# Quantum hall plasmonics for quantum computation

• Quanten-Hall-Plasmonik für Quantencomputing

Since its first discovery, the quantum Hall effect has captured the attention of many researchers because of its fascinating physics and of its potential real-world applications. In fact, materials in the quantum Hall regime have striking physical properties that can prove useful in several branches of applied science. In this thesis, we look for ways to employ these materials in the context of quantum computation. Quantum Hall systems are insulating in the bulk but at the edges they present gapless states that provide dissipationless channels of conductance. For this reason, the response to externally applied electric fields is associated to low-energy excitations that are localized at the boundary of the sample. We present a model to describe the dynamics of these excitations and we specialize to systems where the quantum Hall material is capacitively coupled to external electrodes driven by time-dependent potentials. Because in these structures the time-reversal symmetry is broken, typically by an external magnetic field, the low-energy excitations propagate chirally along the edges of the material, and so they can be used to realize low-loss non-reciprocal devices such as gyrators and circulators. Circulators are key components for directional control of solid state qubits, reducing the thermal noise coming into the fridges to the level required for quantum computation. In a quantum computer, one expects to have at least a circulator per readout circuit.State-of-the-art circulators are typically based on the Faraday effect and although they work well in terms of losses, they cannot be scaled below the wavelength of the signal. In the microwave regime, where the wavelengths are of few centimeters, this constraint results in inconveniently bulky devices, whose size drastically limits the scalability of solid state quantum processors composed of a large number of qubits. In contrast, microwave non-reciprocal quantum Hall effect devices are technologically advantageous because they can be made compactly on-chip. Another useful feature of the quantum Hall effect is that a small amount of current forced in the system causes a large potential drop between the opposite edges. We discuss how this property can be exploited to manufacture low-loss microwave transmission lines and resonators with a characteristic impedance of the order of the quantum of resistance $R_K\approx 25.8 \ \mathrm{k}\Omega$. The high value of the impedance guarantees that the voltage per photon is high and consequently high impedance resonators hold promise for engineering a large electrostatic coupling between microwave photons and systems with a small charge dipole, such as spin qubits.