Abstract
We study the controllability of a central spin guided by a classical field and interacting with a spin bath and show that the central spin is fully controllable independently of the number of bath spins. Additionally we find that for unequal system-bath couplings even the bath becomes controllable by acting on the central spin alone. We then analyze numerically how the time to implement gates on the central spin scales with the number of bath spins and conjecture that for equal system-bath couplings it reaches a saturation value. We provide evidence that sometimes noise can be effectively suppressed through control.
Highlights
The last decades have witnessed a spectacular technological progress to the extent that the implementation of high-fidelity quantum technologies can be thought of as a goal belonging to the not-so-distant future
The general idea behind quantum control is to use the interaction of a quantum system with a properly tailored classical control field to steer its dynamics towards the desired outcome
By performing repeated commutators of iH0 and iHc and taking their real linear combinations, we can obtain the operators iσα, iJα and iσαJβ with α, β = x, y, z. This implies that the full su(2) algebra acting on the Hilbert space of the central spin is contained in the dynamical Lie algebra regardless of the number of bath spins
Summary
The last decades have witnessed a spectacular technological progress to the extent that the implementation of high-fidelity quantum technologies can be thought of as a goal belonging to the not-so-distant future. On the one hand the quest for a fundamental understanding of the sources and mechanisms of decoherence attracts substantial research effort, while on the other the development of strategies to minimize its detrimental effect in view of practical applications is a major research focus. More flexible methods to counteract noise in such a way to allow quantum computing and in general survival of quantum coherence on useful timescales are highly desirable. The general idea behind quantum control is to use the interaction of a quantum system with a properly tailored classical control field to steer its dynamics towards the desired outcome. In this perspective error correction and dynamical decoupling can be regarded as specific instances of quantum control. We go in this direction by considering a spin bath controlled through the central system, and completely characterizing the theoretical control properties of both the bath and the central system
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