Session B38: Topological Platforms: Device, Transport, Braiding

Vortex-enabled Andreev processes in quantum Hall-superconductor hybrids

Quantum Hall-superconductor heterostructures provide possible platforms for both Majorana zero modes and parafermionic generalizations.  Motivated by several recent experiments that successfully integrated these phases, we investigate transport through a proximitized integer quantum Hall edge---paying particular attention to the impact of vortices in the superconductor.  By examining the downstream conductance, we identify regimes in which sub-gap vortex levels mediate Andreev processes that would otherwise be frozen out in a vortex-free setup.  Moreover, we show that at finite temperature, and in the limit of a large number of vortices, the downstream conductance averages to zero, indicating that the superconductor effectively behaves like a normal contact.  We discuss these results in the context of existing transport measurements on quantum Hall-superconductor hybrids.    

SWAP gate between a Majorana qubit and a parity-protected superconducting qubit

In a noisy quantum computing environment, fast gates are necessary to overcome limitations from decoherence. At the same time, the storage of quantum information requires long-lived disconnected subspaces, where information can be stored before and after actual quantum computation.  We propose transduction of information by coupling a Majorana qubit to a parity-protected superconducting qubit based on π-periodic Josephson junctions, where tunneling of pairs of Cooper pairs preserves the Cooper pair parity. In the regime EC ≤ E_J the charging energy can resolve one Cooper pair in the superconducting island and thus distinguish the two states of the Majorana qubit. We show how this enables the implementation of a C-phase gate, and through proper driving of the Majorana qubit we can obtain a SWAP gate between the two. The point of the coupled circuit is that fast gates can be performed with the superconducting qubit and the information can be swapped and stored in the Majorana qubit.   

Braiding Majorana Fermions with Magnetic Skyrmions

After a decade of intense theoretical and experimental efforts, demonstrating braiding of Majorana fermions remains an unsolved problem in condensed matter physics due to platform specific challenges. In this work, we propose topological superconductor (tSC) – magnetic multilayer (MML) heterostructures, with on-chip microwave cavity readout, as a novel platform for initializing, braiding, and reading out Majorana fermions. Stray fields from a skyrmion (Sk) in the MML can nucleate a vortex (Vx) in the tSC, known to host Majorana bound states (MBS) at its core. We show that our nucleation and braiding scheme can be achieved with a variety of existing options for tSC and MML. We further demonstrate that the Sk and the Vx bind strongly and move together without dissociation up to speeds enough to complete Majorana braiding within quasiparticle poisoning time. By patterning the MML into a track and by driving Sks in the MML with local spin-orbit torques, we show that the Sk-Vx compound objects can be efficiently moved along the track, thereby facilitating braiding of the Majorana modes at the centers of the Vxs. Finally, we show that the coupling of the MBS to the cavity field leads to easily observable parity dependent dispersive shift of the resonator frequency.   

Coupling of SET to lateral S-TI-S Josephson junction for parity readout and fusion of Majorana bound states

Current developments toward topologically protected quantum computing rely heavily on the verification of the existence of Majorana bound states (MBS). A measurement of the parity of MBS is necessary for their implementation in topological qubit operations. We propose experiments for probing parity of MBS in Superconductor-Topological Insulator-Superconductor (S-TI-S) lateral Josephson junctions, in which MBS are nucleated at Josephson vortex cores where the phase difference across the junction is an odd multiple of π. We design two types of single-electron transistors (SETs) for parity experiments: the Al/AlO_x/Al SET which is sensitive to the parity of MBS pairs, and a SET with an Au quantum dot for demonstrating fusion of MBS. We report progress toward implementing these devices with S-TI-S junctions for the purpose of incorporation into circuits for qubit braiding operations.   

Open quantum dot model based on three-dimensional topological insulator nanoribbon

The visibility of the protected surface states of a three-dimensional topological insulator (TI) in transport experiments is strongly suppressed due to the residual bulk contribution to electronic transport. However, TI nanoribbons (TINR) have proven very effective in enhancing the surface state contribution as has been experimentally evidenced by Aharonov-Bohm oscillations. We propose a TINR geometry that can potentially confine the surface electronic states also in the second direction, along the TINR. In this geometry, in the sub-gap region, we find resonant transmission due to the formation of bound states at certain energies. We theoretically study the resonant electron tunnelling through such a quantum dot (QD) attached to TINR leads as a function of the system parameters within the Landauer-Buttiker formalism. External magnetic and electric field tunability of the quantum dot level structure makes the dot feasible for industrial applications. We also investigate the smooth and sharp interfaces incorporating the effect of spin-connection which plays an important role in the motion of the Dirac particles in curved space. Further, we analyse the effect of the Coulomb blockade on the properties of the TI QD and discuss relevant system parameters that are useful to experimentally realize a QD based on the TINR.    

Active correction of fermionic parity-preserving errors in an individual Majorana qubit

Quantum information stored in the Majorana modes of a topological superconductor is only partially protected against fermionic parity-preserving local errors, due to finite-size effects. We address the problem whether total protection against such errors can be achieved by employing active error-correction techniques on an individual Majorana qubit. Majorana qubits in the tetron architecture are modeled by a pair of Kitaev chains. We show numerically that, for any parameter values in the topological phase, the two degenerate ground states that act as the physical qubit levels form an approximate error-correcting code, which can correct fermionic parity-preserving local errors on any one of the chains. We further propose a method to construct quasi-local syndrome measurements and correction procedures, and demonstrate our method for a few generic parameter values. Our results are achieved by re-expressing the spectrally flattened Hamiltonian of the Kitaev chain as a sum of commuting quasi-local terms. Our results indicate that each individual topological qubit can be made fully robust against fermionic parity-preserving local errors, thereby reducing the number of physical qubits required for fault-tolerant computation in comparison to the existing schemes.   

