**QUANTUM SIMULATOR**

We have a challenge: understanding quantum collective effects is hard. Even relatively simple systems — like the one drawn on the right — whose equations can be easily written down, cannot be solved by pen a paper. With the help of a computer it wouldn’t be any easier: it would take a classical *supercomputer* with the *size of the universe* — by this we mean we would have to use all the protons in the existing universe — to simulate and classically store the information of 300 quantum particles.

But as Richard Feynman memorably said:

*“…nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy…”*

That is why Quantum Simulators are being used to study fundamental theories of quantum matter. *We use a quantum system to mimic other quantum systems that are of interest to us*, and then we let the simulator answer all our questions. Some of the systems and phenomena that can be simulated are:

Our project aims to build a specific type of simulator made up of (exciton-)polaritons. These are *pseudoparticles* made of strongly interacting light (a photon) and matter (an electron-hole pair called exciton). The main difference of the polariton simulator over other platforms —such as cold atoms or superconducting circuits— is that polaritons are easily dissipated and must be externally driven, thus they are intrinsically *out-of-equilibrium*. This poses some great challenges but also some great advantages:

**SOME ASPECTS ABOUT POLARITONS**

From the theoretical point of view, exciton-polaritons have a *Schrödinger cat* structure. These quantum particle consists of two alternatives: cat alive when the exciton exists, or dead cat when instead of an exciton a photon exists in the system. Description of such particles requires methods of quantum physics. Moreover, when many such particles interact strongly with each other, they can form so called “many-body quantum states”. Such states are very non-classical, and their behavior cannot be understood even in terms of the single-particle Schrödinger equation. On the other hand, they can be extremely useful for applications such as quantum computing or quantum simulation. It is believed that controllable many-body quantum states will be a building block of future technologies.

An important obstacle in utilizing many-body quantum states is their fragility to the interaction with the environment. They are so fragile that loss of just a single particle out of tens or hundreds may result in *decoherence* — the loss of superposed states — which renders the whole state useless. Therefore, it is important to protect these states in a careful way. A promising method to achieve this is *topological protection*, which can be realized in carefully designed lattices. This is expected to significantly extend the lifetime of quantum states, making the quantum simulations easier to implement.