Majorana Superconducting Qubit

We propose a platform for universal quantum computation that uses conventional $s$-wave superconducting leads to address a topological qubit stored in spatially separated Majorana bound states in a multi-terminal topological superconductor island. Both the manipulation and read-out of this "Majorana superconducting qubit" are realized by tunnel couplings between Majorana bound states and the superconducting leads. The ability of turning on and off tunnel couplings on-demand by local gates enables individual qubit addressability while avoiding cross-talk errors. By combining the scalability of superconducting qubit and the robustness of topological qubits, the Majorana superconducting qubit may provide a promising and realistic route towards quantum computation

Parity-controlled 2π2\pi Josephson effect mediated by Majorana Kramers pairs

We study a time-reversal-invariant topological superconductor island hosting spatially separated Majorana Kramers pairs, with weak tunnel couplings to two s-wave superconducting leads. When the topological superconductor island is in the Coulomb blockade regime, we predict that a Josephson current flows between the two leads due to a non-local transfer of Cooper pairs mediated by the Majorana Kramers pairs. Interestingly, we find that the sign of the Josephson current is controlled by the joint parity of all four Majorana bound states on the island. Consequently, this parity-controlled Josephson effect can be used for qubit read-out in Majorana-based quantum computing

Spin-valley density wave in moir\'e materials

We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined

Quantum Computing with Majorana Kramers Pairs

We propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the "Majorana Kramers Qubit". All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic fields - which typically reduce the superconducting gap size of the island - suggests a unique robustness of our qubit to quasiparticle poisoning due to thermal excitations. Consequently, the Majorana Kramers Qubit should benefit from prolonged coherence times and may provide an alternative route to a Majorana-based quantum computer

Dissipationless Nonlinearity in Quantum Material Josephson Diodes

Dissipationless nonlinearities for three-wave mixing are a key component of many superconducting quantum devices, such as amplifiers and bosonic qubits. So far, such third-order nonlinearities have been primarily achieved with circuits of concatenated Josephson tunnel junctions. In this work, we theoretically develop an alternative approach to realize third-order nonlinearities from gate-tunable and intrinsically symmetry-broken quantum material Josephson junctions. We illustrate this approach on two examples, an Andreev interferometer and a magnetic Josephson junction. Our results show that both setups enable Kerr-free three-wave mixing for a broad range of frequencies, an attribute that is highly desirable for amplifier applications. Moreover, we also find that the magnetic junction constitutes a paradigmatic example for three-wave mixing in a minimal single-junction device without the need for any external biases. We hope that our work will guide the search of dissipationless nonlinearities in quantum material superconducting devices and inspire new ways of characterizing symmetry-breaking in quantum materials with microwave techniques

Proximity-induced Josephson π\pi-Junctions in Topological Insulators

We study two microscopic models of topological insulators in contact with an $s$-wave superconductor. In the first model the superconductor and the topological insulator are tunnel coupled via a layer of scalar and of randomly oriented spin impurities. Here, we require that spin-flip tunneling dominates over spin-conserving one. In the second model the tunnel coupling is realized by an array of single-level quantum dots with randomly oriented spins. It is shown that the tunnel region forms a $\pi$-junction where the effective order parameter changes sign. Interestingly, due to the random spin orientation the effective descriptions of both models exhibit time-reversal symmetry. We then discuss how the proposed $\pi$-junctions support topological superconductivity without magnetic fields and can be used to generate and manipulate Kramers pairs of Majorana fermions by gates

