 Award ID(s):
 1846109
 NSFPAR ID:
 10320816
 Date Published:
 Journal Name:
 Nature Communications
 Volume:
 12
 Issue:
 1
 ISSN:
 20411723
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract Indistinguishability of particles is a fundamental principle of quantum mechanics 1 . For all elementary and quasiparticles observed to date—including fermions, bosons and Abelian anyons—this principle guarantees that the braiding of identical particles leaves the system unchanged 2,3 . However, in two spatial dimensions, an intriguing possibility exists: braiding of nonAbelian anyons causes rotations in a space of topologically degenerate wavefunctions 4–8 . Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the welldeveloped mathematical description of nonAbelian anyons and numerous theoretical proposals 9–22 , the experimental observation of their exchange statistics has remained elusive for decades. Controllable manybody quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solidstate platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the manybody wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective nonAbelian Ising anyons 9,10 , we implement a generalized stabilizer code and unitary protocol 23 to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about nonAbelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards faulttolerant quantum computing.more » « less

BACKGROUND The past decade has witnessed considerable progress toward the creation of new quantum technologies. Substantial advances in present leading qubit technologies, which are based on superconductors, semiconductors, trapped ions, or neutral atoms, will undoubtedly be made in the years ahead. Beyond these present technologies, there exist blueprints for topological qubits, which leverage fundamentally different physics for improved qubit performance. These qubits exploit the fact that quasiparticles of topological quantum states allow quantum information to be encoded and processed in a nonlocal manner, providing inherent protection against decoherence and potentially overcoming a major challenge of the present generation of qubits. Although still far from being experimentally realized, the potential benefits of this approach are evident. The inherent protection against decoherence implies better scalability, promising a considerable reduction in the number of qubits needed for error correction. Transcending possible technological applications, the underlying physics is rife with exciting concepts and challenges, including topological superconductors, nonabelian anyons such as Majorana zero modes (MZMs), and nonabelian quantum statistics. ADVANCES In a wideranging and ongoing effort, numerous potential material platforms are being explored that may realize the required topological quantum states. Nonabelian anyons were first predicted as quasiparticles of topological states known as fractional quantum Hall states, which are formed when electrons move in a plane subject to a strong perpendicular magnetic field. The prediction that hybrid materials that combine topological insulators and conventional superconductors can support localized MZMs, the simplest type of nonabelian anyon, brought entirely new material platforms into view. These include, among others, semiconductorsuperconductor hybrids, magnetic adatoms on superconducting substrates, and Febased superconductors. Onedimensional systems are playing a particularly prominent role, with blueprints for quantum information applications being most developed for hybrid semiconductorsuperconductor systems. There have been numerous attempts to observe nonabelian anyons in the laboratory. Several experimental efforts observed signatures that are consistent with some of the theoretical predictions for MZMs. A few extensively studied platforms were subjected to intense scrutiny and indepth analyses of alternative interpretations, revealing a more complex reality than anticipated, with multiple possible interpretations of the data. Because advances in our understanding of a physical system often rely on discrepancies between experiment and theory, this has already led to an improved understanding of Majorana signatures; however, our ability to detect and manipulate nonabelian anyons such as MZMs remains in its infancy. Future work can build on improved materials in some of the existing platforms but may also exploit new materials such as van der Waals heterostructures, including twisted layers, which promise many new options for engineering topological phases of matter. OUTLOOK Experimentally establishing the existence of nonabelian anyons constitutes an outstandingly worthwhile goal, not only from the point of view of fundamental physics but also because of their potential applications. Future progress will be accelerated if claims of Majorana discoveries are based on experimental tests that go substantially beyond indicators such as zerobias peaks that, at best, suggest consistency with a Majorana interpretation. It will be equally important that these discoveries build on an excellent understanding of the underlying material systems. Most likely, further material improvements of existing platforms and the exploration of new material platforms will both be important avenues for progress toward obtaining solid evidence for MZMs. Once that has been achieved, we can hope to explore—and harness—the fascinating physics of nonabelian anyons such as the topologically protected ground state manifold and nonabelian statistics. Proposed topological platforms. (Left) Proposed state of electrons in a high magnetic field (evendenominator fractional quantum Hall states) are predicted to host Majorana quasiparticles. (Right) Hybrid structures of superconductors and other materials have also been proposed to host such quasiparticles and can be tailored to create topological quantum bits based on Majoranas.more » « less

