Topological Qubits Research Articles

Topological superconductivity and Majorana fermion

Topological superconductor is described by a full pairing gap in the bulk with nonzero topological number and gapless surface states consisting of Majorana fermion that is a hypothetical particle of its own. Here, being its own means that a Majorana fermion should be an equal superposition of an electron and a hole state. The emergence of Majorana fermions is the most prominent characteristic of topological superconductors. In particle physics, it is still unclear if there are some elementary particles that are Majorana fermions, but importantly, they are likely to exist as quasiparticle excitations in certain condensed matter systems. It has drawn much attention in the content of Majorana fermions recently in particular the condensed matter physics area, since these Majorana states are ideal platform for non-Abelian statistics studies and can be used to fabricate as topological qubit, thus having great potential application in fault-tolerant topological quantum computation. A general introduction to the remarkable properties of Majorana fermions in condensed matter systems will be introduced following the story from Dirac equation to Majorana equation. Then this review elaborates a variety of routes to topological superconductivity in the realm of condensed mater physics, from Majorana modes in zero dimension to one dimension, that is, Majorana bound state and Majorana edge state. These Majorana states are localized states and propagating states respectively, but still obey non-Abelian statistics and remain their topological properties. Specifically, one-dimensional tight-binding model of a p-wave superconductor and a magnetic Fe chain with superconducting pairing are representative platforms for hosting Majorana bound states at the wires ends. Some emergent topological material systems, such as topological insulator, quantum spin Hall insulator, and quantum anomalous Hall insulator are two-dimensional material systems that can not only accommodate Majorana bound states but also Majorana edge states. Different material systems, from one-dimension quantum wire to two-dimension material system, from hybridized system to intrinsic system, will also be discussed specifically. Relevant theoretical studies and experimental results that show possible signatures of topological superconductivity and Majorana states are summarized as well. Particularly, experimental signatures of these Majorana states, such as zero-bias conductance peaks in tunneling spectra due to Majorana bound states, quantization of conductance in magneto-electric transport measurements due to chiral Majorana edge states, and some unconventional superconductivities in intrinsic topological superconductors will be briefly reviewed. Insights about methods to perspectives to realize topological quantum computation is provided at the end, emphasizing the braiding using different Majorana states. The goal of this review is to provide a general introduction to the subject for either experimentalists or theorists who are new to this field, focusing on the aspects and current progresses which are most important for understanding these basic physics.

Topological Qubits from Valence Bond Solids.

Topological qubits based on SU(N)-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with twofold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical Z rotation by an angle 2π/N, for any integer N>2, is provided by a global twist operation, which is of a topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.

What Are the Limits of Manipulating Nature?

The article discusses scientists' efforts to control quantum mechanic properties of nature, including of electrons and photons and the creation of topological qubits. An overview of quantum entanglement, including research conducted on entanglement by physicist Dirk Englund, is provided.

Soft phonon modes driven huge difference on lattice thermal conductivity between topological semimetal WC and WN.

Topological semimetals are currently attracting increasing interest due to their potential applications in topological qubits and low-power electronics, which are closely related to their thermal transport properties. Recently, the triply degenerate nodal points near the Fermi level of WC are observed by using angle-resolved photoemission spectroscopy. In this work, by solving the Boltzmann transport equation based on first-principles calculations, we systematically investigate the phonon transport properties of topological semimetals WC and WN. The predicted room-temperature lattice thermal conductivities of WC (WN) along the a and c directions are 1140.64 (7.47) W m-1 K-1 and 1214.69 (5.39) W m-1 K-1. Considering the similar crystal structure of WC and WN, it is quite interesting to find that the thermal conductivity of WC is more than two orders of magnitude higher than that of WN. It is found that, different from WN, the large acoustic-optical (a-o) gap prohibits the acoustic+acoustic → optical (aao) scattering, which gives rise to very long phonon lifetimes, leading to ultrahigh lattice thermal conductivity in WC. For WN, the lack of an a-o gap is due to soft phonon modes in optical branches, which can provide more scattering channels for aao scattering, producing very short phonon lifetimes. Further deep insight can be attained from their different electronic structures. Distinctly different from that in WC, the density of states of WN at the Fermi level becomes very sharp, which leads to destabilization of WN, producing soft phonon modes. It is found that the small shear modulus G and C44 limit the stability of WN, compared with WC. Our studies provide valuable information for phonon transports in WC and WN, and motivate further experimental studies to study their lattice thermal conductivities.

Template-Assisted Scalable Nanowire Networks.

