April 23, 2024

Nature Reviews Chemistry (2024) [arxiv]

Ion chains not only have qubits, but also have motional modes, which are quantum harmonic oscillators. A 20-ion chain has 20 qubits and 60 harmonic oscillators. What can we do with all these?

Of course, we can run quantum simulations of a model with qubits and harmonic oscillators. It is crazy to think that we can encode information into these nanometer-scale quantum vibrations of the ions. But many experiments have reached such precise level of control! There have been several works on using qubits and motional modes to simulate toy models of molecules. See the conical intersection works by C. H. Valahu et al. and J. Whitlow et al.

The model we primarily consider is the Linear Vibronic Coupling Model (LVCM), consisting of electronic states and vibrational modes. Electronic states can be mapped to qubits, and vibrational modes can be mapped to motional modes of trapped ions.

There have been lots of amazing works on efficiently simulating such models on classical computers. But classical simulations fundamentally struggle in the strong coupling regime. Meanwhile, experimental time for trapped-ion simulations scale favorably with coupling strength. Of course, trapped ions have noise, which has larger effects for simulating models with stronger coupling. We numerically simulate how accurately trapped-ion systems of state-of-art noise level can simulate a toy model, and compare with numerically exact & approximate classical simulation methods.

Classical simulations struggle even more when the connectivity between the components is complicated as in actual molecular systems. Meanwhile, all-to-all connectivity is granted for ion chains! This makes us hopeful that with improved noise levels in the future, a few tens of trapped ions will be capable of going beyond what classical computers can do.

And quantum advantage might be even closer by going beyond the LVCM! Adding dissipation or considering higher-order interactions makes it even harder to find an efficient classical simulation method. Ofc, this is a challenge for trapped ions as well, which we’re excited about.

This Review is a stepping stone for all the exciting quantum simulation experiments to happen soon, so stay tuned!