Perspectives of Quantum Information Processing with Rydberg Ions

Trapped cold ions are among the most advanced systems to implement quantum information processing. In current experiments entanglement of the qubits, represented by long-lived internal atomic states, is achieved via quantum control of the collective motion of the ion crystal. Instead, here we propose an unprecedented experimental program supported by theory, where the huge dipole moments associated with Rydberg excited ions are the basis of strong spin-dependent long range interactions, and thus exceptionally fast entangling operations as basic building blocks for quantum computing and quantum simulation. While in the short term the fundamental questions to be explored are the understanding of Rydberg excitation and dynamics of single and multiple ions stored in linear Paul traps, and the various ways of manipulating this dynamics with external electromagnetic fields, the long term promise of this project is a potentially scalable very fast ion trap quantum processor, and in particular also novel schemes for quantum simulation. The contribution of the Innsbruck team to the consortium will focus on the theoretical exploration of long-term prospects that Rydberg ions might offer for potentially scalable quantum information processing and quantum simulation. In this context, Innsbruck will contribute the main work to the development of new two- and multi-ion entangling gates via Rydberg interactions. Here, the aim is to employ external microwave and laser dressing fields to tailor the interactions between energetically well-isolated Rydberg states, which encode effective spin or qubit degrees of freedom. First, the range of validity of the effective spin description will be determined by quantitatively characterizing the dominant sources of decoherence such as thermal motion of the ions, radiative decay from Rydberg states as well as undesired coupling to near-degenerate states. Second, protocols for the creation of multi- ion entanglement via the Rydberg blockade mechanism as well as schemes for quantum simulation of coherent and dissipative dynamics of effective spin models with Rydberg ions will be developed and analyzed. In addition, the Innsbruck team will take the lead in the exploration of the potential of fast and long-range Rydberg gates as a possible key-element to interconnect ions separated by distances larger than ten microns, possibly stored in adjacent micro-traps. Such long-range entangling schemes might constitute an alternative to shuttling of ions, and thereby complement current efforts, which are undertaken towards the goal of scalable ion-trap quantum computing architectures.

Trapped cold ions are among the most advanced systems to implement quantum information processing. In current experiments entanglement of the qubits, represented by long-lived internal atomic states, is achieved via quantum control of the collective motion of the ion crystal. Instead, in this project we propose an unprecedented experimental program supported by theory, where the huge dipole moments associated with Rydberg excited ions are the basis of strong spin-dependent long range interactions, and thus exceptionally fast entangling operations as basic building blocks for quantum computing and quantum simulation. While in the short term the fundamental questions to be explored were the understanding of Rydberg excitation and dynamics of single and multiple ions stored in linear Paul traps, and the various ways of manipulating this dynamics with external electromagnetic fields, the Innsbruck group was mainly involved in the long term promise of this project to build a potentially scalable very fast ion trap quantum processor, and, in particular, also novel schemes for quantum simulation. In this context, Innsbruck contributed to the development of novel two- and multi-ion entangling gates via Rydberg interactions. We showed that the extremely large polarisability of ionic Rydberg states leads to strong mechanical forces during the excitation process. This mechanism is useful in the context of dynamical mode shaping. It permits the splitting of large ion crystals into smaller sub-crystals in each of which quantum information processing protocols can be executed independently and in parallel. We further delved theoretically on the possibility to use long-range dipolar interactions for the creation of fast and robust quantum gates. We have shown that the strength of these interactions can be conrolled via microwave fields and have theoretically demonstrated the feasibility of a two-qubit gate based on this mechanism. This mechanism and the dynamical mode shaping could represent a viable step forward towards a scalable quantum information and simulation architecture in an ion trap setting. Furthermore, we investigated the power of this method to implement a quantum simulator for studying exotic quantum magnetism on a two-dimensional setup, where the trapped ions form a triangular crystal. We utilized the state dependent trapping frequencies of ions, hence exciting to a Rydberg state (or alternatively one may use a pinning laser), in order to create localized modes, which realize exotic plaquette interactions among the ions in a hexagonal ring. Such interactions impose non-local energetic constraints. This allows to access a series of interesting models: 1) the Balents-Fisher-Girvin model where topological spin liquid phase has been predicted, 2) to observe Bose metal in a Honey-comb lattice with XY interactions and 3) to provide ion-lattice implementations for U(1) lattice gauge theories. In addition, exotic spin-models can also be implemented via so-called Rydberg dressing. This approach has been investigated in great detail and a number of spin-models for quantum magnetism has been studied and discussed. Here, proposed a realization of quantum-ice dynamics in a system of ultra-cold Rydberg atoms/ions trapped in two-dimensional optical lattice potentials. Ultimately, this realizes various quantum spin-models, in particular related to frustrated magnetism, in which the low energy/temperature Physics is governed by emergent dynamical gauge fields.