Topological qubits based on Majorana Fermions have the potential to revolutionize the emerging field of quantum computing by making information processing significantly more robust to decoherence. Nanowires are a promising medium for hosting these kinds of qubits, though branched nanowires are needed to perform qubit manipulations. Here we report a gold-free templated growth of III-V nanowires by molecular beam epitaxy using an approach that enables patternable and highly regular branched nanowire arrays on a far greater scale than what has been reported thus far. Our approach relies on the lattice-mismatched growth of InAs on top of defect-free GaAs nanomembranes yielding laterally oriented, low-defect InAs and InGaAs nanowires whose shapes are determined by surface and strain energy minimization. By controlling nanomembrane width and growth time, we demonstrate the formation of compositionally graded nanowires with cross-sections less than 50 nm. Scaling the nanowires below 20 nm leads to the formation of homogeneous InGaAs nanowires, which exhibit phase-coherent, quasi-1D quantum transport as shown by magnetoconductance measurements. These results are an important advance toward scalable topological quantum computing.

Ultrahigh lattice thermal conductivity in topological semimetal TaN caused by a large acoustic-optical gap

Topological semimetals may have potential applications such as in topological qubits, spintronics and quantum computations. Efficient heat dissipation is a key factor for the reliability and stability of topological semimetal-based nano-electronics devices, which is closely related to high thermal conductivity. In this work, the elastic properties and lattice thermal conductivity of TaN are investigated using first-principles calculations and the linearized phonon Boltzmann equation within the single-mode relaxation time approximation. According to the calculated bulk modulus, shear modulus and C44, TaN can be regarded as a potential incompressible and hard material. The room-temperature lattice thermal conductivity is predicted to be 838.62 along the a axis and 1080.40 along the c axis, showing very strong anisotropy. It is found that the lattice thermal conductivity of TaN is several tens of times higher than other topological semimetals, such as TaAs, MoP and ZrTe, which is due to the very longer phonon lifetimes for TaN than other topological semimetals. The very different atomic masses of Ta and N atoms lead to a very large acoustic-optical band gap, and then prohibit the scattering between acoustic and optical phonon modes, which gives rise to very long phonon lifetimes. Calculated results show that isotope scattering has little effect on lattice thermal conductivity, and that phonons with mean free paths larger than 20 (80) along the c direction at 300 K have little contribution to the total lattice thermal conductivity. This work implies that TaN-based nano-electronics devices may be more stable and reliable due to efficient heat dissipation, and motivates further experimental works to study lattice thermal conductivity of TaN.

Anisotropic lattice thermal conductivity in three-fold degeneracy topological semimetal MoP: a first-principles study

Recently, three-component new fermions in topological semimetal MoP are experimentally observed (2017 Nature 546 627), which may have potential applications like topological qubits, low-power electronics and spintronics. These are closely related to thermal transport properties of MoP. In this work, the phonon transport of MoP is investigated by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). The calculated room-temperature lattice thermal conductivity is 18.41 and 34.71 along the in- and cross-plane directions, exhibiting very strong anisotropy. The isotope and size effects on the lattice thermal conductivity are also considered. It is found that isotope scattering produces little effect, and phonon has little contribution to the lattice thermal conductivity, when phonon mean free path (MFP) is larger than 0.15 at 300 K. It is noted that average room-temperature lattice thermal conductivity of MoP is lower than that of representative Weyl semimetal TaAs, which is due to smaller group velocities and larger Grüneisen parameters. Our works provide valuable informations for the thermal management of MoP-based nano-electronics devices, and motivate further experimental works to study thermal transport of MoP.

Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level.

Non-Abelian anyons are a type of quasiparticle with the potential to encode quantum information in topological qubits protected from decoherence. Experimental systems that are predicted to harbour non-Abelian anyons include p-wave superfluids, superconducting systems with strong spin-orbit coupling, and paired states of interacting composite fermions that emerge at even denominators in the fractional quantum Hall (FQH) regime. Although even-denominator FQH states have been observed in several two-dimensional systems, small energy gaps and limited tunability have stymied definitive experimental probes of their non-Abelian nature. Here we report the observation of robust even-denominator FQH phases at half-integer Landau-level filling in van der Waals heterostructures consisting of dual-gated, hexagonal-boron-nitride-encapsulated bilayer graphene. The measured energy gap is three times larger than observed previously. We compare these FQH phases with numerical and theoretical models while simultaneously controlling the carrier density, layer polarization and magnetic field, and find evidence for the paired Pfaffian phase that is predicted to host non-Abelian anyons. Electric-field-controlled level crossings between states with different Landau-level indices reveal a cascade of FQH phase transitions, including a continuous phase transition between the even-denominator FQH state and a compressible composite fermion liquid. Our results establish graphene as a pristine and tunable experimental platform for studying the interplay between topology and quantum criticality, and for detecting non-Abelian qubits.