Superconducting Circuits for Probing Quantum Materials

Superconducting quantum circuits are a natural platform for probing and understanding existing and new quantum materials, capitalizing on the precise control and detection of microwave excitations offered by the circuit QED toolbox. We propose to realize a transmon-like qubit fabricated with superconductor-topological insulator-superconductor (S-TI-S) junctions. Spectroscopic and time-domain measurements of this TI-transmon could reveal coherent transport properties of the TI material at the single quantum level. I will describe our experimental progress, and discuss other related efforts on using superconducting circuits to probe material excitations.   

Engineered Topological Quantum Networks

Contemporary quantum devices suffer from our inability to control quantum noise. Hypothesised emergent condensed matter excitations, such as Majorana modes, offer in principle protection against the effects of noise since they are protected by the system's symmetries. However, such native topological particles have proven extremely difficult to identify, verify and control. In parallel to these developments, topology has been successfully used in classical metamaterials and topological phenomena originally thought of as purely quantum have been observed and reproduced. In this work, we apply the principles of classical topological metamaterial design to the engineering of novel quantum devices. Specifically, we utilise topology appropriately in order to control quantum systems in the presence of noise. We design engineered topological quantum networks consisting of experimentally accessible quantum device components and simulate their ability to transfer quantum information in a topologically protected manner under realistic experimental conditions. We present a thorough proposal for the experimentally verifiable quantum device where quantum information is transferred as an emergent effect of the topological structure of the quantum network.   

Nonabelian time evolution in a chaotic Majorana billiard

We discuss signatures of the nonabelian nature of Majorana bound states in a quantum-chaotic setting. We consider a "chaotic Majorana billiard", which consists of a chaotic cavity coupled to topological superconductors via point contacts. In the limit of vanishing transmission, each of these contacts hosts a Majorana zero mode. Close to a cavity resonance, a finite transparency of the contacts couples the Majorana modes, but a ground-state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the cavity exceeds five. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold can be achieved. We characterize the corresponding nonabelian Berry phase using random matrix theory and discuss a measurable signature of the nonabelian time evolution in terms of the cavity charge as well as differences between the cases of a cavity coupled to Majorana zero modes and to Andreev bound states.   

Protocol for Detecting the Non-locality of the Multi-Majorana Systems

Majorana zero modes (MZMs) are non-abelian anyons that can be used to build topologically protected qubits. MZMs can encode quantum information non-locally and therefore is potentially useful for building fault tolerant quantum computer. If a multi-Majorana system is physically divided into two subsystems in some special ways, there is always non-trivial quantum correlation between the two parts. However, in physical systems, if the preparation of MZMs fails, the system can include trivial fermionic modes, in which the non-locality no longer present. In our work, we developed a protocol using an entanglement witness to measure the nonlocality of the Majorana systems, and also to distinguish perfect Majorana system from the systems contaminated by fermionic modes. The witness only requires parity measurements, and we also design a platform for potentially performing the protocol experimentally. We found that for a simple example, the probability of success is about 42%. We also looked into the performance of the witness in systems with environmental noise.   

Universal conductance scaling of Andreev reflections using a dissipative prob: Majorana vs Andreev

We study the dissipative quantum tunneling due to Andreev reflections.  We obtain the special scaling behaviors of the tunneling conductance with the temperature or the voltage. We show that the tunneling conductance to a normal Andreev bound state (ABS) will be suppressed with special power-law behaviors when decreasing the temperature, which shows a sharp contrast with that to a Majorana zero mode. Various specific cases have been studied, including the cases that two charges involved in an Andreev reflection process maintain/lose coherence before dissipated, and also the cases with multiple ABSs along with and without a Majorana mode.  We also give the characteristics of con-ductance peaks in each case, which will help experimenters identify the state observed, especially distinguish between the Majorana resonance and the normal Andreev resonance. Finally, we will discuss the experimental progresses on hybrid superconductor-semiconductor nanowire using this dissipative prob.   

Zero-bias conductance peaks induced by Yu-Shiba-Rusinov spin screening in double quantum dots

The subgap states of hybrid superconducting semiconductor nanowire devices possess rich physical phenomena, including Andreev bound states and Majorana bound states. Most transport experiments distinguish them by measuring the zero-bias conductance peaks (ZBCPs), which is still ambiguous. In this work, we demonstrate that robust ZBCPs can be induced by Yu-Shiba-Rusinov (YSR) spin screening in such hybrid device with a double-quantum-dot structure, one coupled to a normal metal and another to a superconductor. Through tunneling spectroscopy, we identified several regimes of different coupling strength in gate space, as well as the singlet and doublet states with or without YSR spin screening. Interestingly, when an axial magnetic field was applied, we observed robust ZBCPs for the spin screened states, but not for the unscreened states. This provides an important mechanism for the formation of ZBCPs and a relevant comparison to benchmark Majorana bound states.   

Majorana zero modes in a nanowire network

We study theoretically ways to use physical Majorana zero modes in semiconductor nanowire junctions to build logical Majorana zero-mode states on a network. Employing symmetry arguments, we determine the number of zero modes that can exist on junctions of arbitrary coordination and for various magnetic and spin-orbit field configurations. We use these results to construct a honeycomb network of zero-mode-carrying wires and compute several of its spectral characteristics, such as local and global density of states. We also study ways to perform non-Abelian braiding operations on zero modes supported by the honeycomb network.