Abstract Atomic manybody phase transitions and quantum criticality have recently attracted much attention in nonstandard optical lattices. Here we perform an experimental study of finite temperature superfluid transition of bosonic atoms confined in a three dimensional triangular lattice, whose structure can be continuously deformed to dimensional crossover regions including quasione and two dimensions. This nonstandard lattice system provides a versatile platform to investigate manybody correlated phases. For the three dimensional case, we find that the finite temperature superfluid transition agrees quantitatively with the Gutzwiller mean field theory prediction, whereas tuning towards reduced dimensional cases, both quantum and thermal fluctuation effects are more dramatic, and the experimental measurement for the critical point becomes strongly deviated from the mean field theory. We characterize the fluctuation effects in the whole dimension crossover process. Our experimental results imply strong manybody correlations in the system beyond mean field description, paving a way to study quantum criticality near Mottsuperfluid transition in finite temperature dimensioncrossover lattices.

We present a formulation for investigating quench dynamics acrossquantum phase transitions in the presence of decoherence. We formulatedecoherent dynamics induced by continuous quantum nondemolitionmeasurements of the instantaneous Hamiltonian. We generalize thewellstudied universal KibbleZurek behavior for linear temporal driveacross the critical point. We identify a strong decoherence regimewherein the decoherence time is shorter than the standard correlationtime, which varies as the inverse gap above the groundstate. In thisregime, we find that the freezeout time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})} t  ∼ τ 2 ν z / ( 1 + 2 ν z ) for when the system falls out of equilibrium and the associatedfreezeout length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})} ξ ‾ ∼ τ ν / ( 1 + 2 ν z ) show powerlaw scaling with respect to the quench rate 1/\tau 1 / τ ,where the exponents depend on the correlation length exponent \nu ν and the dynamical exponent z z associated with the transition. The universal exponents differ fromthose of standard KibbleZurek scaling. We explicitly demonstrate thisscaling behavior in the instance of a topological transition in a Cherninsulator system. We show that the freezeout time scale can be probedfrom the relaxation of the Hall conductivity. Furthermore, onintroducing disorder to break translational invariance, we demonstratehow quenching results in regions of imbalanced excitation densitycharacterized by an emergent length scale which also shows universalscaling. We perform numerical simulations to confirm our analyticalpredictions and corroborate the scaling arguments that we postulate asuniversal to a host of systems.more » « less

Abstract The proposal of faulttolerant quantum computations, which promise to dramatically improve the operation of quantum computers and to accelerate the development of the compact hardware for them, is based on topological quantum field theories, which rely on the existence in Nature of physical systems described by a Lagrangian containing a nonAbelian (NA) topological term. These are solidstate systems having twodimensional electrons, which are coupled to magneticfluxquanta vortexes, forming complex particles, known as anyons. Topological quantum computing (TQC) operations thus represent a physical realization of the mathematical operations involving NA representations of a braid group B n , generated by a set of n localized anyons, which can be braided and fused using a “tweezer” and controlled by a detector. For most of the potential TQC material systems known so far, which are 2Delectron–gas semiconductor structure at high magnetic field and a variety of hybrid superconductor/topologicalmaterial heterostructures, the realization of anyon localization versus tweezing and detecting meets serious obstacles, chief among which are the necessity of using current control, i.e., mobile particles, of the TQC operations and high density electron puddles (containing thousands of electrons) to generate a single vortex. Here we demonstrate a novel system, in which these obstacles can be overcome, and in which vortexes are generated by a single electron. This is a ~ 150 nm size many electron InP/GaInP 2 selforganized quantum dot, in which molecules, consisting of a few localized anyons, are naturally formed and exist at zero external magnetic field. We used highspatialresolution scanning magnetophotoluminescence spectroscopy measurements of a set of the dots having five and six electrons, together with manybody quantum mechanical calculations to demonstrate spontaneous formation of the anyon magnetoelectron particles ( e ν ) having fractional charge ν = n / k, where n = 1–4 and k = 3–15 are the number of electrons and vortexes, respectively, arranged in molecular structures having a builtin (internal) magnetic field of 6–12 T. Using direct imaging of the molecular configurations we observed fusion and braiding of e ν  anyons under photoexcitation and revealed the possibility of using charge sensing for their control. Our investigations show that InP/GaInP 2 anyonmolecule QDs, which have intrinsic transformations of localized e ν  anyons compatible with TQC operations and capable of being probed by charge sensing, are very promising for the realization of TQC.more » « less