Adiabatic time evolution of highly excited states

TL;DR

This paper demonstrates that quantum many-body scar states can be adiabatically evolved similarly to gapped ground states, offering new possibilities for quantum state manipulation despite the absence of an energy gap.

Contribution

It shows that scar states are suitable for adiabatic evolution, expanding the scope of quantum systems where adiabatic techniques can be effectively applied.

Findings

Scar states perform similarly to gapped ground states at high fidelity levels.

Maximum adiabatic speed decreases polynomially with system size for scar states.

Fidelity deviation scales linearly with ramp speed for scar states, quadratically for gapped ground states.

Abstract

Adiabatic time evolution of quantum systems is a widely used tool with applications ranging from state preparation through simplifications of computations and topological transformations to optimization and quantum computing. Adiabatic time evolution generally works well for gapped ground states, but not for thermal states in the middle of the spectrum that lack a protecting energy gap. Here we show that quantum many-body scars -- a particular type of highly excited states -- are suitable for adiabatic time evolution despite the absence of a protecting energy gap. Considering two rather different models, namely a one-dimensional model constructed from tensor networks and a two-dimensional fractional quantum Hall model with anyons, we find that the quantum scars perform similarly to gapped ground states with respect to adiabatic dynamics when the required final adiabatic fidelity is around 0.99. The maximum speed at which the scar state of the one-dimensional model can be adiabatically transformed decreases as a power law with system size, as opposed to exponentially for both generic thermal and disorder-driven localized states. At constant and very low ramp speed, we find that the deviation of the fidelity from unity scales linearly with ramp speed for scar states, but quadratically for gapped ground states. The gapped ground states hence perform better when the required adiabatic fidelities are very high, such as 0.9999 and above. We identify two mechanisms for leakage out of the scar state and use them to explain our results. While manipulating a single, isolated ground state is common in quantum applications, adiabatic evolution of scar states provides the flexibility to manipulate an entire tower of ground-state-like states simultaneously in a single system.