Session C31: Quantum Computing with Topological Superconductors

Live

By using a unique ring-shaped device based on h-BN sandwiched graphene with two electrostatic p-n junctions (pnJs) we have experimentally probed the interactions between integer quantum-Hall edge-states along the physical edges of graphene and at electrostatic edges defined by the pnJs. A first pnJ is used to decouple the edge-state of the energetically lowest Landau level (LL) from the others while a second pnJ senses the amount of interaction between the lowest LL and the rest. These multiple-pnJ measurements show that all edge-states interact strongly and equilibrate along the graphene physical edge while also confirming our previous results [1] that the lowest LL edge-state is decoupled from the other LL’s along the electostatic pnJ. By combining electrostatic and etched edges, chiral edge-states can be spatially separated at appropriate pnJs and then returned and mixed at physical boundaries. These results illustrate methods to manipulate chiral edge-states in graphene and are an advancement towards demonstrating the control of topologically protected chiral systems necessary for quantum logic operations.
[1] NN Klimov, et al., Phys. Rev B 92, 241301 (2015).   

Not Participating

Contextuality has been reported to be a resource for quantum computation, analogous to non-locality which is a known resource for quantum communication and cryptography. We show that the presence of contextuality places new lower bounds on the memory cost for classically simulating restricted classes of quantum computation. We apply this result to the simulation of a model of quantum computation based on the braiding of Majorana fermions, namely topological quantum computation (TQC) with Ising anyons, finding a saturable lower bound in log-linear in the number of physical modes for the memory cost. TQC model lies in the intersection between two computational models: the Clifford group and the fermionic linear optics (FLO), a framework analogous to bosonic linear optics. We extend our results and prove that the lower bound in the memory required in an approximate simulation of the FLO model is quadratic in the number of physical modes.   

Live

Andreev bound states (ABS) in semiconductor-superconductor hybrid structures have attracted considerable attention in the past decade.
We present a novel device geometry based on a semiconducting InAs two-dimensional electron gas proximitized by superconducting Al. The device allows for tunneling spectroscopy at the ends of a gate-defined nanowire with a grounded parent superconductor.
Preliminary results from a 600 nm long nanowire show that ABS can be induced and controlled in the nanowire by electrostatic gating. The bound states appear correlated at both ends of the nanowire in tunneling spectroscopy. To further demonstrate the high level of control, the ABS in the nanowire is brought on resonance with a local quantum-dot level. The effect of the resulting hybridization on the bound state is observed at the other end of the nanowire, which strongly indicates that we are indeed measuring an extended quantum state at two separate locations.   

Live

A semiconductor nanowire with strong spin-orbit coupling and induced superconductivity can host Majorana bound states. Using them in topological quantum computation usually requires braiding them as well as nucleating and fusing pairs of Majorana fermions. In all these processes, the time evolution should be adiabatic in order to prevent any qubit errors triggered by transitions above the bandgap. In this study, we investigate the maximum speed for remaining in the adiabatic limit during these manipulations. In particular, we derive the criteria for nucleation and fusion of Majorana bound states to remain adiabatic. To obtain our results, we use the density-matrix renormalization group and exact diagonalization as numerical techniques and compare those to analytical results from perturbation theory.   

Live

Semiconductor/superconductor hybrid nanowire-based devices in a cQED implementation are a promising platform for the detection of properties related to topological superconductivity. Here we study a gate-controlled Josephson junction, formed by selectively removing Al in a lithographically defined segment of a hybrid InAs/Al half-shell nanowire. The junction is incorporated in a transmon device geometry which enables both low-frequency transport studies and coherent time domain qubit control via cQED techniques. Variation of voltages on nearby electrostatic gates allows for drastic changes in the qubit frequency response as function of parallel magnetic field. The effects observed experimentally are in agreement with a theoretical model that suggests flux-modulated energies of Andreev bound states within the junction.   

Live

I will provide a status report on the progress toward topological quantum computing using non-Abelian Majorana qubits in the semiconductor-superconductor hybrid platform. I will cover theory, experiments, materials development, and device fabrication. Much has happened, but a lot still needs to be done. I will propose a roadmap for the future.   

Live

By now, there has been a lot of evidence of the existence of Majorana bound states (MBSs) at the ends of topological superconductors (TSs) [1]. However, a definitive proof of their topological origin will rely on the demonstration of their non-abelian statistics, emerging after the exchange of two or more MBSs in real space. Alternatively, MBSs can be exchanged in parameter space using charge-transfer operations using a quantum dot (QD) coupled to two TSs [2]. In this presentation I will analyze the efficiency of these operations [3]. Using a full counting statistics analysis, we set bounds to the optimal operation time scales. The lower bound depends on the phase difference, due to a partial decoupling of the different parity sectors. The upper bound is determined by poisoning processes due to the tunneling of quasiparticles to the MBSs. Using realistic parameters, we find that operations can be performed with a fidelity close to unity in the μs to ms timescales, demonstrating the absence of dephasing and accumulated dynamical phases.

