arXiv subjects

Yidun Wan

Publications and source records attributed to Yidun Wan.

At least 37 records · Page 2Linked to original sources

arXiv2023

Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model

In this paper, we construct an exactly solvable lattice Hamiltonian model to investigate the properties of a composite system consisting of multiple topological orders separated by gapped domain walls. There are interdomain elementary excitations labeled by a pair of anyons in different domains of this system; This system also has elementary excitations with quasiparticles in the gapped domain wall. Each set of elementary excitations corresponds to a basis of the ground states of this composite system on the torus, reflecting that the ground-state degeneracy matches the number of either set of elementary excitations. The characteristic properties of this composite system lie in the basis transformations, represented by the $S$ and $T$ matrices: The $S$ matrix encodes the mutual statistics between interdomain excitations and domain-wall quasiparticles, and the $T$ matrix encapsulates the topological spins of interdomain excitations. Our model realizes a spatial counterpart of a temporal phase transition triggered by anyon condensation, bringing the abstract theory of anyon condensation into manifestable spatial interdomain excitation states.

cond-mat.str-el↗

arXiv2023

Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries

In this paper, we apply the method of Fourier transform and basis rewriting developed in arXiv:1910.13441 for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group $G$) of three-dimensional topological orders. We find that the gapped boundary condition of the gauge theory model is characterized by a Frobenius algebra in the representation category $\mathcal Rep(G)$ of $G$, which also describes the charge splitting and condensation on the boundary. We also show that our Fourier transform maps the three-dimensional gauge theory model with input data $G$ to the Walker-Wang model with input data $\mathcal Rep(G)$ on a trivalent lattice with dangling edges, after truncating the Hilbert space by projecting all dangling edges to the trivial representation of $G$. This Fourier transform also provides a systematic construction of the gapped boundary theory of the Walker-Wang model. This establishes a correspondence between two types of topological field theories: the extended Dijkgraaf-Witten and extended Crane-Yetter theories.

cond-mat.str-el↗

arXiv2022

Experimental realization of a topologically protected Hadamard gate via braiding Fibonacci anyons

Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local disturbances. The topological protection, however, requires rather complicated lattice models and hard-to-manipulate dynamics; even the simplest system that can realize universal TQC--the Fibonacci anyon system--lacks a physical realization, let alone braiding the non-Abelian anyons. Here, we propose a disk model that can realize the Fibonacci anyon system, and construct the topologically protected logical spaces with the Fibonacci anyons. Via braiding the Fibonacci anyons, we can implement universal quantum gates on the logical space. Our proposal is platform-independent. As a demonstration, we implement a topological Hadamard gate on a logical qubit through a sequence of $15$ braiding operations of three Fibonacci anyons with merely $2$ nuclear spin qubits. The gate fidelity reaches 97.18% by randomized benchmarking. We further prove by experiment that the logical space and Hadamard gate are topologically protected: local disturbances due to thermal fluctuations result in a global phase only. Our work is a proof of principle of TQC and paves the way towards fault-tolerant quantum computation.

quant-ph↗

arXiv2022

Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions

A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of realizing topological quantum computation. To facilitate the study of such boundary defects, in this paper, we construct an exactly solvable Hamiltonian model of topological orders with gapped boundary junctions, where the boundary defects reside, by placing the Levin-Wen model on a disk, whose gapped boundary is separated into multiple segments by junctions. We find that the Hamiltonian of a gapped boundary junction is characterized by either a morphism between or a common Frobenius subalgebra of the two Frobenius algebras (in the input fusion category) characetrizing the two boundary segments joint by the junction. We derive a formula of the ground state degeneracy and an explicit ground-state basis of our model. We propose the notion of mobile and immobile charges on the boundary and find that they are quantum observables and label the ground-state basis. Our model is computation friendly.

cond-mat.str-el↗

arXiv2022

A saddle-point finder and its application to the spin foam model

We introduce a saddle-point finder that can find the complex saddle points for any analytically continued action. We showcase our saddle-point finder by two examples in the EPRL spin foam model: the single vertex case and the case of triangulation $Δ_3$. In both cases, the complex saddle points are found, and each saddle point's contribution to the partition function is estimated. We also discuss the geometrical interpretation of each saddle point.

gr-qc↗

arXiv2021

Anyon Condensation: Coherent states, Symmetry Enriched Topological Phases, Goldstone Theorem, and Dynamical Rearrangement of Symmetry

