Finite-size criticality in fully connected spin models on superconducting quantum hardware

Abstract

The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different approaches to study quantum phase transitions. In this work, we exploit the new resources offered by quantum algorithms to detect the quantum critical behaviour of fully connected spin$-1/2$ models. We define a suitable Hamiltonian depending on an internal anisotropy parameter $\gamma ,$ that allows us to examine three paradigmatic examples of spin models, whose lattice is a fully connected graph. We propose a method based on variational algorithms run on superconducting transmon qubits to detect the critical behavior for systems of finite size. We evaluate the energy gap between the first excited state and the ground state, the magnetization along the easy-axis of the system, and the spin-spin correlations. We finally report a discussion about the feasibility of scaling such approach on a real quantum device for a system having a dimension such that classical simulations start requiring significant resources.

arXiv comment13 pages, 10 figures. Comments are welcome

References in corpus (60)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• The density-matrix renormalization group
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Scaling of Entanglement close to a Quantum Phase Transitions
• Noisy intermediate-scale quantum (NISQ) algorithms
• Critical Phenomena and Renormalization-Group Theory
• Quantum Convolutional Neural Networks
• Continuous Quantum Phase Transitions
• Parameterized quantum circuits as machine learning models
• Evaluating analytic gradients on quantum hardware
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Extending the computational reach of a noisy superconducting quantum processor
• Practical Quantum Error Mitigation for Near-Future Applications
• A simple all-microwave entangling gate for fixed-frequency superconducting qubits
• Variational Quantum Computation of Excited States
• Tools for quantum simulation with ultracold atoms in optical lattices
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum Superposition States of Bose-Einstein Condensates
• Cloud Quantum Computing of an Atomic Nucleus
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Subspace-search variational quantum eigensolver for excited states
• Scalable mitigation of measurement errors on quantum computers
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• A Quantum Computing View on Unitary Coupled Cluster Theory
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Fundamental limits of quantum error mitigation
• Resource Efficient Zero Noise Extrapolation with Identity Insertions
• Entanglement dynamics in the Lipkin-Meshkov-Glick model
• Quantum Phase Transition in the Finite Jaynes-Cummings Lattice Systems
• Quantum metrology in Lipkin-Meshkov-Glick critical systems
• Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Quantum-Classical Transition of the Escape Rate of a Uniaxial Spin System in an Arbitrarily Directed Field
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information
• Quantum computing of the ${}^6$Li nucleus via ordered unitary coupled clusters
• Variational approaches to constructing the many-body nuclear ground state for quantum computing
• Solving Nuclear Structure Problems with the Adaptive Variational Quantum Algorithm
• Variational Quantum Eigensolver for Frustrated Quantum Systems
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Lipkin model on a quantum computer
• Quantum phase detection generalisation from marginal quantum neural network models
• Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver
• Variational Quantum Anomaly Detection: Unsupervised mapping of phase diagrams on a physical quantum computer
• Simulating excited states of the Lipkin model on a quantum computer
• The Lipkin-Meshkov-Glick model as a particular limit of the SU(1,1) Richardson-Gaudin integrable models
• Quantum criticality using a superconducting quantum processor
• Improving the variational quantum eigensolver using variational adiabatic quantum computing
• Thermal transistor effect in quantum systems
• Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model
• Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
• Benchmarking near-term quantum devices with the Variational Quantum Eigensolver and the Lipkin-Meshkov-Glick model
• Quantum Thermal Amplifiers with Engineered Dissipation
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models

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