Introduction to Adiabatic Evolution

David Guéry-Odelin, A. Ruschhaupt, Anthony Kiely +3 more

Adiabatic evolution along the instantaneous eigenstate of a time-dependent Hamiltonian is used for robust and high fidelity state transfer in atomic and molecular physics. Shortcuts to adiabaticity (STA) are systematic approaches to accomplish the same final state transfer in a faster manner. This article presents an introduction to STA and reviews different theoretical approaches and applications of STA to a range of scientific and engineering tasks in quantum physics and beyond.

Jonas Larson, Erik Sjöqvist, Patrik Öhberg

Francesco Petiziol, Benjamin Dive, Florian Mintert +1 more

We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at all times. The strategy is based on the introduction of an effective counterdiabatic scheme: a correcting Hamiltonian is constructed which approximatively cancels nonadiabatic effects, inducing an evolution tracking the adiabatic states closely. This can be absorbed into the initial Hamiltonian by adding a fast oscillation in the control parameters. We show that a consistent speedup can be achieved without requiring strong control Hamiltonians, using it both as a stand-alone shortcut to adiabaticity and as a weak correcting field. A number of examples are treated, dealing with quantum state transfer in avoided-crossing problems and entanglement creation.

Alain Joye, Charles‐Edouard Pfister

Mária Kieferová, Nathan Wiebe

A major challenge facing adiabatic quantum computing is that algorithm design and error correction can be difficult for adiabatic quantum computing. Recent work has considered addressing his challenge by using coherently controlled adiabatic evolutions in the place of classically controlled evolution. An important question remains: what is the relative power of controlled adiabatic evolution to traditional adiabatic evolutions? We address this by showing that coherent control and measurement provides a way to average different adiabatic evolutions in ways that cause their diabatic errors to cancel, allowing for adiabatic evolutions to combine the best characteristics of existing adiabatic optimizations strategies that are mutually exclusive in conventional adiabatic QIP. This result shows that coherent control and measurement can provide advantages for adiabatic state preparation. We also provide upper bounds on the complexity of simulating such evolutions on a circuit based quantum computer and provide sufficiency conditions for the equivalence of controlled adiabatic evolutions to adiabatic quantum computing.

Jie Liu, Sheng-Chang Li, Libin Fu +1 more