[1] R. Lutchyn et al. Nat. Rev. Mat. 3, 52 (2019).
[2] K. Flensberg, Phys. Rev. Lett. 106, 090503 (2011).
[3] R. Seoane Souto, K. Flensberg and M. Leijnse. Phys. Rev. B 101, 081407 (2020)   

Live

Hybrid topological-superconducting systems engineered by combining superconducting circuits with 1D Majorana Bound States (MBS) have been proposed as possible platforms for quantum computation. In these systems the topological states are formed by inducing p-wave superconductivity in nanowires in contact with the superconducting leads. Among these proposals there is the recent idea of encoding the quantum information in a basis of fermion parity states originating from an additional hybridization between MBSs of different nanowires placed across a Josephson Junction [1]. Even if the coupling between the two Majorana fermions sacrifices their full topological protection, the system gains a highly anharmonic spectrum and it has been proposed that it can be used for engineering a coherent qubit [2]. Here we focus on the theoretical study of this system's dynamics in the case of time-dependent voltage bias. Within this scenario, we investigate possible protocols for implementing single qubit gates in the system, together with an analysis of the effect of the charge noise on them.
[1] E. Ginossar and E. Grosfeld, Nat. Commun. 5, 4772 (2014); [2] K. Yavilberg, E. Ginossar and E. Grosfeld, Phys. Rev. B 92 (7), 075143 (2015);   

Live

We theoretically study a scheme to distinguish the two ground states of a one-dimensional topological superconductor, which could serve as a basis for the readout of Majorana qubits. The scheme is based on parity-to-charge conversion, i.e., the ground-state parity of the superconductor is converted to the charge occupation on a tunnel-coupled auxiliary quantum dot. We describe how certain error mechanisms degrade the quality of the parity-to-charge conversion process. We consider (i) leakage due to a strong readout tunnel pulse, (ii) incomplete charge Rabi oscillations due to slow charge noise, and (iii) charge relaxation due to phonon emission and absorption. In a case study based on InAs heterostructure device parameters, we estimate that the parity-to-charge conversion error is mainly due to slow charge noise for weak tunnel pulses and leakage for strong tunnel pulses. Journal reference: Phys. Rev. B 101, 235441 (2020).   

Live

Superconducting transmon qubits are frontrunners in the race to build a scalable quantum computer. Gatemons are a transmon variant with the metal-oxide Josephson junction replaced by a voltage-controlled semiconductor, eliminating crosstalk and heating from flux-bias currents, and enabling new topologically-protected modes of operation. Gatemons with proximitized III-Vs are difficult to scale [1], or have short relaxation times due to losses in the host substrate [2]. Both require substantial magnetic fields to tune to the topological regime. Here we introduce a new gatemon platform based on V-VI semiconductor (Bi_xSb_1-x)₂Te₃ 3D topological insulators. We use selective area growth and nanostencil lithography on silicon for scalable fabrication of low-loss TI-gatemon (timon) circuits, and explore the prospect of using magnetic dopants to induce topological protection at zero field. Initial results suggest the timon platform is reliable and robust enough for next-generation gatemons [3].

[1] T. W. Larsen, et al., Phys. Rev. Lett. 115, 127001 (2015)
[2] L. Casparis, et al., Nature Nanotech. 13, 915–919 (2018)
[3] T. W. Schmitt, et al., arXiv:2007.04224 (2020)   

Live

Hybrid superconductor-semiconductor nanowires are considered a prime candidate for hosting Majorana zero modes. For their creation, readout and manipulation, one relies on tunable tunnel gates. More specifically, these gates govern the coupling between a nanowire and another system, including quantum dots, leads or another nanowire. Constructing a fault-tolerant topological quantum computer relies on having fine-tuned tunnel couplings between all the sub-systems. These couplings are probed in transport, by controlling the conductance of an island using tunnel gates. We employ the Mahaux-Weidenmüller formula to calculate the scattering matrix for an island connected to leads. Splitting off the tunnel junctions, one retrieves the tunneling matrix elements between the leads and system. Hence, we utilize this Barrier-Integrated Mahaux-Weidenmüller formula to estimate tunnel couplings to Majorana zero modes in a range of geometries, including realistic devices.