Digital simulation of zero-temperature spontaneous symmetry breaking in a superconducting lattice processor
Chang-Kang Hu, Guixu Xie, Kasper Poulsen, Yuxuan Zhou, Ji Chu, C. L. Liu, Ruiyang Zhou, Haolan Yuan, Yuecheng Shen, Song Liu, Nikolaj Thomas Zinner, Dian Tan, Alan C. Santos, Dapeng Yu
Quantum simulators are ideal platforms to investigate quantum phenomena that are inaccessible through conventional means, such as the limited resources of classical computers to address large quantum systems or due to constraints imposed by fundamental laws of nature. Here, through a digitized adiabatic evolution, we report an experimental simulation of antiferromagnetic (AFM) and ferromagnetic (FM) phase formation induced by spontaneous symmetry breaking (SSB) in a three-generation Cayley tree-like superconducting lattice. We develop a digital quantum annealing algorithm to mimic the system dynamics, and observe the emergence of signatures of SSB-induced phase transition through a connected correlation function. We demonstrate that the signature of a transition from classical AFM to quantum FM-like phase state happens in systems undergoing zero-temperature adiabatic evolution with only nearest-neighbor interacting systems, the shortest range of interaction possible. By harnessing properties of the bipartite Rényi entropy as an entanglement witness, we observe the formation of entangled quantum FM and AFM phases. Our results open perspectives for new advances in condensed matter physics and digitized quantum annealing. Recently, spontaneous symmetry breaking was reported in 1D and 2D lattices with long-range interactions on analogue quantum simulators. Here, using a digital quantum annealing algorithm, Hu et al. observe this effect in a tree-like superconducting qubit lattice with short-range interactions at zero temperature.
Quantum simulators are ideal platforms to investigate quantum phenomena that are inaccessible through conventional means, such as the limited resources of classical computers to address large quantum systems or due to constraints imposed by fundamental laws of nature. Here, through a digitized adiabatic evolution, we report an experimental simulation of antiferromagnetic (AFM) and ferromagnetic (FM) phase formation induced by spontaneous symmetry breaking (SSB) in a three-generation Cayley tree-like superconducting lattice. We develop a digital quantum annealing algorithm to mimic the system dynamics, and observe the emergence of signatures of SSB-induced phase transition through a connected correlation function. We demonstrate that the signature of a transition from classical AFM to quantum FM-like phase state happens in systems undergoing zero-temperature adiabatic evolution with only nearest-neighbor interacting systems, the shortest range of interaction possible. By harnessing properties of the bipartite Rényi entropy as an entanglement witness, we observe the formation of entangled quantum FM and AFM phases. Our results open perspectives for new advances in condensed matter physics and digitized quantum annealing. Recently, spontaneous symmetry breaking was reported in 1D and 2D lattices with long-range interactions on analogue quantum simulators. Here, using a digital quantum annealing algorithm, Hu et al. observe this effect in a tree-like superconducting qubit lattice with short-range interactions at zero temperature.
Quantum simulation platforms such as cold atoms, superconducting circuits, and trapped ions enable the experimental investigation of quantum many-body systems, with important implications for quantum technologies. In this thesis, we investigate how entanglement and correlations develop in such systems and how they can be harnessed both for the theoretical study of models relevant to condensed matter physics and for practical applications in quantum metrology. We begin by focusing on the adiabatic preparation of quantum many-body ground states. In particular, we show that quantum simulators can probe the link between spectral degeneracy and Spontaneous Symmetry Breaking, as pioneered by P.W. Anderson. We prove that odd-sized spin-½ systems exhibiting time-reversal symmetry sustain a net magnetization even away from the thermodynamic limit, thanks to an exact spectral degeneracy. Moreover, the symmetry-broken state exhibits scalable spin squeezing, a key resource for quantum metrology. We then turn to a different paradigm of evolution: quench dynamics. In particular, we show that monitoring the real-time evolution of correlations allows for the experimental measurement of the dispersion relation of fundamental excitations. In the case of two-dimensional long-range ordered systems, such as the dipolar XY model, these excitations are spin waves, leading to sharp features in the evolution of two-point correlation functions. Conversely, in one-dimensional systems, fundamental excitations have a fermionic nature, and their detection requires the measurement of non-local correlation functions. The latter, while inaccessible in condensed matter, are instead well suited to quantum simulators with individually addressable degrees of freedom.