Majorana bound states in topological insulators and nanowires

Quantum computers outperform classical computers by achieving exponential increases in calculation speed for certain types of problems and for that reason have great potential to revolutionize computing. Compared to their classical counterparts the elementary units of information in a quantum computer are not the classical bits, zero and one, but rather the so-called quantum bits (or qubits) which most generally are quantum mechanical superpositions of the zero and one state. Unfortunately, the quantum bits are highly sensitive to the effects of environmental noise and consequently storing the quantum information in a robust manner represents a major challenge. Historically, it was Kitaev in 2001 who first proposed that this problem can be circumvented by using Majorana bound states as the building block for robust, so-called topologically protected, qubits. Subsequently, it was Fu et al. in 2008 who proposed the first realistic setup for generating Majorana bound states, namely topological insulator-superconductor heterostructures where the Majorana bound states can emerge within vortex cores. Moreover, in 2010 Lutchyn et al. as well as Oreg et al. put forward that Majorana bound states can also appear at the ends of semiconductor Rashba nanowires which are proximity-coupled to an s-wave superconductor and subject to a magnetic field. Finally, in 2013 Klinovaja et al. found that Majorana bound states can arise in chains of magnetic atoms that are deposited on a superconducting substrate. Within the last years these theoretical proposals have all been implemented experimentally and the first signatures for Majorana bound states, such as zero-bias conductance peak measurements, were reported. However, despite these encouraging experimental results, there still exists a broad range of open questions and hurdles. In this thesis, we address some of the most important experimental challenges and present new theoretical solutions. In the first part of this thesis, we introduce two new platforms for generating Majorana bound states based on proximity-induced Pi Josephson junctions in topological insulators and crossed-Andreev pairing between semiconductor Rashba nanowires. Unlike the current experimental setups, the proposed schemes require either low magnetic fields or no magnetic fields at all. The latter characteristic constitutes a compelling improvement over current experimental setups for two reasons: (1) The detrimental effects of the magnetic fields on the superconductivity are either reduced or completely avoided. (2) In current experimental schemes the proximity-induced superconducting gap, which assures the topological protection of the Majorana qubits, is well-defined only at low magnetic fields (``hard gap"). At strong magnetic fields, a finite subgap conductance arises (``soft gap") and destroys the topological protection . Hence, with regards to future experiments on quantum information procession with Majorana bound states, a setup operated at lower magnetic field is highly desirable. In the second part of this thesis, we propose a new method for detecting Majorana bound states based on quantum dot Phi_0 Josephson junctions. Here, we are motivated by the search for new, more conclusive indicators for Majorana bound states which is one of the most urgent challenges following the experimental results mentioned above. In fact, the recent zero-bias conductance peak measurements only constitute a sufficient, but not a necessary condition for the emergence of Majorana bound states. That is to say, the zero-bias conductance peaks can be explained by a multitude of different physical effects which are completely unrelated to the presence or absence of Majorana bound states. Interestingly, in the case of quantum dot Phi_0 Josephson junctions, the required ingredients largely overlap with those necessary to obtain Majorana bound states in Rashba nanowire systems. This motivated us to compare both the trivial superconducting and the topologically superconducting regimes of quantum dot Phi_0 Josephson junction and work out qualitative differences that can serve as new indicators for Majorana bound states. In the final part of the thesis, we put forward a scalable scheme for quantum computation based on both Majorana bound state qubits and conventional spin qubits. The motivation for this part is three-fold: (1) The topological Majorana qubits are not universal for quantum computation. That is to say, not every logical quantum gate necessary to perform a quantum computation can be executed using Majorana braiding alone. For that reason, we couple the Majorana qubit to another type of qubit, namely the spin qubit, which can supplement the logical quantum gates that cannot be carried out on the Majorana qubits. (2) Spin and Majorana qubits are complementary with regards to their strengths and weaknesses. For example, unlike spin qubits, the Majorana qubits are intrinsically robust against unwanted perturbations and noise. At the same time spin qubits allow for significantly faster operations times compared to Majorana qubits. The hybrid spin-Majorana qubit which we develop in this chapter allows us to combine the best features of both worlds. (3) To utilize the full power of a quantum computer, it is not enough to consider a single qubit alone. What we need is a collection of many qubits making up a so-called surface code architecture on which many operations can run in parallel. We thus show how to construct a scalable network of the spin-Majorana hybrid qubits that can readily be experimentally implemented based on recent breakthroughs in the lithographic fabrication of Majorana nanowires in InAs/Al heterostructures

Entangling transmons with low-frequency protected superconducting qubits

Novel qubits with intrinsic noise protection constitute a promising route for improving the coherence of quantum information in superconducting circuits. However, many protected superconducting qubits exhibit relatively low transition frequencies, which could make their integration with conventional transmon circuits challenging. In this work, we propose and study a scheme for entangling a tunable transmon with a Cooper-pair parity-protected qubit, a paradigmatic example of a low-frequency protected qubit that stores quantum information in opposite Cooper-pair parity states on a superconducting island. By tuning the external flux on the transmon, we show that non-computational states can mediate a two-qubit entangling gate that preserves the Cooper-pair parity independent of the detailed pulse sequence. Interestingly, the entangling gate bears similarities to a controlled-phase gate in conventional transmon devices. Hence, our results suggest that standard high-precision gate calibration protocols could be repurposed for operating hybrid qubit devices

Low-field Topological Threshold in Majorana Double Nanowires

A hard proximity-induced superconducting gap has recently been observed in semiconductor nanowire systems at low magnetic fields. However, in the topological regime at high magnetic fields, a soft gap emerges and represents a fundamental obstacle to topologically protected quantum information processing with Majorana bound states. Here we show that in a setup of double Rashba nanowires that are coupled to an s-wave superconductor and subjected to an external magnetic field along the wires, the topological threshold can be significantly reduced by the destructive interference of direct and crossed-Andreev pairing in this setup, precisely down to the magnetic field regime in which current experimental technology allows for a hard superconducting gap. We also show that the resulting Majorana bound states exhibit sufficiently short localization lengths, which makes them ideal candidates for future braiding experiments