Topological Quantum Error Correction

The construction of a large-scale fault-tolerant quantum computer is an outstanding scientific and technological goal. It holds the promise to allow us to solve a variety of computationally hard problems such as factoring of large numbers, rapid database search, and the quantum simulation of many-body quantum systems. A main challenge is to protect quantum states and operations from errors. Here, one of the most realistic and promising approaches towards achieving practical quantum computers are topological quantum error correcting codes. Recently, in a collaboration with the experimental ion-trap group in Innsbruck, we have been able to realise in the laboratory the first complete topological quantum error correcting code using seven trapped-ion qubits.

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Logical Qubits with Trapped Ions 

One of the outstanding challenges in quantum error correction is the realisation of logical encoded qubits, which outperform their physical constituent qubits. 

In this project, we develop and theoretically explore new extensible and fault-tolerant schemes to achieve such robust logical qubits, based on state-of-the-art experimental segmented and multi-species ion-trap architectures. Our work is realised in an international collaboration with leading experimental groups in Innsbruck, Zurich, Mainz, Sydney, as well as with theory colleagues in Oxford. 

For an overview, please see our recent work on Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation



Certified Topological Quantum Computation
In this international CETO-collaboration, together with the experimental ion-trap group in Innsbruck and theory colleagues in Madrid, Waterloo and Sydney, we aim at developing and testing new scalable methods to characterise, verify and certify quantum states and processes. Such techniques are essential in view of quantum processors of increasingly larger sizes, which are currently being developed and for which the application of standard quantum tomography techniques becomes impractical. In this context, in a recent work, we have developed a new, rigorous method to quantify the amount of correlations in the dynamics of quantum systems.

Quantum simulation with trapped ions

The idea of quantum simulators is to map the dynamics of complex, interacting many-particle quantum systems of interest onto other, controlled quantum devices, to study their properties and time evolution in a more accessible and controlled way. This provides a promising route to study otherwise intractable interacting many-body systems from various fields ranging from condensed matter, quantum chemistry, to high-energy physics and potentially even biological systems where quantum effects might play a role. Trapped ions can be used to build such quantum simulators. These allow one so realise digital universal simulation by stroboscopic sequences of quantum gate operations. Furthermore, an open-system quantum simulator enables the simulation of dynamics in open quantum systems, by engineering the coupling to a tailored environment. This opens new possibilities to study the competition of coherent and dissipative dynamics in driven, open many-body systems.

Topological phases with cold atoms
Topological insulators are a new type of quantum phases, which evade a classification by the standard Landau-Ginzburg theory of phases, and offer potential applications for quantum computing. A particularly interesting representative are topological Mott insulators, for which the topological insulating phase is generated dynamically, i.e. from fermionic interactions rather than by background gauge fields. We have developed realistic implementation proposals for an observation of this new phase in cold Rydberg atom experiments. Furthermore, we have developed a numerical method to reliably and efficiently calculate the topological contribution to the conductivity (Berry conductivity) in insulating and metallic topological phases.


Trapped Rydberg ions

Trapped, laser-excited Rydberg ions are a new experimental system, which promises to combine excellent level of quantum control in trapped ion systems with strong, switchable and long-range Rydberg interactions. Interestingly, Rydberg ions in a Paul trap can no longer be described as a point-like charged particle, but rather as a composite object of a charged core and an outer electron. This influences their trapping properties and the interactions with neighboring ions. Laser excitation and microwave dressing of Rydberg ions allows one to use this system as an analog quantum simulator for interacting spin models, the study of coherent excitation transfer and for quantum computing applications.


Quantum information processing
with Rydberg atoms

Rydberg atoms are highly excited atoms that interact strongly over inter-atomic distances of several micrometers. Laser excitation and de-excitation of the ground-state atoms to Rydberg states allows one to switch these interactions on and off in a controlled way. This enables the implementation of fast quantum gate operations between pairs or ensembles of atoms.
Such a many-particle entangling gate can serve a central building block of a universal digital quantum simulator. This envisioned device allows one to realise coherent Hamiltonian as well as dissipative open-system time evolution of spin models involving n-body interactions, such as e.g. Kitaev's toric code and more complex lattice gauge theories from condensed matter and high-energy physics.