Decoherence of Topological Qubit in Linear Motions: Decoherence Impedance, Anti-Unruh and Information Backflow

In this work we study the decoherence of topological qubits in linear motions. The topological qubit is made of two spatially-separated Majorana zero modes which are the edge excitations of Kitaev chain [1]. In a previous work [2], it was shown by one of us and his collaborators that the decoherence of topological qubit is exactly solvable, moreover, topological qubit is robust against decoherence in the super-Ohmic environments. We extend the setup of [2] to consider the effect of motions on the decoherence of the topological qubits. Our results show the thermalization as expected by Unruh effect. Besides, we also find the so-called “anti-Unruh” phenomena which shows the rate of decoherence is anti-correlated with the acceleration in short-time scale. Moreover, we modulate the motion patterns of each Majorana modes and find information backflow and the preservation of coherence even with nonzero accelerations. This is the characteristics of the underlying non-Markovian reduced dynamics. We conclude that he topological qubit is in general more robust against decoherence than the usual qubits, and can be take into serious consideration for realistic implementation to have robust quantum computation and communication. This talk is based on our work in [3].

Majorana qubits in a topological insulator nanoribbon architecture

We describe designs for the realization of topological Majorana qubits in terms of proximitized topological insulator nanoribbons pierced by a uniform axial magnetic field. This platform holds promise for particularly robust Majorana bound states, with easily manipulable inter-state couplings. We propose proof-of-principle experiments for initializing, manipulating, and reading out Majorana box qubits defined in floating devices dominated by charging effects. We argue that the platform offers design advantages which make it particularly suitable for extension to qubit network structures realizing a Majorana surface code.

Modifying the band-structure and properties of zirconium telluride using phosphorus addition

Layered materials of metal based tellurides such as ZrTe5 have been investigated recently as 3D Dirac semi-metals using ARPES and Landau level spectroscopy. These materials have exhibited exotic transport, topological, diamagnetic and chiral magnetic properties making them potentially useful for spintronics and topological qubits applications. In this line of investigation, we study a novel class of possible substitutional solid solutions of Zr-Te-P from first principle calculations. It was observed that due to the intrinsic disturbance of symmetry in the crystal structure of Zr-Te-P, there are nodes along certain points of the Brillouin zone. In addition, there was also a drastic change in the density of states in the vicinity of the Fermi energy level, leading to altered carrier transport compared to pristine ZrTe. Moreover, crystals of Zr-Te-P were also synthesized in vacuum through condensed system combustion at elevated temperatures. Morphological, structural, compositional, and electrical investigation of the phosphorus modified Zr-Te crystals were carried out comprehensively in this study. Density functional theory (DFT) simulation results and electrical transport observations suggest the potential utility of this novel class of solid solution materials of Zr-Te-P in research frontiers of new Dirac materials and electronic applications.

Teleportation-based quantum information processing with Majorana zero modes

We present a new measurement-based scheme for performing braiding operations on Majorana zero modes and for detecting their non-Abelian statistics without moving or hybridizing them. In our scheme, the topological qubit encoded in any pair of well-separated Majorana zero modes in a mesoscopic superconductor island is read out from the transmission phase shift in electron teleportation through the island in the Coulomb blockade regime. We propose experimental setups to measure the teleportation phase shift via conductance in an electron interferometer or persistent current in a closed loop.

Readout of Majorana parity states using a quantum dot

We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBS) using a tunnel coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir, and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved and charge transfer between the MBS and dot only occurs through resonant tunnelling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wavefunctions. The latter splitting can be tuned from zero (topologically protected regime) to a finite value by gate-driven shortening of the topological wire. Simulations show that the oscillatory nature of the MBS splitting is not a fundamental obstacle to readout, but requires precise gate control of the MBS spatial position and dot potential. With experimentally realistic parameters, we find that high-fidelity parity readout is achievable given nanometer-scale spatial control of the MBS, and that there is a tradeoff between required precisions of temporal and spatial control. Use of the scheme to measure the MBS splitting versus separation would present a clear signature of topological order, and could be used to test the robustness of this order to spatial motion, a key requirement in certain schemes for scalable topological qubits. We show how the scheme can be extended to distinguish valid parity measurements from invalid ones due to gate calibration errors.

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems.

Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g., superconducting circuits or quantum dots, is studied in this Letter. Errors caused by topologically unprotected quantum systems need to be corrected with error-correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about 1,000 normal qubits.

Milestones Toward Majorana-Based Quantum Computing

We introduce a scheme for preparation, manipulation, and readout of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate-control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current; (2) validation of a prototype topological qubit; and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and readout schemes as well.

