Understanding periodically driven quantum systems is currently a major line of research.

These Floquet systems provide versatile platforms to investigate new physical phenomena such as time crystals, and can also be used to create fault-tolerant states for quantum computing.

What’s important here is the ability to precisely control the behaviour of the quantum system by designing its effective Hamiltonian – the mathematical object that governs how the system evolves over time.

When researchers want a system to behave in a very specific way, they engineer the Hamiltonian to match a desired target. This is called Floquet engineering.

Unfortunately, it’s not possible to create a simple (analytical) Floquet Hamiltonian for any given system, and mathematical tools such as the Magnus expansion are usually required to get a Hamiltonian that is sufficiently precise.

However, when you engineer a Hamiltonian using approximations, you get errors – not great for most applications and especially quantum computing.

Mitigating these errors is possible to some degree although up until now it’s been a one system at a time approach. What we really need is a systematic approach for mitigating these errors for any given system.

This is the problem that the latest paper by researchers Xu and Guo tries to address.

They used symmetries (like rotational or mirror symmetry) to simplify the design of these correction terms. This makes the calculations more manageable and the system more predictable.

They also provided a numerical method to calculate these corrections efficiently, which is important for practical implementation

They validated their method by creating Hamiltonians that are directly relevant for quantum computers.

The authors expect to further refine their method in the future, but this represents a big step forward towards practically engineering arbitrary Floquet Hamiltonians.