Robustness of Energy Landscape Control for Spin Networks Under Decoherence

Abstract

Quantum spin networks form a generic system to describe a range of quantum devices for quantum information processing and sensing applications. Understanding how to control them is essential to achieve devices with practical functionalities. Energy landscape shaping is a novel control paradigm to achieve selective transfer of excitations in a spin network with surprisingly strong robustness towards uncertainties in the Hamiltonians. Here we study the effect of decoherence, specifically generic pure dephasing, on the robustness of these controllers. Results indicate that while the effectiveness of the controllers is reduced by decoherence, certain controllers remain sufficiently effective, indicating potential to find highly effective controllers without exact knowledge of the decoherence processes.

Robust Control Performance for Open Quantum Systems

“…3, A and S are N 2 × N 2 matrices of rank ≤ N 2 − N with equality in the generic case. More specifically, A and S are simultaneously diagonalizable [5] by a complex unitary matrix U ,…”

“…II, we introduce in Sec. III a novel, general formalism that reduces robustness against all uncertainties to enforcing the single transmission Tz,w to be robust against Hamiltonian parameter uncertainties [4] and decoherence strength [5]. Preparation error response requires a different formulation departing from classical robust performance, as treated in [6], [7].…”

Robustness of Quantum Systems Subject to Decoherence: Structured Singular Value Analysis?

“…It was shown in previous work [16] that these controllers have interesting robustness properties in that the differential sensitivity of the transfer fidelity for superoptimal controllers, i.e., controllers that achieve unit-fidelity transfer, vanishes, which runs counter to the trade-off between performance and robustness that is commonly seen for classical systems [15]. However, other work indicates that this performance advantage disappears in the presence of decoherence [14], [17]. Moreover, differential sensitivity gives no information how the system responds to larger perturbations over a prolonged period of time, or what the critical frequencies are.…”

Robust Control Performance for Open Quantum Systems

“…1. The heuristic approach s ≈ 0 has been attempted [5], [6], but proper treatment requires a modification of the matrix inversion lemma. Some matrix pseudo-inversion lemmas [2], [3] have been proposed but do not apply in this context because their application is restricted to symmetric matrices.…”

“…After reviewing quantum dynamics in Sec. II, the general error dynamics with transfer matrix T z,w that should be robust against uncertainties in the Hamiltonian [4] and decoherence [5] is introduced in Sec. III.…”