Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems

Abstract

Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits. Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo. Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems. Hence, the Trotterized MERA VQE is a promising route for the efficient investigation of strongly-correlated quantum many-body systems on quantum computers. Furthermore, we show how the convergence can be substantially improved by building up the MERA layer by layer in the initialization stage and by scanning through the phase diagram during optimization. For the Trotter circuits being composed of single-qubit and two-qubit rotations, it is experimentally advantageous to have small rotation angles. We find that the average angle amplitude can be reduced considerably with negligible effect on the energy accuracy. Benchmark simulations suggest that the structure of the Trotter circuits for the TMERA tensors is not decisive; in particular, brick-wall circuits and parallel random-pair circuits yield very similar energy accuracies.

11 pages, 7 figures, 2 tables; substantial extension of the part on a quantum advantage, in addition to the common classical fMERA optimization based on exact energy gradients (EEG), we now also compare the TMERA VQE to fMERA VMC, TMERA EEG, and TMERA VMC and discuss alternative classical algorithms; further minor improvements; published version

References in corpus (80)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Noisy intermediate-scale quantum (NISQ) algorithms
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Entanglement renormalization
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• A class of quantum many-body states that can be efficiently simulated
• Quantum Monte Carlo with Directed Loops
• Scalable Quantum Simulation of Molecular Energies
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• Variational ansatz-based quantum simulation of imaginary time evolution
• Experimental Comparison of Two Quantum Computing Architectures
• Benchmarking an 11-qubit quantum computer
• Quantum Natural Gradient
• Robust determination of molecular spectra on a quantum processor
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Optimal Creation of Entanglement Using a Two--Qubit Gate
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• A geometric theory of non-local two-qubit operations
• Algorithms for entanglement renormalization
• Towards Quantum Machine Learning with Tensor Networks
• Solving strongly correlated electron models on a quantum computer
• Simulating quantum many-body dynamics on a current digital quantum computer
• Fast Reset and Suppressing Spontaneous Emission of a Superconducting Qubit
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Fermionic Projected Entangled Pair States
• Accelerated Variational Quantum Eigensolver
• Meron-Cluster Solution of Fermion Sign Problems
• Quantum Circuits for Isometries
• Fast and Unconditional All-Microwave Reset of a Superconducting Qubit
• Optimal Quantum Measurements of Expectation Values of Observables
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Fermionic multi-scale entanglement renormalization ansatz
• Entanglement renormalization in two spatial dimensions
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• Variational Quantum Eigensolver with Fewer Qubits
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach
• Exact Quantum Monte Carlo Process for the Statistics of Discrete Systems
• Unitary circuits for strongly correlated fermions
• Holographic quantum algorithms for simulating correlated spin systems
• The Variational Power of Quantum Circuit Tensor Networks
• Critical behavior of the S=3/2 antiferromagnetic Heisenberg chain
• Self-Consistent Tensor Product Variational Approximation for 3D Classical Models
• Faster identification of optimal contraction sequences for tensor networks
• Pulsed reset protocol for fixed-frequency superconducting qubits
• Riemannian optimization of isometric tensor networks
• Experimental quantum computational chemistry with optimised unitary coupled cluster ansatz
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Suppression of mid-circuit measurement crosstalk errors with micromotion
• Variational quantum algorithm with information sharing
• Real-space renormalization yields finite correlations
• Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study
• Critical properties and Rényi entropies of the spin-3/2 XXZ chain
• Stripe Ansatzs from Exactly Solved Models
• Holographic simulation of correlated electrons on a trapped ion quantum processor
• Topological effects at short antiferromagnetic Heisenberg chains
• Fermionic tensor network methods
• Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• The N-Leg spin-S Heisenberg ladders: A DMRG study
• Quantum-classical eigensolver using multiscale entanglement renormalization
• Low-energy physics of isotropic spin-1 chains in the critical and Haldane phases
• Probing critical states of matter on a digital quantum computer
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo

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