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Quantum Cluster State Spin Chain with Ising Fusion Category Symmetry: A Perspective from Weak Hopf SymTFT
Authors:
Zhian Jia
Abstract:
In this work, we present a construction of a cluster state lattice Hamiltonian that exhibits the symmetry of the Ising fusion algebra. This construction is formulated within the framework of weak Hopf symmetry topological field theory (SymTFT), where we assign smooth and rough boundaries to the weak Hopf quantum double model, thereby extending the conventional cluster state model. Central to our c…
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In this work, we present a construction of a cluster state lattice Hamiltonian that exhibits the symmetry of the Ising fusion algebra. This construction is formulated within the framework of weak Hopf symmetry topological field theory (SymTFT), where we assign smooth and rough boundaries to the weak Hopf quantum double model, thereby extending the conventional cluster state model. Central to our construction is the weak Hopf Ising boundary tube algebra $\mathcal{T}_{\mathsf{Ising}}$, whose representation category is equivalent to the Ising fusion category $\mathsf{Ising}$. We take this algebra as the input data for the weak Hopf quantum double model. The resulting model exhibits Ising fusion symmetry on both open and closed $1\text{d}$ manifolds. On open manifolds, the symmetry is governed by $\mathcal{T}_{\mathsf{Ising}} \otimes \mathcal{T}_{\mathsf{Ising}}^{\vee}$; on closed manifolds, it reduces to $\operatorname{Cocom}(\mathcal{T}_{\mathsf{Ising}}) \otimes \operatorname{Cocom}(\mathcal{T}_{\mathsf{Ising}}^{\vee})$. Since the Ising fusion algebra embeds into $\operatorname{Cocom}(\mathcal{T}_{\mathsf{Ising}}^{\vee})$, the model faithfully realizes the symmetry of the Ising fusion category.
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Submitted 4 August, 2025;
originally announced August 2025.
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Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
Authors:
Qiang Jia,
Zhian Jia
Abstract:
Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to subsystem symmetries and develop subsystem SymTFT as a systematic tool to characterize and classify subsystem symmetry-protected topological (SSPT) phases. For…
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Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to subsystem symmetries and develop subsystem SymTFT as a systematic tool to characterize and classify subsystem symmetry-protected topological (SSPT) phases. For $(2+1)$D gapped phases, we introduce a 2-foliated $(3+1)$D exotic tensor gauge theory (which is equivalent to 2-foliated $(3+1)$D BF theory via exotic duality) as the subsystem SymTFT and systematically analyze its topological boundary conditions and linearly rigid subsystem symmetries. Taking subsystem symmetry groups $G = \mathbb{Z}_N$ and $G=\mathbb{Z}_N \times \mathbb{Z}_M$ as examples, we demonstrate how to recover the classification scheme $\mathcal{C}[G] = H^{2}(G^{\times 2}, U(1)) / \left( H^2(G, U(1)) \right)^3$, which was previously derived by examining topological invariant under linear subsystem-symmetric local unitary transformations in the lattice Hamiltonian formalism. To illustrate the correspondence between field-theoretic and lattice descriptions, we further analyze $\mathbb{Z}_2 \times \mathbb{Z}_2$ and $\mathbb{Z}_N \times \mathbb{Z}_M$ cluster state models as concrete examples.
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Submitted 16 September, 2025; v1 submitted 28 May, 2025;
originally announced May 2025.
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Quantum Cluster State Model with Haagerup Fusion Category Symmetry
Authors:
Zhian Jia
Abstract:
We propose a (1+1)D lattice model, inspired by a weak Hopf algebra generalization of the cluster state model, which realizes Haagerup fusion category symmetry and features a tensor product Hilbert space. The construction begins with a reconstruction of the Haagerup weak Hopf algebra $H_3$ from the Haagerup fusion category, ensuring that the representation category of $H_3$ is equivalent to Haageru…
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We propose a (1+1)D lattice model, inspired by a weak Hopf algebra generalization of the cluster state model, which realizes Haagerup fusion category symmetry and features a tensor product Hilbert space. The construction begins with a reconstruction of the Haagerup weak Hopf algebra $H_3$ from the Haagerup fusion category, ensuring that the representation category of $H_3$ is equivalent to Haagerup fusion category. Utilizing the framework of symmetry topological field theory (SymTFT), we develop an ultra-thin weak Hopf quantum double model, characterized by a smooth topological boundary condition. We show that this model supports Haagerup fusion category symmetry. Finally, we solve the ground state of the model in terms of a weak Hopf matrix product state, which serves as a natural generalization of the cluster state, embodying Haagerup fusion category symmetry.
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Submitted 11 August, 2025; v1 submitted 27 December, 2024;
originally announced December 2024.
