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arXiv:2111.05048 · Physical Review Research

Observation of emergent Z2 gauge invariance in a superconducting circuit

Zhan Wang, Zi-Yong Ge, Zhongcheng Xiang, Xiaohui Song, Rui-Zhen Huang, Pengtao Song, Xueyi Guo, Luhong Su, Kai Xu, Dongning Zheng, Heng Fan

Published Jun 17, 2022• 37 citations
arXivHTMLPDF

Abstract

Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests in quantum simulations.Here we experimentally investigate the emergent Z 2 gauge invariance in a 1D superconducting circuit with 10 transmon qubits.By precisely adjusting staggered longitudinal and transverse fields to each qubit, we construct an effective Hamiltonian containing anLGT and gauge-broken terms.The corresponding matter sector can exhibit a localization, and there also exists a 3-qubit operator, of which the expectation value can retain nonzero for a long time in low-energy regimes.The above localization can be regarded as the confinement of matter fields, and the 3-body operator is the Z 2 gauge generator.These experimental results demonstrate that, despite the absence of gauge structure in the effective Hamiltonian, Z 2 gauge invariance can still emerge in low-energy regimes.Our work provides a method for both theoretically and experimentally studying the rich physics in quantum many-body systems with emergent gauge invariance.

DOI
10.1103/physrevresearch.4.l022060

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Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests in quantum simulations.Here we experimentally investigate the emergent Z 2 gauge invariance in a 1D superconducting circuit with 10 transmon qubits.By precisely adjusting staggered longitudinal and transverse fields to each qubit, we construct an effective Hamiltonian containing anLGT and gauge-broken terms.The corresponding matter sector can exhibit a localization, and there also exists a 3-qubit operator, of which the expectation value can retain nonzero for a long time in low-energy regimes.The above localization can be regarded as the confinement of matter fields, and the 3-body operator is the Z 2 gauge generator.These experimental results demonstrate that, despite the absence of gauge structure in the effective Hamiltonian, Z 2 gauge invariance can still emerge in low-energy regimes.Our work provides a method for both theoretically and experimentally studying the rich physics in quantum many-body systems with emergent gauge invariance.
Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate ℤ2 LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. By using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the ℤ2 LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.
We propose an implementation to approximate Z2\mathbb{Z}_2Z2​ lattice gauge theory (LGT) on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. Using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gaussian law of the Z2\mathbb{Z}_2Z2​ LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the existence of an approximate Gaussian law under the strong transverse field, the matter degree can also exhibit a confinement which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.
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A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Matter-induced plaquette terms in a Z2\mathbb{Z}_2Z2​ lattice gauge theory
Lattice gauge theories (LGTs) provide a powerful framework for studying confinement, topological order, and exotic quantum matter. In particular, the paradigmatic phenomenon of confinement, where dynamical matter is coupled to gauge fields and forms bound states, remains an open problem. In addition, LGTs can provide low-energy descriptions of quantum spin liquids, which is the focus of ongoing experimental research. However, the study of LGTs is often limited theoretically by their numerical complexity and experimentally in implementing challenging multi-body interactions, such as the plaquette terms crucial for the realization of many exotic phases of matter. Here we investigate a (2+1)(2+1)(2+1)D Z2\mathbb{Z}_2Z2​ LGT coupled to hard-core bosonic matter featuring a global U(1) symmetry, and show that dynamical matter naturally induces sizable plaquette interactions even in the absence of explicit plaquette terms in the Hamiltonian. Using a combination of density matrix renormalization group simulations and neural quantum state calculations up to a system size of 20×2020 \times 2020×20, we analyze the model across different fillings and electric field strengths. At small coupling strength, we find a large plaquette expectation value, independent of system size, for a wide range of fillings, which decreases in the presence of stronger electric fields. Furthermore, we observe signatures of a confinement-deconfinement transition at weak coupling strengths. Our results demonstrate that dynamical U(1) matter can induce complex multi-body interactions, suggesting a natural route to the realization of strong plaquette terms and paving the way for realizing a topological quantum spin liquid protected by a large gap.
While universal quantum computers remain under development, analog quantum simulators offer a powerful alternative for understanding complex systems in condensed matter, chemistry, and high-energy physics. One compelling application is the characterization of real-time lattice gauge theories (LGTs). LGTs are nonperturbative tools, utilizing discretized space-time to describe gauge-invariant models. They hold immense potential for understanding fundamental physics but require enforcing local constraints analogous to electromagnetism's Gauss's law. These constraints, which arise from gauge symmetries and dictate the form of the interaction between matter and gauge fields, are a significant challenge for simulators to enforce. Implementing these constraints at the hardware level in analog simulations is crucial. This requires realizing multibody interactions between matter and gauge-field elements, enabling them to evolve together while suppressing unwanted two-body interactions that violate the gauge symmetry. In this paper, we propose and implement a parametrically activated three-qubit interaction within a circuit quantum electrodynamics architecture. We experimentally demonstrate a minimal U(1)\text{U}(1)U(1) spin-12\frac{1}{2}21​ model with a time evolution that intrinsically satisfies Gauss's law in the system. This design serves as the foundational block for simulating LGTs on a superconducting photonic lattice.