arXiv subjects

Penghua Chen

Publications and source records attributed to Penghua Chen.

6 recordsLinked to original sources

arXiv2025

Representing arbitrary ground states of toric code by a restricted Boltzmann machine

We systematically analyze the representability of toric code ground states by Restricted Boltzmann Machine with only local connections between hidden and visible neurons. This analysis is pivotal for evaluating the model's capability to represent diverse ground states, thus enhancing our understanding of its strengths and weaknesses. Subsequently, we modify the Restricted Boltzmann Machine to accommodate arbitrary ground states by introducing essential non-local connections efficiently. The new model is not only analytically solvable but also demonstrates efficient and accurate performance when solved using machine learning techniques. Then we generalize our the model from $Z_2$ to $Z_n$ toric code and discuss future directions.

cond-mat.dis-nn↗

arXiv2024

Floquet Codes from Coupled Spin Chains

We propose a novel construction of the Floquet 3D toric code and Floquet $X$-cube code through the coupling of spin chains. This approach not only recovers the coupling layer construction on foliated lattices in three dimensions but also avoids the complexity of coupling layers in higher dimensions, offering a more localized and easily generalizable framework. Our method extends the Floquet 3D toric code to a broader class of lattices, aligning with its topological phase properties. Furthermore, we generalize the Floquet $X$-cube model to arbitrary manifolds, provided the lattice is locally cubic, consistent with its Fractonic phases. We also introduce a unified error-correction paradigm for Floquet codes by defining a subgroup, the Steady Stabilizer Group (SSG), of the Instantaneous Stabilizer Group (ISG), emphasizing that not all terms in the ISG contribute to error correction, but only those terms that can be referred to at least twice before being removed from the ISG. We show that correctable Floquet codes naturally require the SSG to form a classical error-correcting code, and we present a simple 2-step Bacon-Shor Floquet code as an example, where SSG forms instantaneous repetition codes. Finally, our construction intrinsically supports the extension to $n$-dimensional Floquet $(n,1)$ toric codes and generalized $n$-dimensional Floquet $X$-cube codes.

quant-ph↗

arXiv2024

Quantum circuits for toric code and X-cube fracton model

We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil 2L+2+log_{2}(d)+\frac{L}{2d} \rceil$ time steps, where $L$ refers to the system size and $d$ represents the maximum distance to constrain the application of the CNOT gates. Our algorithm reformulates the problem into a purely geometric one, facilitating its extension to attain the ground state of certain 3D topological phases, such as the 3D toric model in $3L+8$ steps and the X-cube fracton model in $12L+11$ steps. Furthermore, we introduce a gluing method involving measurements, enabling our technique to attain the ground state of the 2D toric code on an arbitrary planar lattice and paving the way to more intricate 3D topological phases.

cond-mat.str-el↗

arXiv2024

Generalized Kitaev Spin Liquid model and Emergent Twist Defect

The Kitaev spin liquid model on honeycomb lattice offers an intriguing feature that encapsulates both Abelian and non-Abelian anyons. Recent studies suggest that the comprehensive phase diagram of possible generalized Kitaev model largely depends on the specific details of the discrete lattice, which somewhat deviates from the traditional understanding of "topological" phases. In this paper, we propose an adapted version of the Kitaev spin liquid model on arbitrary planar lattices. Our revised model recovers the toric code model under certain parameter selections within the Hamiltonian terms. Our research indicates that changes in parameters can initiate the emergence of holes, domain walls, or twist defects. Notably, the twist defect, which presents as a lattice dislocation defect, exhibits non-Abelian braiding statistics upon tuning the coefficients of the Hamiltonian on a standard translationally invariant lattice. Additionally, we illustrate that the creation, movement, and fusion of these defects can be accomplished through natural time evolution by linearly interpolating the static Hamiltonian. These defects demonstrate the Ising anyon fusion rule as anticipated. Our findings hint at possible implementation in actual physical materials owing to a more realistically achievable two-body interaction.

cond-mat.str-el↗

arXiv2022

Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras

Kitaev's quantum double model is a family of exactly solvable lattice models that realize two dimensional topological phases of matter. Originally it is based on finite groups, and is later generalized to semi-simple Hopf algebras. We rigorously define and study ribbon operators in the generalized Kitaev quantum double model. These ribbon operators are important tools to understand quasi-particle excitations. It turns out that there are some subtleties in defining the operators in contrast to what one would naively think. In particular, one has to distinguish two classes of ribbons which we call locally clockwise and locally counterclockwise ribbons. Moreover, this issue already exists in the original model based on finite non-Abelian groups. We show how certain properties would fail even in the original model if we do not distinguish these two classes of ribbons. Perhaps not surprisingly, under the new definitions ribbon operators satisfy all properties that are expected. For instance, they create quasi-particle excitations only at the end of the ribbon, and the types of the quasi-particles correspond to irreducible representations of the Drinfeld double of the input Hopf algebra. However, the proofs of these properties are much more complicated than those in the case of finite groups. This is partly due to the complications in dealing with general Hopf algebras rather than just group algebras.

cond-mat.str-el↗

arXiv2017

Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution

We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians defined in this way are non-Hermitian, but satisfy symmetry properties that have previously been identified in the literature as "pseudo Hermiticity" and "anti-PT symmetry". We show how simple one-channel and two-channel models exhibit transitions between real, imaginary, and complex eigenvalue pairs.

physics.optics↗