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Quantum DeepONet: Neural operators accelerated by quantum computing
Authors:
Pengpeng Xiao,
Muqing Zheng,
Anran Jiao,
Xiu Yang,
Lu Lu
Abstract:
In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as deep operator network (DeepONet), which learn mappings between infinite-dimensional function spaces, promise efficient computation of PDE solutions for a new co…
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In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as deep operator network (DeepONet), which learn mappings between infinite-dimensional function spaces, promise efficient computation of PDE solutions for a new condition in a single forward pass. However, classical DeepONet entails quadratic complexity concerning input dimensions during evaluation. Given the progress in quantum algorithms and hardware, here we propose to utilize quantum computing to accelerate DeepONet evaluations, yielding complexity that is linear in input dimensions. Our proposed quantum DeepONet integrates unary encoding and orthogonal quantum layers. We benchmark our quantum DeepONet using a variety of PDEs, including the antiderivative operator, advection equation, and Burgers' equation. We demonstrate the method's efficacy in both ideal and noisy conditions. Furthermore, we show that our quantum DeepONet can also be informed by physics, minimizing its reliance on extensive data collection. Quantum DeepONet will be particularly advantageous in applications in outer loop problems which require exploring parameter space and solving the corresponding PDEs, such as uncertainty quantification and optimal experimental design.
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Submitted 30 May, 2025; v1 submitted 23 September, 2024;
originally announced September 2024.
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Experimental evidence that a photon can spend a negative amount of time in an atom cloud
Authors:
Daniela Angulo,
Kyle Thompson,
Vida-Michelle Nixon,
Andy Jiao,
Howard M. Wiseman,
Aephraim M. Steinberg
Abstract:
When a pulse of light traverses a material, it incurs a time delay referred to as the group delay. Should the group delay experienced by photons be attributed to the time they spend as atomic excitations? However reasonable this connection may seem, it appears problematic when the frequency of the light is close to the atomic resonance, as the group delay becomes negative in this regime. To addres…
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When a pulse of light traverses a material, it incurs a time delay referred to as the group delay. Should the group delay experienced by photons be attributed to the time they spend as atomic excitations? However reasonable this connection may seem, it appears problematic when the frequency of the light is close to the atomic resonance, as the group delay becomes negative in this regime. To address this question, we use the cross-Kerr effect to probe the degree of atomic excitation caused by a resonant transmitted photon, by measuring the phase shift on a separate beam that is weak and off-resonant. Our results, over a range of pulse durations and optical depths, are consistent with the recent theoretical prediction that the mean atomic excitation time caused by a transmitted photon (as measured via the time integral of the observed phase shift) equals the group delay experienced by the light. Specifically, we measure mean atomic excitation times ranging from $(-0.82\pm 0.31) τ_0$ for the most narrowband pulse to $(0.54\pm 0.28) τ_0$ for the most broadband pulse, where $τ_0$ is the non-post-selected excitation time, given by the scattering (absorption) probability multiplied by the atomic lifetime $τ_{\rm sp}$. These results suggest that negative values taken by times such as the group delay have more physical significance than has generally been appreciated.
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Submitted 5 September, 2024;
originally announced September 2024.
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Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
Authors:
Zhian Jia,
Sheng Tan,
Dagomir Kaszlikowski
Abstract:
We investigate the multifusion generalization of string-net ground states and lattice Hamiltonians, delving into its associated weak Hopf symmetry. For the multifusion string-net, the gauge symmetry manifests as a general weak Hopf algebra, leading to a reducible vacuum string label; the charge symmetry, serving as a quantum double of gauge symmetry, constitutes a connected weak Hopf algebra. This…
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We investigate the multifusion generalization of string-net ground states and lattice Hamiltonians, delving into its associated weak Hopf symmetry. For the multifusion string-net, the gauge symmetry manifests as a general weak Hopf algebra, leading to a reducible vacuum string label; the charge symmetry, serving as a quantum double of gauge symmetry, constitutes a connected weak Hopf algebra. This implies that the associated topological phase retains its characterization by a unitary modular tensor category (UMTC). The bulk charge symmetry can also be captured by a weak Hopf tube algebra. We offer an explicit construction of the weak Hopf tube algebra structure and thoroughly discuss its properties. The gapped boundary and domain wall models are extensively discussed, with these $1d$ phases characterized by unitary multifusion categories (UMFCs). We delve into the gauge and charge symmetries of these $1d$ phases, as well as the construction of the boundary and domain wall tube algebras. Additionally, we illustrate that the domain wall tube algebra can be regarded as a cross product of two boundary tube algebras. As an application of our model, we elucidate how to interpret the defective string-net as a restricted multifusion string-net.
