Classical Correspondence of Shortcuts to Adiabaticity
• Counterdiabatic Hamiltonians for multistate Landau-Zener problem

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