Majorana spintronics

We propose a systematic magnetic-flux-free approach to detect, manipulate, and braid Majorana fermions in a semiconductor-nanowire-based topological Josephson junction by utilizing the Majorana spin degree of freedom. We find an intrinsic $\ensuremath{\pi}$-phase difference between spin-triplet pairings enforced by the Majorana zero modes (MZMs) at the two ends of a one-dimensional spinful topological superconductor. This $\ensuremath{\pi}$ phase is identified to be a spin-dependent superconducting phase, referred to as the spin phase, which we show to be tunable by controlling spin-orbit coupling strength via electric gates. This electric controllable spin phase not only affects the coupling energy between MZMs but also leads to a fractional Josephson effect in the absence of any applied magnetic flux, which enables the efficient topological qubit readout. We thus propose an all-electrically controlled superconductor-semiconductor hybrid circuit to manipulate MZMs and to detect their non-Abelian braiding statistics properties. Our work on spin properties of topological Josephson effects potentially opens up a new thrust for spintronic applications with Majorana-based semiconductor quantum circuits.

Decoherence of topological qubit in linear and circular motions: decoherence impedance, anti-Unruh and information backflow

In this paper, we consider the decoherence patterns of a topological qubit made of two Majorana zero modes in the generic linear and circular motions in the Minkowski spacetime. We show that the reduced dynamics is exact without Markov approximation. Our results imply that the acceleration will cause thermalization as expected by Unruh effect. However, for the short-time scale, we find the rate of decoherence is anti-correlated with the acceleration, as kind of decoherence impedance. This is in fact related to the "anti-Unruh" phenomenon previously found by studying the transition probability of Unruh-DeWitt detector. We also obtain the information backflow by some time modulations of coupling constant or acceleration, which is a characteristic of the underlying non-Markovian reduced dynamics. Moreover, by exploiting the nonlocal nature of the topological qubit, we find that some incoherent accelerations of the constituent Majorana zero modes can preserve the coherence instead of thermalizing it.

Topological quantum memory interfacing atomic and superconducting qubits

We propose a scheme to manipulate a topological spin qubit which is realized with cold atoms in a one-dimensional optical lattice. In particular, by introducing a quantum opto-electro-mechanical interface, we are able to first transfer a superconducting qubit state to an atomic qubit state and then to store it into the topological spin qubit. In this way, an efficient topological quantum memory could be constructed for the superconducting qubit. Therefore, we can consolidate the advantages of both the noise resistance of the topological qubits and the scalability of the superconducting qubits in this hybrid architecture.

Quantum information transfer between topological and conventional charge qubits**Project supported by the National Natural Science Foundation of China (Grant No. 11304031).

We propose a scheme to realize coherent quantum information transfer between topological and conventional charge qubits. We first consider a hybrid system where a quantum dot (QD) is tunnel-coupled to a semiconductor Majorana-hosted nanowire (MNW) via using gated control as a switch, the information encoded in the superposition state of electron empty and occupied state can be transferred to each other through choosing the proper interaction time to make measurements. Then we consider another system including a double QDs and a pair of parallel MNWs, it is shown that the entanglement information transfer can be realized between the two kinds of systems. We also realize long distance quantum information transfer between two quantum dots separated by an MNW, by making use of the nonlocal fermionic level formed with the pared Majorana feimions (MFs) emerging at the two ends of the MNW. Furthermore, we analyze the teleportationlike electron transfer phenomenon predicted by Tewari et al. [Phys. Rev. Lett. 100, 027001 (2008)] in our considered system. Interestingly, we find that this phenomenon exactly corresponds to the case that the information encoded in one QD just returns back to its original place during the dynamical evolution of the combined system from the perspective of quantum state transfer.

Robust interface between flying and topological qubits.

Hybrid architectures, consisting of conventional and topological qubits, have recently attracted much attention due to their capability in consolidating robustness of topological qubits and universality of conventional qubits. However, these two kinds of qubits are normally constructed in significantly different energy scales, and thus the energy mismatch is a major obstacle for their coupling, which can support the exchange of quantum information between them. Here we propose a microwave photonic quantum bus for a strong direct coupling between the topological and conventional qubits, where the energy mismatch is compensated by an external driving field. In the framework of tight-binding simulation and perturbation approach, we show that the energy splitting of Majorana fermions in a finite length nanowire, which we use to define topological qubits, is still robust against local perturbations due to the topology of the system. Therefore, the present scheme realizes a rather robust interface between the flying and topological qubits. Finally, we demonstrate that this quantum bus can also be used to generate multipartitie entangled states with the topological qubits.