State Engineering of Unsteerable Hamiltonians

TL;DR

This paper explores how open-system Lindbladian dynamics can be used to steer many-body quantum states, including frustrated Hamiltonians, towards ground states, revealing new possibilities and limitations in quantum state engineering.

Contribution

It introduces a broad class of frustrated Hamiltonians where ground state steering is feasible and establishes bounds on how close one can get to the ground state when steering is not possible.

Findings

Steering of degenerate ground states is possible in certain frustrated Hamiltonians.

A 'glass floor' limits the fidelity achievable in non-steerable Hamiltonians.

The work provides a systematic framework for quantum state manipulation of complex many-body states.

Abstract

Lindbladian dynamics of open systems may be employed to steer a many-body system towards a non-trivial ground state of a local Hamiltonian. Such protocols provide us with tunable platforms facilitating the engineering and study of non-trivial many-body states. Steering towards a degenerate ground state manifold provides us with a protected platform to employ many-body states as a resource for quantum information processing. Notably, ground states of frustrated local Hamiltonians have been known not to be amenable to steering protocols. Revisiting this intricate physics we report two new results: (i) we find a broad class of (geometrically) frustrated local Hamiltonians for which steering of the ground state manifold is possible through a sequence of discrete steering steps. Following the steering dynamics, states within the degenerate ground-state manifold keep evolving in a non-stationary manner. (ii) For the class of Hamiltonians with ground states which are non-steerable through local superoperators, we derive a "glass floor" on how close to the ground state one can get implementing a steering protocol. This is expressed invoking the concept of cooling-by-steering (a lower bound of the achievable temperature), or through an upper bound of the achievable fidelity. Our work provides a systematic outline for studying quantum state manipulation of a broad class of strongly correlated states.