Abstract
The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. Due to the unavailability of invariants for systems with more than one spatial dimension, the benefits of this framework have not yet been exploited in multi-dimensional systems. We construct a multi-dimensional Gaussian quantum invariant that permits the design of time-dependent potentials that let the ground state of an initial potential evolve towards the ground state of a final potential. The scope of this framework is demonstrated with the task of shuttling an ion around a corner which is a paradigmatic control problem in achieving scalability of trapped ion quantum information technology.
Highlights
The development of hardware for quantum information processing has reached a stage in which tens of qubits can be accurately controlled [1, 2]
Since trapped ion quantum logic usually requires the motional states of ions to be close to their quantum mechanical ground state [6], it is desirable that any such shuttling process should transfer ions to their motional ground state with high fidelity
Any shuttling process needs to end with a stage of deceleration in which an originally rapidly moving ion is being transferred to its quantum mechanical motional ground state
Summary
The development of hardware for quantum information processing has reached a stage in which tens of qubits can be accurately controlled [1, 2]. Invariant-based inverse engineering has motivated the study of fast transport of spin-orbit-coupled Bose-Einstein condensates [24], and quantum invariants have been used as a theoretical tool to compute topological phases in planar waveguides [25] and minispace quantum cosmologies [26]. They may be constructed for light beam propagation in nonlinear inhomogeneous media [27]. We develop a framework of quantum invariants that is suitable for optimal control of Gaussian wave-packets in any number of spatial dimensions via invariantbased inverse engineering. A reader who is more interested in the underlying framework than in its application to a specific control problem, can skip Sec. 4 or read Secs. 5 and 6 in any order
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