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Submitted 14 May, 2024; v1 submitted 7 March, 2024;
originally announced March 2024.
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A theoretical analysis and determination of the technical requirements for a Bragg diffraction-based cold atom interferometry gravimeter
Authors:
Qing-Qing Hu,
Jun Yang,
Yu-Kun Luo,
Ai-Ai Jia,
Chun-Hua Wei,
Ze-Huan Li
Abstract:
We present here a new type of cold atom interferometry gravimeter based on Bragg diffraction, which is able to increase the gravity measurement sensitivity and stability of common Raman atom gravimeters significantly. By comparing with Raman transition, the principles and advantages of Bragg diffraction-based atom gravimeters have been introduced. The theoretical model for a time-domain Bragg atom…
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We present here a new type of cold atom interferometry gravimeter based on Bragg diffraction, which is able to increase the gravity measurement sensitivity and stability of common Raman atom gravimeters significantly. By comparing with Raman transition, the principles and advantages of Bragg diffraction-based atom gravimeters have been introduced. The theoretical model for a time-domain Bragg atom gravimeter with atomic incident direction parallels to the wave vector of Bragg lasers has been constructed. Some key technical requirements for an nth-order Bragg diffraction-based atom gravimeter have been deduced, including the temperature of atom cloud, the diameter, curvature radius, frequency, intensity, and timing sequence of Bragg lasers, etc. The analysis results were verified by the existing experimental data in discussion. The present study provides a good reference for the understanding and construction of a Bragg atom gravimeter.
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Submitted 15 May, 2018;
originally announced May 2018.
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Scheme for suppressing atom expansion induced contrast loss in atom interferometers
Authors:
Qing-Qing Hu,
Yu-Kun Luo,
Ai-Ai Jia,
Chun-Hua Wei,
Shu-Hua Yan,
Jun Yang
Abstract:
The loss of contrast due to atom expansion induced non-perfect Raman pulse area in atom interferometers is investigated systematically. Based on the theoretical simulation, we find that the expansion of the atomic cloud results in a decrease of the π pulse fidelity and a change of the π pulse duration, which lead to a significant reduction in fringe contrast. We propose a mitigation strategy of in…
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The loss of contrast due to atom expansion induced non-perfect Raman pulse area in atom interferometers is investigated systematically. Based on the theoretical simulation, we find that the expansion of the atomic cloud results in a decrease of the π pulse fidelity and a change of the π pulse duration, which lead to a significant reduction in fringe contrast. We propose a mitigation strategy of increasing the intensities of the second and third Raman pulses. Simulation results show that the fringe contrast can be improved by 13.6% in a typical atom interferometer gravimeter using this intensity compensation strategy. We also evaluate the effects of this mitigation strategy in the case of a lower atomic cloud temperature and a larger Raman beam size under different Raman pulse time interval conditions. This mitigation strategy has potential applications in increasing the sensitivity of atom interferometer-based precision measuring, including precision measuring of the gravity, gravity gradient, rotation, and magnetic field gradient, as well as testing of the Einstein equivalence principle.
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Submitted 15 May, 2018;
originally announced May 2018.
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Losses-based test of wave-particle duality with Mach-Zehnder interferometers
Authors:
Chen Yang,
Aiai Jia,
Xue Deng,
Yuchi Zhang,
Gang Li,
Shiyao Zhu,
Tiancai Zhang
Abstract:
Wave-particle duality of photons with losses in the Mach-Zehnder interferometer (MZI) is investigated experimentally and theoretically. The experiment is done with the standard MZI with the beam splitter or the beam merger being continuously varied. The losses are deliberately introduced either inside the MZI (the two arms between the beam splitter and beam mergers) or outside the MZI (after the b…
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Wave-particle duality of photons with losses in the Mach-Zehnder interferometer (MZI) is investigated experimentally and theoretically. The experiment is done with the standard MZI with the beam splitter or the beam merger being continuously varied. The losses are deliberately introduced either inside the MZI (the two arms between the beam splitter and beam mergers) or outside the MZI (after the beam merger). It is proved that the unbalanced losses have great influence on the predictability $P$ (particle nature) and visibility $V$ (wave nature). For the former case the duality inequality holds while for the later the duality inequality is ``violated''. We get $P^2+V^2>1$. This ``violation'' could be eliminated in principle by switching the two paths and detectors and then averaging the results. The observed results can be exactly explained theoretically. The experiment is done with coherent beam, instead of single photons, and we have proved that they are exactly equivalent in duality experiment with MZI.
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Submitted 7 February, 2014; v1 submitted 3 February, 2014;
originally announced February 2014.