A core concept in condensed matter physics is geometric frustration that leads to emergent spin phases in magnetic materials.These distinct phases, which depart from the conventional ferromagnet or the antiferromagnet, require unique computational techniques to decipher.In this study, we use the canonical Ising Shastry-Sutherland lattice to demonstrate new techniques for solving frustrated Hamiltonians using a quantum annealer of programmable superconducting qubits.This Hamiltonian can be tuned to produce a variety of intriguing ground states ranging from short-and long-range orders and fractional order parameters.We show that a large-scale finite-field quantum annealing experiment is possible on 468 logical spins of this model embedded into the quantum hardware.We determine microscopic spin configurations using an iterative quantum annealing protocol and develop mean-field boundary conditions to attenuate finitesize effects and defects.We not only recover all phases of the Shastry-Sutherland Ising model-including the well-known fractional magnetization plateau in a longitudinal field-but also predict the spin behavior at the critical points with significant ground-state degeneracy and in the presence of defects.The results lead us to establish the connection to the diffuse neutron scattering experiments by calculation of the static structure factors.
Direct continuous quantum phase transitions between phases that break distinct symmetries challenge the conventional Landau-Ginzburg-Wilson paradigm and provide a framework for deconfined quantum criticality. Here, we investigate a Landau-forbidden ferromagnetic-to-valence-bond-solid (FM-VBS) transition in a frustrated one-dimensional spin chain using superconducting quantum processors. Combining matrix-product-state-assisted circuit preparation with quantum-hardware measurements, we resolve the suppression of long-range ferromagnetic correlations and the redistribution of competing-order fluctuations across the transition. Distance-resolved correlations and finite-size analyses reveal signatures consistent with critical behavior. We further extend our investigation to nonequilibrium dynamics, directly preparing dimerized states and tracking the evolution of VBS order and joint FM-VBS fluctuations under local unitary interactions. Our results establish a versatile quantum-hardware framework for probing competing orders, critical correlations, and many-body dynamics beyond conventional Landau theory.
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.
Spontaneous symmetry breaking (SSB) is crucial to the occurrence of phase transitions. Once a phase transition occurs, a quantum system presents degenerate eigenstates that lack the symmetry of the Hamiltonian. After crossing the critical point, the system is essentially evolved to a quantum superposition of these eigenstates until decoherence sets in. Despite the fundamental importance and potential applications in quantum technologies, such quantum-mechanical SSB phenomena have not been experimentally explored in many-body systems. We here present an experimental demonstration of the SSB process in the Lipkin-Meshkov-Glick model, governed by the competition between the individual driving and intraqubit interaction. The model is realized in a circuit quantum electrodynamics system, where 6 Xmon qubits are coupled in an all-to-all manner through virtual photon exchange mediated by a resonator. The observed nonclassical correlations among these qubits in the symmetry-breaking region go beyond the conventional description of SSB, shedding new light on phase transitions for quantum many-body systems.
At the interface of quantum information and condensed matter physics, the study of entanglement in quantum many-body systems requires a new toolset which combines concepts from each. This thesis introduces a set of computational methods to study phases and phase transitions in lattice models of quantum systems, using the Renyi entropies as a means of quantifying entanglement. The scaling of entanglement entropy can give valuable insight into the phase of a condensed matter system. It can be used to detect exotic types of phases, to pinpoint transitions between phases, and can give us universal information about a system. \nThe first approach in this thesis is a technique to measure entanglement in finite size \nlattice systems using zero-temperature quantum Monte Carlo simulations. The algorithm \nis developed, implemented, and used to explore anomalous entanglement scaling terms in \nthe spin-1/2 Heisenberg antiferromagnet. \nIn the second part of this thesis, a new and complementary numerical technique is introduced to study entanglement not just in finite size systems, but as we approach the thermodynamic limit. This “numerical linked-cluster expansion” is used to study two different systems at their quantum critical points — continuous phase transitions occurring at zero temperature, at which these systems exhibit universal properties. Remarkably, these universal properties can be reflected in the scaling of entanglement. \nEntanglement offers a new perspective on condensed matter systems, one which takes us closer to genuinely understanding what goes on in these materials at the quantum mechanical level. This thesis demonstrates the first steps in developing an extensive list of computational tools that can be used to study entanglement over a wide range of interacting quantum many-body systems. With the ever increasing computational power available, it may be only a matter of time before these tools are used to create a comprehensive framework for the characterization of condensed matter phases and phase transitions.