Session Z52: Topological Qubits and Phases

Microwave spectroscopy of Andreev bound states in topological insulator-based Josephson junctions

An interest in topological superconductivity is fueled by the promise to realize non-Abelian excitations, a pursuit which has both an intellectual and a practical appeal.  One of the first proposals to realize a topological superconductor is a heterostructured material that combines a topological insulator (TI) and a conventional superconductor (SC). Despite a decade of intense studies, supercurrent dynamics in TI/SC Josephson junctions is poorly understood. One of the hallmarks of a topological Josephson junction is the 4$pi$ periodicity of the energy spectrum of in-gap Majorana excitations, which distinguishes these modes from 2$pi$ periodic Andreev states. The difference is most apparent when a phase difference of $pi$ is applied across the junction, at this phase bias Majorana modes cross at zero energy, while Andreev states remain gapped. We report investigation of low energy spectrum of in-gap excitation in TI/SC Josephson junctions using microwave spectroscopy. The junctions are fabricated from topological insulator BiSbTeSe2 nanoribbons with Ti/Al superconducting electrodes. The junctions are incorporated into an rf-SQUID coupled inductively to a high-Q microwave resonator circuit. Using the microwave photons as a probe, in-gap excitations can be coherently coupled to microwave photons and transition energy between states can be readout by the response of the coupled microwave resonator.   

Signatures of Majorana States in the Current-Phase Relation of Lateral S-TI-S Josephson Junctions

Superconductor-Topological Insulator-Superconductor (S-TI-S) lateral Josephson junctions are explored as a platform for topologically-protected Majorana-based quantum computing. In the S-TI-S junction barrier, Majorana bound states (MBS) are nucleated at the cores of Josephson vortices where the local phase difference is an odd multiple of π. Due to the presence of MBS, the current-phase relation of an S-TI-S junction is modified to include a 4π-periodic contribution. We describe and present results from two experiments designed to measure the current-phase relation directly via phase-sensitive Josephson interferometry in two regimes. The first uses a SQUID interferometer circuit that allows measurement of the CPR in the absence of an applied magnetic field and is sensitive to extended Majorana states in the junction. The second uses transport measurements of the magnetic field dependence of the critical current in asymmetric SQUIDs that yields the CPR of the smaller junction and is sensitive to localized Majorana states.   

Microwave Spectroscopy in Hybrid Semiconductor-based Josephson Junctions

Planar semiconductor-based Josephson junctions (JJs) offer a unique platform for realizing tunable qubits and the potential for hosting topological qubits. When these junctions are inserted in a cavity quantum electrodynamic (QED) circuit, the energy spectrum of Andreev bound states (ABSs) in the junction, can be probed using microwave spectroscopy. We study the ABSs of Al-InAs JJs by inductively coupling the JJ in a superconducting loop to a coplanar waveguide superconducting resonator. By monitoring the resonator's response using dispersive readout techniques, we probe for transitions between ABSs and quasiparticle poisoning events.   

Realizing Majorana zero modes using Josephson Junction arrays

We design a 1-D array of Josephson junctions that features Majorana zero modes (MZM) at its edges.  This analog quantum circuit is described by the quantum Sine-Gordan (qSG) model, a prototypical example of an integrable system exhibiting Symmetry Protected Topological (SPT) phases.  By tuning various parameters in the circuit, one can probe the qSG model in both the semi-classical regime and quantum regime where the qSG corresponds to the Massive Thirring (MT) model.  In the quantum regime, the phase accumulations correspond to genuine quantum numbers associated with Majorana zero modes (MZM) which are protected by the symmetries of the system.  By virtue of its tunability, the system also provides a platform to investigate the stability of the MZM in the face of integrability-breaking perturbations.   

First Principles Assessment of ZnTe and CdSe as Tunnel Barriers for the InAs/Al Interface

Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise at interfaces between a superconductor and a semiconductor with strong spin-orbit coupling, such as Al on InAs. 

However, proximity to the superconductor may also adversely affect the semiconductor’s local properties. A tunnel barrier inserted at the interface could resolve this issue by tuning the coupling strength. We assess the wide band gap semiconductors, ZnTe and CdSe, as candidate materials to mediate the coupling between Al and InAs. 

To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization. We study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer and tri-layer interfaces. DFT simulations indicate the relevant barrier thickness range to investigate experimentally.    

