Complex Quantum Simulations (COMQUATS)

Over the last few years it has been shown that small strings of trapped ions can be used to precisely simulate and calculate properties of other quantum systems. If the size and complexity of these simulators can be increased by a modest amount, then they have the potential to simulate otherwise intractable quantum systems. Such a device could be a powerful tool for scientific research capable of providing new insight into a wide range of many-body quantum systems and generating new quantum states with complex non-classical correlations. Here we present a research plan to experimentally investigate such a scale-up, starting with one of the most advanced trapped-ion quantum simulators, already in our laboratory. We begin by describing improvements to our system to significantly increase the number of ions available for precise simulations from the current paradigm of strings with less than 10 to those with more than 30. This corresponds to an increase in the dimension of the simulator Hilbert space by more than 6 orders of magnitude. Secondly we outline a plan to improve and extend established control techniques to allow precise complex quantum operations on these long ion strings. Besides definitively identifying and reducing sources of decoherence, we will develop techniques to directly simulate systems whose dynamics rapidly become too complex to simulate using existing methods. In the last section, a plan to implement a range of quantum simulations is outlined. Simulation accuracy, efficiency and complexity will be investigated as the simulation size is increased. Firstly, quantum systems are considered which can be readily simulated on a classical computer. This will allow detailed benchmarking of simulation performance as the simulated system size is increased an essential step before moving into classically intractable regimes. Lastly, quantum systems are considered which quickly become classically intractable to simulate as they are scaled up. A strong focus will be on investigating the generation and characterisation of non-classical correlations. The funding applied for in this application is to provide salaries for two Ph.D. students and one post- doctoral scientist to carry out this research.

A larger number of elementary models have been developed in order to describe the physics of the interactions coupling particles in quantum many-body systems. Yet, the big challenge is to deduce the physical phenomena that result from the interactions described by the model. One approach towards this goal consists in learning about the system by carrying out numerical simulations of the model. However, for exact simulations, this approach is limited to a small number of particles due to the exponentially increasing cost of carrying out the simulations with growing particle numbers. Quantum simulation constitutes an alternative approach that overcomes this problem by using a well-controlled quantum system as the computational device for investigating the physics of a particular model of interest. Over the last decade, quantum simulations have been experimentally studied in systems such as ultracold neutral atoms, trapped ions, superconducting qubits or other solid state systems. The COMQUAT project employed trapped and laser-cooled strings of ions for the investigation of quantum models of magnetic interactions: an elementary magnet was encoded in the electronic quantum state of each ion in the string, and laser pulses interacting with the ions were used to simulate the interactions between the elementary magnets. This approach had been carried out before with small ion crystals used for investigating the ground state properties of the simulated system. The goal of the COMQUAT project was to increase the number of particle, to investigate how closely the laser-ion interactions realized the magnetic interactions to be simulated, and to investigate the entanglement growth created by the interactions when starting with the system in a non-equilibrium state. The model studied within COMQUAT was the so-called quantum Ising model with long-range interactions. It was realized by subjecting a chain of up to 20 ions to laser pulses from a highly stable laser. In a first step, the resulting magnetic interactions were characterized using a seven-ion string. In a first major experiment, the magnetic system was first prepared in the lowest energy state which was subsequently perturbed locally. This enabled a study of how entanglement started to propagate in the system as a result of the local perturbation, and of the influence of the range of interactions on the observed dynamics. In a second experiment, the energies of the lowest-lying states were spectroscopically investigated by preparing the system in an initial state whose subsequent dynamics was easy to analyze and to connect to the parameters of the system. A third project led to the first realization of methods that enable a major characterization of the systems quantum state without requiring measurement resources that grow exponentially with the size of the system. The system sizes realized within COMQUAT (20 particles) are still small enough to make the system amenable to numerical simulations. The investigation, however, demonstrates that experiments with 50 or more particles should become possible in the near future and thus explore a domain where exact simulations of the systems dynamical properties will no longer be possible by computer simulations.