Theoretical understanding indicates that Majorana zero modes in solid-state systems could be utilized for fault-tolerant quantum information processing. The ability to reliably detect these excitations, however, remains a challenge and many of their properties are still unknown. In this Master's project, devices that implement a circuit quantum electrodynamics architecture and are predicted to host Majorana zero modes have been fabricated and characterized at temperatures below 50 mK. Single-junction as well as split-junction geometries have been investigated. In neither case have the expected Majorana signatures been detected. A primary difficulty is operating the devices in magnetic fields large enough to induce the presence of Majorana zero modes. Effects in which the signatures are expected to occur, charge dispersion for the single-junction case and flux dependence for the split-junction case, have been resolved at in-plane fields of approximately 150 mT and 300 mT, respectively. Although non-affirmative of the existence of Majorana states in the devices, the results represent a step toward detection and eventually utilization of Majorana zero modes in superconducting circuits.
Theoretical understanding indicates that Majorana zero modes in solid-state systems could be utilized for fault-tolerant quantum information processing. The ability to reliably detect these excitations, however, remains a challenge and many of their properties are still unknown. In this Master's project, devices that implement a circuit quantum electrodynamics architecture and are predicted to host Majorana zero modes have been fabricated and characterized at temperatures below 50 mK. Single-junction as well as split-junction geometries have been investigated. In neither case have the expected Majorana signatures been detected. A primary difficulty is operating the devices in magnetic fields large enough to induce the presence of Majorana zero modes. Effects in which the signatures are expected to occur, charge dispersion for the single-junction case and flux dependence for the split-junction case, have been resolved at in-plane fields of approximately 150 mT and 300 mT, respectively. Although non-affirmative of the existence of Majorana states in the devices, the results represent a step toward detection and eventually utilization of Majorana zero modes in superconducting circuits.
Quantum computation is a multifaceted field of research aiming for the physical realization of quantum systems and their manipulation. This thesis discusses the combination of two notable approaches in the pursuit of a fully operational quantum computer---circuit quantum electrodynamics and topological quantum computation based on Majorana quasiparticles. In circuit quantum electrodynamics quantum information is stored into small superconducting circuit elements whose interaction with electromagnetic radiation in the range of microwaves allows to process quantum information very efficiently. This approach has proven extremely useful for control and readout of superconducting qubits, i.e., small circuit elements that carry quantum information. Because of remarkably strong light-matter couplings that can be achieved for superconducting qubits in microwave resonators, the circuit quantum electrodynamics architecture is particularly useful to perform highly sensitive quantum measurements.Superconductivity by itself is an intriguing state of matter that shows a great variety of different phenomena. In particular, the discovery of topological phases in superconductors opened new horizons for quantum computation. One notable system that admits topological superconductivity is a semiconductor-superconductor nanowire with special zero modes occurring at its ends. These so-called Majorana zero modes are remarkably robust against decoherence and therefore well-suited for fault-tolerant quantum computation.The first part of this thesis examines the coupling of Majorana zero modes to electromagnetic radiation with microwave frequencies. The light-matter coupling mechanism that is considered here arises for Majorana zero modes located at a voltage-biased superconducting tunneling junction. The emission of microwave radiation in presence of Majorana zero modes gives rise to coherent radiation which is emitted at half of the usual Josephson frequency. On the basis of this fractional Josephson radiation, we propose a microwave readout scheme for Majorana qubits. As usual for typical measurements in circuit quantum electrodynamics, the proposed readout implements a quantum non-demolition measurement for Majorana qubit.In the last part of the thesis we propose a novel scheme for the implementation of measurement-induced entanglement between remote superconducting qubits as required for quantum communication. By detecting a single photon, that passes a Mach-Zehnder interferometric setup, deterministic entanglement with single-shot efficiency is achieved. This scheme essentially relies on the strong coupling between the qubits and the photon.
The technology of quantum computing is believed to solve certain computational problems significantly faster than classical computers, enabling classically inaccessible problems. However, the technology is still in its infancy and it is still too early to conclude which physical system(s) will form the basis of tomorrow's quantum computer. Small-scale quantum processors, built on the superconducting transmon qubit, demonstrated already the anticipated quantum speed-up. Despite this tremendous milestone, scaling up to a full-fledged quantum computer is far from trivial: with these qubits, the flux-control causes crosstalk between qubits and heating, the room-temperature microwave control is hardly scalable and comes with high energetic radiation, and most importantly, the loss of quantum information in time leads to computational errors. Recent advances in various hybrid semiconductor materials enabled novel voltage-controlled transmons, gatemons, which are less susceptible to heating and crosstalk. Even more exciting, gatemons can be designed to host Majorana zero modes in a way that renders the qubit inherently protected against decoherence. In order to induce Majorana zero modes in such nanowire systems strong magnetic fields are required. Problematically, magnetic fields destroy the superconductivity that these microwave circuits rely on. In this thesis we integrate three types of hybrid Josephson junctions in magnetic field compatible microwave devices. Chapter 4 demonstrates the first graphene-based transmon. Due to the mono-atomic thickness of graphene in combination with magnetic field resilient coplanar waveguide resonators, we are able to operate the transmon circuit at an in-plane magnetic field of 1 Tesla. Chapter 5 embeds an InAs-Al semiconducting nanowire Josephson junction in a high quality factor superconducting transmission line resonator, demonstrating on-chip microwave generation. The gate-controllable semiconducting platform lends itself for fast pulse control, providing a perspective for the coherent on-chip manipulation of artificial two-level systems, in particular superconducting qubits such as transmons. Chapter 6 continues the development of InAs-Al nanowire transmons. The offset-charge-sensitive regime, additional plunger gates and magnetic field compatibility prepares the platform for the detection of coherent coupling between Majorana zero modes, a phenomena which unfortunately still remains unobserved. Additionally, we realise the first InSb-Al gatemon. The higher spin-orbit coupling makes InSb to be a preferred material in the search for Majorana signatures. Chapter 7 reports on the dynamics of quasiparticle tunneling events in real-time across the InAs-Al nanowire junction in a transmon architecture. The magnetic field compatibility of our device up to 1 Tesla together with in-situ voltage-controlled quasiparticle trap engineering, allows us to measure the survival of the charge-parity lifetime up to strong magnetic fields. A result which is extremely important in the research field of topological quantum computing, where the qubit space is defined in the charge-parity.