Exploring Mobility in ZnTe-Coated InAs Nanowires

Nanowire-based devices have rapidly emerged as key elements in the realm of

nanoelectronics and quantum computing. ZnTe is a wide bandgap semiconductor

material that can be used to create heterostructures when combined with other

semiconductor materials, such as InAs. These heterostructures can be host to

quantum wells and quantum dots, which makes them valuable for quantum

computing and photonics technology. Due to the heterovalent nature of the

interface, a better understanding of the electronic properties is necessary. Our

research explores how ZnTe shell coatings influence the mobility of InAs nanowires.

Our analysis will include TEM results showing lattice structure and thickness of ZnTe

shells.   

Qubits and gate operations in a topologically protected system of a toroidal flux coupled to an electron

We study a model of quantized toroidal magnetic flux coupled to a charged particle through field-free interaction. We solve this model and show that the topological and nonlocal aspects of this Aharonov-Bohm-like system can have profound applications in quantum information. We show how these flux qubits are protected from the environmental noise, and how to do nonlocal operations on them including creating entanglement between them.   

Multi-qubit Gates for Fibonacci Topological Qubits

We construct braiding patterns that approximate Toffoli and fan-out gates for Fibonacci anyons. These new constructions considerably reduce the implementation cost of logical fault-tolerant quantum computation with Fibonacci anyons.   

Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation

All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-onsite symmetry, which is unable to deterministically teleport gates and which is characterized by a non-degenerate entanglement spectrum. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry.   

Torus algebra and logical operators at low energy

We can study all universal properties of 2+1D topologically ordered states under the unitary monoidal tensor category (UMTC) descriptions. In this work, we investigate the torus algebra, originally introduced by Ma etc. [Phys. Rev. B 107, 085123 (2023)], and show that it is exactly the algebra of all local operators acting on the low energy subspaces of a topologically ordered state on a torus. The simple modules over torus algebra (irreducible blocks after decomposition) enumerates all possible low-energy subspaces. We discovered the underlying vector spaces of modules corresponding to the ground state subspaces of a punctured torus. We also discuss an example of idempotent decomposition of a chiral ising model using our algorithm.   

Exotic gapped boundaries of fracton phases in the Checkerboard model

Fracton topological order characterizes a new class of unconventional phases of matter and/or quantum error correcting codes. It involves exotic excitations with restricted mobility and ground-state degeneracy (GSD) growing with the size of the system. However, fracton models are often defined for infinite systems, and our understanding of their boundary theories is still incomplete. Here, we investigate possible boundaries for the Checkerboard model, a paradigmatic fracton model on the 3D cubic lattice. We focus on two cases: a horizontal boundary, along the (001) plane, and an oblique boundary, along the (111) plane, with periodic boundary conditions in the other directions. We discuss the GSD and the properties of boundary excitations (braiding statistics and boundary condensation) in these two cases. Finally, we discuss enforcing open boundary conditions in all directions, and the robustness of the GSD and of the logical qubits to such boundary conditions.   

Optimized preparation of magic state for parafermionic qudits via non-adiabatic braiding

Parafermionic zero modes (PZMs) offer some benefits compared to Majorana zero modes (MZMs), exhibiting resilience against dissipation, realizing a full many-qudit Clifford group, and allowing more efficient magic state distillation. Notwithstanding, neither PZMs nor MZMs support topological non-Clifford gates, and thus, per Gottesman--Knill theorem, can be classically simulated. However, adiabatic manipulations yielding geometric phases can realize high-quality magic gates in MZMs, enabling universal computation.

We show that such an approach is not applicable to parafermions: any adiabatic manipulation that preserves the ground state degeneracy yields Clifford gates. We suggest an alternative protocol, using non-adiabatic effects to construct the magic gate for qudits realized by parafermions while preserving a fixed number of zero modes and thus avoiding dynamical phase accumulation.

We show that protocol parameters, such as speed and coupling strength, can be optimized, resulting in a protocol robust against generic low-frequency noise with a specified yield of high-fidelity magic states.   

Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits

We use dual-unitary circuits, which are unitary even when read 'sideways', as the basis of a new framework for measurement-based quantum computation (MBQC). In particular, applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. We study the dynamics of the 1D kicked Ising chain and find that after k time-steps, equivalent to a depth-k quantum circuit, we obtain a resource state for universal MBQC on ∼3k/4 logical qubits. This removes the usual requirement of going to 2D to achieve universality, thereby reducing the demands imposed on potential experimental platforms. We also show that our resource states belong to a new class of symmetry-protected topological phases with spatially modulated symmetries, and that our protocol is robust to symmetric deformations.