Although the mathematics of anyon condensation in topological phases has been studied intensively in recent years, a proof of its physical existence is tantamount to constructing an effective Hamiltonian theory. In this paper, we concretely establish the physical foundation of anyon condensation by building the effective Hamiltonian and the Hilbert space, in which we explicitly construct the vacuum of the condensed phase as the coherent states that are the eigenstates of the creation operators that create the condensate anyons. Along with this construction, which is analogous to Laughlin's construction of wavefunctions of fractional quantum hall states, we generalize the Goldstone theorem in the usual spontaneous symmetry breaking paradigm to the case of anyon condensation. We then prove that the condensed phase is a symmetry enriched (protected) topological phase by directly constructing the corresponding symmetry transformations, which can be considered as a generalization of the Bogoliubov transformation.

cond-mat.str-el↗

arXiv2021

Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam propagator on a 4-simplex, by adapting the methods of Lefschetz thimble and Markov Chain Monte-Carlo to oscillatory spinfoam integrals. Our method can compute any spinfoam observables at relatively large spins. We obtain the numerical results of the propagators at different spins and demonstrate their consistency with the expected spinfoam semi-classical behavior in the large spin limit. Our results exhibit significant quantum corrections at smaller spins. Our method is reliable and thus can be employed to discover the semi-classical and quantum behaviors of the spinfoam model.

gr-qc↗

arXiv2020

Electric-Magnetic duality in twisted quantum double model of topological orders

We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD$(G,α)$---discrete Dijkgraaf-Witten model---with a finite gauge group $G$, which has an Abelian normal subgroup $N$, and a three-cocycle $α\in H^3(G,U(1))$. Any equivalence between two TQD models, say, TQD$(G,α)$ and TQD$(G',α')$, can be realized as a PEM duality transformation, which exchanges the $N$-charges and $N$-fluxes only. Via the PEM duality, we construct an explicit isomorphism between the corresponding TQD algebras $D^α(G)$ and $D^{α'}(G')$ and derive the map between the anyons of one model and those of the other.

cond-mat.str-el↗

arXiv2020

Observation of Two-Vertex Four-Dimensional Spin Foam Amplitudes with a 10-qubit Superconducting Quantum Processor

Quantum computers are an increasingly hopeful means for understanding large quantum many-body systems bearing high computational complexity. Such systems exhibit complex evolutions of quantum states, and are prevailing in fundamental physics, e.g., quantum gravity. Computing the transition amplitudes between different quantum states by quantum computers is one of the promising ways to solve such computational complexity problems. In this work, we apply a 10-qubit superconducting quantum processor, where the all-to-all circuit connectivity enables a many-body entangling gate that is highly efficient for state generation, to studying the transition amplitudes in loop quantum gravity. With the device metrics such as qubit coherence, control accuracy, and integration level being continuously improved, superconducting quantum processors are expected to outperform their classical counterparts in handling many-body dynamics and may lead to a deeper understanding of quantum gravity.

quant-ph↗

arXiv2020

Dynamical-Invariant-based Holonomic Quantum Gates: Theory and Experiment

Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here, we report a systematic, scalable approach based on dynamical invariants to realize HQGs without using additional Hilbert spaces. While presenting the theoretical framework of our approach, we design and experimentally evaluate single-qubit and two-qubits HQGs for the nuclear magnetic resonance system. The single-qubit gates acquire average fidelity 0.9972 by randomized benchmarking, and the controlled-NOT gate acquires fidelity 0.9782 by quantum process tomography. Our approach is also platform-independent, and thus may open a way to large-scale holonomic quantum computation.

quant-ph↗

arXiv2019

Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries

We generalize the Electric-magnetic (EM) duality in the quantum double (QD) models to the case of topological orders with gapped boundaries. We also map the QD models with boundaries to the Levin-Wen (LW) models with boundaries. To this end, we Fourier transform and rewrite the extended QD model with a finite gauge group $G$ on a trivalent lattice with a boundary. Gapped boundary conditions of the model before the transformation are known to be characterized by the subgroups $K \subseteq G$. We find that after the transformation, the boundary conditions are then characterized by the Frobenius algebras $A_{G,K}$ in $\mathrm{Rep}_G$. An $A_{G,K}$ is the dual space of the quotient of the group algebra of $G$ over that of $K$, and $\mathrm{Rep}_G$ is the category of the representations of $G$. The EM duality on the boundary is revealed by mapping the $K$'s to $A_{G,K}$'s. We also show that our transformed extended QD model can be mapped to an extended LW model on the same lattice via enlarging the Hilbert space of the extended LW model. Moreover, our transformed extended QD model elucidates the phenomenon of anyon splitting in anyon condensation.

