An Open-System Quantum Simulator with Trapped Ions (1104.1146v1)

Abstract: The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating the systems from the environment and coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled coupling to an environment remains largely unexplored. Here we report the first realization of a toolbox for simulating an open quantum system with up to five qubits. Using a quantum computing architecture with trapped ions, we combine multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate this engineering by the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation.

• The paper introduces an experimental toolbox that integrates coherent and dissipative dynamics in a trapped ion system for quantum simulation.
• It achieves high-fidelity entangled state preparation, including Bell state cooling and four-qubit GHZ state generation with target populations up to 91%.
• The research demonstrates robust QND measurements and coherent interactions, paving the way for scalable quantum simulation architectures.

Open-System Quantum Simulation with Trapped Ions

The paper, "An Open-System Quantum Simulator with Trapped Ions," represents a substantial contribution to the field of quantum simulation, focusing on the experimental realization of open quantum system dynamics using trapped ions. This research bridges the gap between coherent control of isolated quantum systems and the more complex task of simulating open systems where coupled interactions with environments are crucial.

Research Objectives and Approach

The primary objective of this research was to demonstrate a toolbox capable of facilitating both coherent and dissipative dynamics in an open quantum system. The experimental platform utilized trapped ions, specifically leveraging a string of $^{40}$Ca$^+$ ions to represent qubits. This setup allowed the researchers to implement coherent operations through multi-qubit gates and integrate dissipation using optical pumping techniques. The paper describes engineering dissipation as a resource, effectively broadening the scope of quantum state preparation and manipulation.

Key Experiments and Results

1. Dissipative State Preparation: At the core of their experimental demonstration was the dissipative preparation of entangled states. The authors successfully implemented Bell-state cooling, wherein a controlled dissipative mechanism was employed to steer a two-qubit system into a specific Bell state. Deterministic and probabilistic cooling were tested, yielding target state populations up to 91% with $p=1$ and capturing asymptotic behavior at lower probabilities.
2. Four-Qubit Stabilizer Pumping: Extending the methodology to larger systems, the paper reports the dissipative preparation of four-qubit Greenberger-Horne-Zeilinger (GHZ) states. Utilizing a sequence of stabilizer operators, the ions were engineered to achieve the desired entangled state, demonstrating the adaptability of the approach to more complex quantum systems.
3. Coherent Interactions: Beyond dissipative dynamics, the experiment effectively simulated coherent four-body interactions, a key feature in realizing Hamiltonian time evolutions such as those found in Kitaev's toric code models. The experimental results showed good fidelity with the expected states, highlighting the potential for simulating intricate n-body interactions digitally.
4. Quantum Non-Demolition (QND) Measurements: The ability to read out multi-qubit observables non-destructively was illustrated via the QND measurement of a four-qubit stabilizer operator. This feature is crucial for practicality in quantum error correction and feedback mechanisms, enhancing the quantum system's robustness against decoherence.

Implications and Future Directions

The implications of this research are notable in both theoretical and practical paradigms. The successful integration of controlled dissipation with coherent quantum operations opens new pathways for developing quantum simulators that can model complex phenomena in fields like condensed matter physics and quantum chemistry. Furthermore, this approach provides a groundwork for utilizing open quantum systems in computations, where dissipative processes can aid in the preparation of specific quantum states desirable for algorithmic operations.

From a theoretical perspective, the analogy between engineered dissipation and concepts of quantum pumping reflects significant progress in quantum control methodologies. Practically, the scalability of the system, particularly with advancements in two-dimensional trap arrays, could lead to large-scale implementations capable of exploring diverse and intricate quantum phenomena.

Future developments in this area may focus on refining the precision of coherent and dissipative operations, thus improving fidelity further and analyzing the robustness of the approach across different types of systems and environmental conditions. The modular nature of the proposed quantum simulation toolbox implies potential for adapting these techniques to other physical architectures, including neutral atom systems and solid-state devices. As these technologies mature, they could drive the adoption of novel computing paradigms based on dissipative quantum computation and simulation.

In conclusion, this paper presents a well-structured and comprehensive exploration of open quantum system simulation within the experimental confines of trapped ions, marking an essential step toward harnessing the full potential of quantum technologies in simulating and understanding complex systems.