Floquet-Engineering Counterdiabatic Protocols in Quantum Many-Body Systems

Abstract

Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at arbitrary pace, where excitations due to non-adiabaticity are exactly compensated by adding an auxiliary driving term to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well-defined in the thermodynamic limit. Furthermore, the resulting CD driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically-driven (Floquet) systems. This is illustrated on few-and many-body quantum systems, where the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity.

Variational Schrieffer-Wolff transformations for quantum many-body dynamics

“…As mentioned previously, it was recently argued by some of us that an accurate approximation to A(µ) can be found through a commutator expansion [11]: (19) where {a} = {a 1 , a 2 , . .…”

“…These diagonalization methods can be reinterpreted in the context of adiabatic gauge potentials (AGPs) [9], which are infinitesimal generators of a unitary transformation diagonalizing a given Hamiltonian. Recent works have allowed for controllable variational approximations to the AGP, which lead to unitary transformations partially diagonalizing the Hamiltonian [9][10][11]. The variational AGP is guaranteed to converge to the exact one if the number of variational parameters becomes sufficiently large.…”

Counterdiabatic driving in the quantum annealing of the p -spin model: A variational approach

“…[12]. In the same section, we show the approximate counterdiabatic operator adopting two different ansätze for the variational potential: The first one is based on the Nested Commutator (NC) approach [14], the sec-ond one is based on a simple Cyclic Ansatz (CA), the origin of this name will be clear in the following. In Section III, we discuss different properties of the p-spin model for p = 1, 2 and 3 in detail.…”

Robustness of STIRAP Shortcuts under Ornstein-Uhlenbeck Noise in the Energy Levels

“…In order to reduce the necessary time and thus improve the efficiency of quantum adiabatic evolution, several methods have been suggested, collectively referred as shortcuts to adiabaticity [10][11][12][13][14][15][16][17][18]. As their name indicates, the main concept behind them is to bring the system to the same final state in shorter time; some of these methods simply bypass the intermediate adiabatic states, while in others, an extra term is added in the system Hamiltonian, which cancels the diabatic transitions and allows the system to evolve along the adiabatic trajectory of the original Hamiltonian.…”