# Quantum Polaritonics

### An international research partnership of state-of-the-art experimental laboratories and theoretical groups between the University of Cambridge, MIT-Skoltech, and the University of Southampton.

# In simple words:

There are problems in science and engineering that require computing time exceeding the age of the universe (14 billion years) or that are by nature incalculable and therefore neither a "classical" nor a "quantum" computer can solve. Some of these challenging problems can be addressed by simulators, also known as optimisers, which we describe below.

### The Quantum Polaritonics international research partnership is driven by our vision to develop an in-house simulator that would allow us to address some of the most fascinating problems of modern science and engineering. To that end, we put together an international team of physical scientists and engineers who share our vision as well as our passion for scientific discovery. There is never ending excitement to unravel the exotic physics underlying quantum phenomena and put them to action in achieving our goal.

The search for an optimal solution is similar to looking for the lowest point in a mountainous terrain with many valleys, trenches, and drops. A hiker may go downhill and think that has reached the lowest point of the entire landscape, but there may be a deeper drop just behind the next mountain. Such a search may seem daunting in natural terrain, but imagine its complexity in a high-dimensional space! This is exactly the problem to tackle when the objective to find the minimum of a system represents a real-life problem with many unknowns, parameters, and constraints.

Modern supercomputers can only deal with a small subset of such problems when the dimensions of the systems to be minimised are relatively small or when the underlying structure of the system offers a shortcut to the global minimum. Even a hypothetical quantum computer, when realised, would offer at best a quadratic speed-up for the “brute-force” search for the global minimum.

Now imagine that one hovers far above the mountains in the direction of the sun, looking for the deepest point from the sky. We would expect that it is possible to measure the deepest point from the air; alas, for the type of problems here the surface of the land is pitch black not allowing for aerial measurements. To find the global minimum of the complex landscape problem above, a problem that in many ways resembles the physical systems we are tackling in our labs, we engineered water into the landscape. Imagine that we start raising the level of water underneath the landscape, while looking for the first glimpse of sun light scattering from the surface of the water. With the water raising from the bottom up, the coordinates where we observe the first reflection from the sun correspond to the deepest point of our complex landscape.

In our case, instead of water we use a quantum fluid that is created by shining a laser on a semiconductor device. The device consists of stacked layers of atoms such as gallium, arsenic, indium, and aluminium; the atoms being deposited with single atomic layer precision. The electrons in these layers absorb and emit light of a specific colour. The admixture of electrons and light leads to the formation of a new type of particle, called polariton, that is ten thousand times lighter than electrons allowing it to achieve sufficient densities to form an exotic state of matter known as a Bose-Einstein condensate. In a Bose-Einstein condensate the quantum phases of polaritons synchronise and create a quantum fluid that can be observed by detecting the light that is emitted from it.

But how to create a potential landscape that corresponds to the function to be minimised and to force polaritons to condense at its lowest point? To do this, we focus on a particular type of optimisation problem, but a type that is general enough so that any other hard problem can be related to it, namely minimisation of the XY model, which is one of the most fundamental models of statistical mechanics. We have shown that we can create polaritons at vertices of an arbitrary graph: as polaritons condense, the quantum phases of polaritons arrange themselves in a configuration that corresponds to the absolute minimum of the objective function.

The XY Model is a universal classical spin model alongside other universal spin models such as the Ising and Heisenberg models. They are characterised by the given degrees of freedom, "spins", by their interactions, "couplings," and by the associated cost function, "Hamiltonian". Various physical platforms have been proposed to simulate such models using superconducting qubits, optical lattices, coupled lasers etc. We introduced polariton graphs as a new platform for finding the global minimum of classical XY Hamiltonians in a variety of geometries and coupling strengths. This system is based on well-established semiconductor and optical control technologies and benefit from flexible tunability and easy readability. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser offering straightforward scalability. Polariton simulators have the potential to reach the global minimum of the XY Hamiltonian in a bottom-up approach by gradually increasing excitation density to threshold. This is an advantage over classical or quantum annealing techniques, where the global ground state is reached through transitions over metastable excited states with an increase of the cost of the search with the size of the system.