Three-Dimensional Quantum Cellular Automata from Chiral Semion Surface Topological Order and beyond

Shirley, Wilbur; Chen, Yu-An; Dua, Arpit; Ellison, Tyler D.; Tantivasadakarn, Nathanan; Williamson, Dominic J.

doi:10.1103/prxquantum.3.030326

Cited by 23 publications

(8 citation statements)

References 45 publications

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“…[5], but their existence is still speculative to date. As a last phase definition one might consider disentangling quantum cellular automata (QCAs), which have been shown to exist for many abelian modular CYWW models [16,17,32] and presumably exist for all such models. However, while a QCA is by definition a locality-preserving automorphism of the operator algebra of a many-body model, it is not itself a microscopic local object and does in particular not directly give rise to an invertible domain wall or a gLU circuit, so it is unclear how well it captures the notion of a phase.…”

Section: Discussionmentioning

confidence: 99%

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Disentangling modular Walker-Wang models via fermionic invertible boundaries

Bauer¹

2022

Preprint

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Walker-Wang models are fixed-point models of topological order in 3 + 1 dimensions constructed from a braided fusion category. For a modular input category M, the model itself is invertible and is believed to be in a trivial topological phase, whereas its standard boundary is supposed to represent a 2 + 1-dimensional chiral phase. In this work we explicitly show triviality of the model by constructing an invertible domain wall to vacuum as well as a disentangling local unitary circuit in the case where M is a Drinfeld center. Moreover, we show that if we allow for fermionic (auxiliary) degrees of freedom inside the disentangling domain wall or circuit, the model becomes trivial for a larger class of modular fusion categories, namely those in the Witt classes generated by the Ising UMTC. In the appendices, we also discuss general (non-invertible) boundaries of general Walker-Wang models.

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Section: Discussionmentioning

confidence: 99%

“…Certainly, non-abelian CYWW models do not have a stabilizer description which is central in Refs. [16,17,32].…”

Section: Discussionmentioning

confidence: 99%

Disentangling modular Walker-Wang models via fermionic invertible boundaries

Bauer¹

2022

Preprint

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“…10. As shown in [47], the Hamiltonian H has a (3+1)D topological order given by 2 gauge theory. The electric particle is generated by string operators C e defined on edges as Fig.…”

Section: Review: Construction Of U(1) 2 Walker-wang Model In (3+1)dmentioning

confidence: 97%

“…Our model utilizes a Hamiltonian model for U(1) 2 Walker-Wang model constructed in [47], so let us review the construction here. To describe a U(1) 2 Walker-Wang model, we start with a Walker-Wang model based on [1] 4 TQFT.…”

Section: Review: Construction Of U(1) 2 Walker-wang Model In (3+1)dmentioning

confidence: 99%

Fermionic defects of topological phases and logical gates

Kobayashi

2023

SciPost Phys.

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We discuss the codimension-1 defects of (2+1)D bosonic topological phases, where the defects can support fermionic degrees of freedom. We refer to such defects as fermionic defects, and introduce a certain subclass of invertible fermionic defects called “gauged Gu-Wen SPT defects” that can shift self-statistics of anyons. We derive a canonical form of a general fermionic invertible defect, in terms of the fusion of a gauged Gu-Wen SPT defect and a bosonic invertible defect decoupled from fermions on the defect. We then derive the fusion rule of generic invertible fermionic defects. The gauged Gu-Wen SPT defects give rise to interesting logical gates of stabilizer codes in the presence of additional ancilla fermions. For example, we find a realization of the CZ logical gate on the (2+1)D \mathbb{Z}_2ℤ2 toric code stacked with a (2+1)D ancilla trivial atomic insulator. We also investigate a gapped fermionic interface between (2+1)D bosonic topological phases realized on the boundary of the (3+1)D Walker-Wang model. In that case, the gapped interface can shift the chiral central charge of the (2+1)D phase. Among these fermionic interfaces, we study an interesting example where the (3+1)D phase has a spatial reflection symmetry, and the fermionic interface is supported on a reflection plane that interpolates a (2+1)D surface topological order and its orientation-reversal. We construct a (3+1)D exactly solvable Hamiltonian realizing this setup, and find that the model generates the \mathbb{Z}_8ℤ8 classification of the (3+1)D invertible phase with spatial reflection symmetry and fermion parity on the reflection plane. We make contact with an effective field theory, known in literature as the exotic invertible phase with spacetime higher-group symmetry.

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“…One particular computational paradigm is provided by quantum cellular automata (QCA) [10,11]. As a quantum generalization of classical cellular automata [12,13] they are usually characterized by a discrete-time, local evolution of an ensemble of identical finite-dimensional quantum systems via a translationally invariant unitary operator, although many different versions exist [14][15][16][17][18][19][20][21][22]. Experimental progress in controlling atomic lattice systems with the ability of single-atom addressing [23][24][25][26][27][28][29] has stimulated research into so-called (1+1)D QCA [30][31][32][33][34][35] (see figure 1).…”

Section: Introductionmentioning

confidence: 99%

Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks

Boneberg,

Carollo,

Lesanovsky

2023

New J. Phys.

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Classical artificial neural networks, built from perceptrons as their elementary units, possess enormous expressive power. Here we investigate a quantum neural network architecture, which follows a similar paradigm. It is structurally equivalent to so-called (1+1)D quantum cellular automata, which are two-dimensional quantum lattice systems on which dynamics takes place in discrete time. Information transfer between consecutive time slices -- or adjacent network layers -- is governed by local quantum gates, which can be regarded as the quantum counterpart of the classical perceptrons. Along the time-direction an effective dissipative evolution emerges on the level of the reduced state, and the nature of this dynamics is dictated by the structure of the elementary gates. We show how to construct the local unitary gates to yield a desired many-body dynamics, which in certain parameter regimes is governed by a Lindblad master equation. We study this for small system sizes through numerical simulations and demonstrate how collective effects within the quantum cellular automaton can be controlled parametrically. Our study constitutes a step towards the utilisation of large-scale emergent phenomena in large quantum neural networks for machine learning purposes.

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Three-Dimensional Quantum Cellular Automata from Chiral Semion Surface Topological Order and beyond

Cited by 23 publications

References 45 publications

Disentangling modular Walker-Wang models via fermionic invertible boundaries

Disentangling modular Walker-Wang models via fermionic invertible boundaries

Fermionic defects of topological phases and logical gates

Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks

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