Programme: Swiss National Science Foundation (SNSF)

Project Participants: IBM Zurich; Quantum Device Lab, ETH Zürich

The intimate relation between geometry and quantum mechanics is exemplified best by the concept of the geometric phase, a quantity acquired during the evolution of a system which is purely defined by the path of the system state in Hilbert space. It depends neither on the energy of the system nor on the evolution time. The concept of geometric phases is at the heart of a multitude of quantum effects: the Aharonov-Bohm effect, the anomalous quantum Hall effect, the polarization change of guided beams of light, the pumped charge in mesoscopic devices, or the emergence of artificial gauge potentials. Moreover, it has attracted particular attention in the field of quantum information processing because its dependence on the path only may lead to robust quantum gates. Superconducting quantum circuits provide an ideal testbed for exploring the peculiar properties of geometric phases and their use for quantum gates in a well-controlled and coherent environment. Moreover, steadily increasing coherence times and the intrinsic scalability of this system are key ingredients for quantum information processing based on geometric gates. The main objective of this project is the experimental realization and characterization of a complete set of geometric quantum gates with superconducting circuits. The basic building block will be a transmon qubit strongly coupled to a microwave cavity in a circuit quantum electrodynamics (QED) architecture. We plan to realize two-qubit geometric gates based on non-Abelian single-qubit operations and cavity-induced geometric phases demonstrated in our recent experiments [Abdumalikov et al., Nature (2013); Pechal et al., Phys. Rev. Lett. (2012)]. Both mechanisms can be extended to multi-qubit gates using current technology. With the successful realization of two-qubit gates, we plan to characterize their noise-resilience by simulating artificial noise using techniques developed in our earlier measurements [Berger et al., arXiv:1302.3305 (2013); Filipp et al., Phys. Rev. Lett. (2009); Leek et al., Science (2007)]. By benchmarking their gate fidelities, we will be able to provide an answer to the open question on the superior robustness of geometric gates as compared to conventional, non-geometric quantum gates. The ultimate goal is to realize a purely geometric quantum algorithm as a milestone experiment towards geometric quantum computation. In a second line of research, we will explore vacuum-induced geometric phases, which originate solely from the zero-point quantum fluctuations of the electro-magnetic field of a microwave cavity. While the geometric phase has been observed in a number of systems by varying the parameters of an external classical field, the particular aspect of a quantized external field has not been experimentally explored so far. We will develop a novel atom-cavity coupling scheme based on a three-level lambda system realized by a transmon device. This method relies on a cavity-assisted Raman process, which allows for in-situ variation of the complex coupling strength using only external control parameters of the microwave. This scheme has potential for a variety of future applications, ranging from the study of multi-mode Jaynes-Cummings models to photon shaping for quantum networks and all-microwave quantum gates. In summary, the main goals of the project are: *) the realization of a universal set of geometric quantum gates consisting of single and two-qubit gates, *) the simulation of the effect of noise and perturbations on geometric gates along with quantitative benchmarking and optimization of the gates, *) the execution of an all-geometric quantum algorithm, *) the realization of a tunable atom-light coupling scheme based on two-photon processes in a three-level artificial atom to investigate the vacuum-induced geometric phase.