Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Abstract

We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.

References in corpus (39)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Machine learning phases of matter
• NMR Techniques for Quantum Control and Computation
• Time-dependent variational principle for quantum lattices
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Quantum criticality
• Quantum control theory and applications: A survey
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• A Theory of Trotter Error
• Quantum Criticality: competing ground states in low dimensions
• Strong and weak thermalization of infinite non-integrable quantum systems
• Machine learning quantum phases of matter beyond the fermion sign problem
• Sequential generation of entangled multi-qubit states
• Towards Quantum Machine Learning with Tensor Networks
• Information Scrambling in Computationally Complex Quantum Circuits
• Identifying topological order through unsupervised machine learning
• Efficient tomography of a quantum many-body system
• Real- and imaginary-time evolution with compressed quantum circuits
• Cluster Dynamical Mean Field analysis of the Mott transition
• Probing the dynamical phase transition with a superconducting quantum simulator
• Isometric Tensor Network States in Two Dimensions
• Dynamics after a sweep through a quantum critical point
• Sequential Generation of Matrix-Product States in Cavity QED
• Observation of dynamical quantum phase transition by a superconducting qubit simulation
• Crossing a topological phase transition with a quantum computer
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Observation of separated dynamics of charge and spin in the Fermi-Hubbard model
• Quantum Simulation of the Sachdev-Ye-Kitaev Model by Asymmetric Qubitization
• Accurately computing electronic properties of a quantum ring
• Sequentially generated states for the study of two dimensional systems
• Quantum error mitigation via matrix product operators
• The Lyapunov Spectrum of Quantum Thermalisation
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Realizing topologically ordered states on a quantum processor

Cited by in corpus (8)

• Quantum Error Mitigation
• Characterizing a non-equilibrium phase transition on a quantum computer
• Optimised Trotter Decompositions for Classical and Quantum Computing
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Time Evolution of Uniform Sequential Circuits
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials
• Two Dimensional Isometric Tensor Networks on an Infinite Strip