Motivated by recent experimental progress towards the measurement and manipulation of Majorana fermions with superconducting circuits, we propose a device interfacing Majorana fermions with circuit quantum electrodynamics. The proposed circuit acts as a charge parity detector changing the resonance frequency of a superconducting $\ensuremath{\lambda}/4$ resonator conditioned on the parity of charges on nearby gates. Operating at both charge and flux sweet spots, this device is highly insensitive to environmental noise. It enables high-fidelity single-shot quantum nondemolition readout of the state of a pair of Majorana fermions encoding a topologically protected qubit. Additionally, the interaction permits the realization of an arbitrary phase gate on the topological qubit, closing the loop for computational completeness. Away from the charge sweet spot, this device can be used as a highly sensitive charge detector with a sensitivity better than ${10}^{\ensuremath{-}4}\text{e}/\sqrt{\text{Hz}}$ and bandwidth larger than 1 MHz.
Majorana zero modes are emergent zero-energy quasiparticle excitations in certain superconducting systems that can be viewed as fractionalized or “half” electrons. These quasiparticles obey non-Abelian braiding statistics which is one manifestation of such half-electron character. Due to such non-Abelian braiding property, Majorana zero mode pairs hold promise as potential qubits for topological quantum computation. It is somewhat surprising that, at least theoretically, ordinary one-dimensional semiconductor systems can be induced to host such esoteric Majorana modes as edge states if some precise experimental conditions are satisfied. Because of the relative simplicity of material and experimental requirements to host Majorana modes, there has been a flurry of experimental effort to realize them in semiconductor nanowire systems. While experimental efforts have produced preliminary evidence for the presence of Majorana zero modes in these systems, a thorough confirmation is lacking. The experimental signature in question is the presence of a zero-bias conductance-peak that, while necessary, is not a sufficient criterion to establish the presence of underlying Majorana modes. Given the importance of Majorana braiding for topological quantum computation and skepticism over the presence of Majorana modes in these experimental systems, it would seem natural to attempt braiding these putative Majorana modes in the near future. In that case, an observation of non-Abelian statistics would provide the necessary and sufficient condition in favor of Majorana presence in the studied experimental systems. This thesis has three distinct parts. First, we assume perfect Majorana modes as given that can be successfully braided. In this case, we calculate the diabatic error due to the finite speed of braiding when the system is coupled to a Bosonic bath. Next, we grant that the mechanism for zero-bias conductance-peak is indeed topological, albeit the underlying Majorana modes may be imperfect (the modes are not precisely at zero energy). We study the interplay of dissipation and finite energy splitting of the Majorana modes and study its consequence regarding the probability of successful braiding. Lastly, we propose studying the correlation between independent left and right conductance measurements as a means to distinguish between a topological versus a non-topological the mechanism underlying the observed zero-bias conductance-peak.
High-temperature superconducting Majorana fermions platforms in the layered Kitaev Materials: Case study of Li2IrO3
Recent advances in Kitaev materials have highlighted their potential to host Majorana fermions without or high-temperature of superconductivity. In this research, we propose Li2IrO3 as a promising High-temperature superconducting platform supporting Majorana edge modes due to its strong spin-orbit coupling, honeycomb lattice structure, and proximity to a quantum spin liquid (QSL) phase. A theoretical and numerical framework based on the Kitaev-Heisenberg Hamiltonian is developed to model spin interactions in Li2IrO3. Here, the existence of topological zero-energy states is demonstrated, and their signatures in the edge-localized spectral weight are identified. A device concept based on this material is also proposed with potential industrial applications in spintronics, magnetic field sensing, and topological quantum memory.
Majorana qubits offer a promising way to store and manipulate quantum information by encoding it into the state of Majorana zero modes. As the information is stored in a topological property of the system, local noise cannot lead to decoherence. Manipulation of the information is achieved by braiding the zero modes. The measurement, however, is challenging as the information is well hidden and thus inherently hard to access. Here, we discuss a setup for measuring the state of a Majorana qubit by employing standard tools of microwave engineering. The basic physical effect that we employ is the fact that a voltage-biased Josephson junction hosting Majorana fermions allows photons to be emitted and absorbed at half the Josephson frequency. We show that in the dispersive regime, our setup allows us to perform a quantum nondemolition measurement and to reach the quantum limit. An appealing feature of our setup is that the interaction of the Majorana qubit with the measurement device can be turned on and off at will by changing the dc bias of the junction.