Many Body Physics with Circuit Quantum Electrodynamics

The physics of a set of interacting particles encompasses a large amount of everyday phenomena ranging from for example the behavior of a large amount of water molecules in their ice, liquid or vapor phase to cars on streets and associated phenomena like traffic jams. The physics of many particle systems can be further subdivided into situations with and without net energy or particle flow. Situations without net energy or particle flows are well understood within the theory of thermodynamics. However situations with net energy or particle flow which are ubiquitous in our daily life, like a bucket of water that rotates or the above mentioned cars on the streets, lack a common theme and are less well understood. If we add quantum mechanics to these systems the physics becomes even more obscure. For example quantum mechanics ascribes particle like features to fields like the oscillation of a drum or light trapped between two mirrors. That implies that these systems can be seen as indivisible units or particles confined in the drum or between the two mirrors. We are interested in the physics of oscillating electrical circuits. Similar to the oscillation of a drum or light trapped between two mirrors these oscillating circuits confine particles called microwave photons. These particles can be examined in situations where there is net energy or particle flow and we may also implement interactions between these particles. However quantum mechanical effects in these systems are very volatile and therefore these experiments have to be conducted in specially shielded environment at very low temperatures. The very low temperatures makes the electrical circuits behave very much like giant atoms rather than the electrical circuits we are used to in every day machines like tv-sets, computers etc. Our main goal is to implement and examine the implications of a special type of interaction between the microwave photons: Imagine a chain of trolls playing a game with balls. Every troll can catch balls from all his left neighbors but never from one of his right neighbors. He may never carry more than one ball. At the same time he may throw the ball he caught from one of his left neighbors to one of his right neighbors. We design oscillating electrical circuits that behave exactly like these trolls and examine the implications of the game. For example: How likely is it to find two neighboring trolls both having a ball in their hands? We call these implications correlations and these are the quantities where the oddities of quantum mechanics reveal themselves. At the same time these correlations could be resources for future information processing tasks.

In the course of this project we devised a design for a quantum computing device that can potentially outperform all classical computers for specific optimization tasks. The device works according to the quantum annealing principle, a quantum computing paradigm that represents the quantum version of annealing, which is used in metallurgy. It is long known that metal, for example for swords, can be heated and subsequently slowly cooled down to get more durable. The heat, which is chaotic motion of the iron atoms, enables rearrangement in the metal such that a configuration of iron atoms is found with less collisions or defects in the lattice. A quantum annealing device uses quantum fluctuations instead of thermal fluctuations to find solutions with less collisions and defects to an optimization problem that can be expressed in terms of yes-no questions. For example, questions like the travelling salesman problem, where we ask which route the travelling salesman has to take in order to travel the least and yet still is able to visit every city once. These kinds of problems are ubiquitous and yet it is known that classical computers cannot solve them efficiently. It is generally believed that quantum processors like the one we designed are able to solve these problems efficiently and are consequently a huge leap forward for humankind. There are already commercially available quantum annealers based on a specific kind superconducting qubit called the flux qubit. However, these quantum annealers have yet to prove their superiority to classical available techniques to solve optimization problems. They are basically hindered by two major obstacles: Their flux qubits exhibit a very weak degree of quantumness and they can only influence each other if they are neighboring. We circumvented both of these obstacles by introducing a new embedding scheme invented by Wolfgang Lechner and using Transmon qubits instead of flux qubits which exhibit much higher values of quantumness. This was made possible because of newly developed techniques to couple Transmon qubits. This coupling circuit not only introduces completely new ways of coupling pairs of Transmons but also enables the coupling of arbitrary many Transmon qubits. The coupling circuit enables completely new designs for quantum annealers that, thanks to the increased quantumness of the Transmon, exceed the capacity to find solutions to optimization problems compared to their classical counterparts.