cond-mat.str-el↗

arXiv2019

Measuring Holographic Entanglement Entropy on a Quantum Simulator

Quantum simulation promises to have wide applications in many fields where problems are hard to model with classical computers. Various quantum devices of different platforms have been built to tackle the problems in, say, quantum chemistry, condensed matter physics, and high-energy physics. Here, we report an experiment towards the simulation of quantum gravity by simulating the holographic entanglement entropy. On a six-qubit nuclear magnetic resonance quantum simulator, we demonstrate a key result of Anti-de Sitter/conformal field theory(\adscft) correspondence---the Ryu-Takayanagi formula is demonstrated by measuring the relevant entanglement entropies on the perfect tensor state. The fidelity of our experimentally prepared the six-qubit state is 85.0\% via full state tomography and reaches 93.7\% if the signal-decay due to decoherence is taken into account. Our experiment serves as the basic module of simulating more complex tensor network states that exploring \adscft correspondence. As the initial experimental attempt to study \adscft via quantum information processing, our work opens up new avenues exploring quantum gravity phenomena on quantum simulators.

quant-ph↗

arXiv2019

Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system is identified with the spectrum of quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the EB. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasiparticles at infinite temperature on the entanglement boundary. We corroborates our results with explicit computation in the quantum double model with/without boundaries. We then systematically construct the reduced density matrices of the quantum double model on generic 2-surfaces with boundaries.

cond-mat.str-el↗

arXiv2018

Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders

We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are compatible with the bulk Hamoltonian. Given the bulk Hamiltonian defined by a gauge group $G$ and a four-cocycle $ω$ in the fourth cohomology group of $G$ over $U(1)$, a boundary Hamiltonian can be defined by a subgroup $K$ of $G$ and a three-cochain $α$ in the third cochain group of $K$ over $U(1)$. The boundary Hamiltonian to be constructed must be gapped and invariant under the topological renormalization group flow (via Pachner moves), leading to a generalized Frobenius condition. Given $K$, a solution to the generalized Frobenius condition specifies a gapped boundary condition. We derive a closed-form formula of the ground state degeneracy of the model on a three-cylinder, which can be naturally generalized to three-spaces with more boundaries. We also derive the explicit ground-state wavefunction of the model on a three-ball. The ground state degeneracy and ground-state wavefunction are both presented solely in terms of the input data of the model, namely, $\{G,ω,K,α\}$.

cond-mat.str-el↗

arXiv2018

Experimental Preparation of Topologically Ordered States via Adiabatic Evolution

Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can arise in two-dimensional spin-lattice models. In this paper, we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution. The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators. Each sector is highly entangled, as shown from the completely reconstructed density matrices. This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.

quant-ph↗

arXiv2018

Entanglement Entropy of Topological Orders with Boundaries

In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum double. We will find very interesting dependence of the entanglement entropy on the boundary conditions particularly when the system is non-Abelian. Along the way, we demonstrate a streamlined procedure to compute the entanglement entropy, which is particularly efficient when dealing with systems with boundaries. We also show how this method efficiently reproduces all the known results in the presence of anyonic excitations.

hep-th↗

arXiv2017

Quantum Spacetime on a Quantum Simulator

We experimentally simulate the spin networks -- a fundamental description of quantum spacetime at the Planck level. We achieve this by simulating quantum tetrahedra and their interactions. The tensor product of these quantum tetrahedra comprises spin networks. In this initial attempt to study quantum spacetime by quantum information processing, on a four-qubit nuclear magnetic resonance quantum simulator, we simulate the basic module -- comprising five quantum tetrahedra -- of the interactions of quantum spacetime. By measuring the geometric properties on the corresponding quantum tetrahedra and simulate their interactions, our experiment serves as the basic module that represents the Feynman diagram vertex in the spin-network formulation of quantum spacetime.

quant-ph↗

arXiv2017

Experimentally Probing Topological Order and Its Breakdown via Modular Matrices

The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much detail of the physics of topological orders can in principle be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices -- characterizing anyonic statistics that are some of the most fundamental finger prints of topological orders -- can be reconstructed with very good accuracy solely by experimental means. This is a first experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle -- that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications both in probing and realistically harnessing these exotic phases of matter.

quant-ph↗