Hamiltonian variational ansatz without barren plateaus

Abstract

Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned. One of the central problems is the trainability of PQCs. The cost function landscape of a randomly initialized PQC is often too flat, asking for an exponential amount of quantum resources to find a solution. This problem, dubbed barren plateaus, has gained lots of attention recently, but a general solution is still not available. In this paper, we solve this problem for the Hamiltonian variational ansatz (HVA), which is widely studied for solving quantum many-body problems. After showing that a circuit described by a time-evolution operator generated by a local Hamiltonian does not have exponentially small gradients, we derive parameter conditions for which the HVA is well approximated by such an operator. Based on this result, we propose an initialization scheme for the variational quantum algorithms and a parameter-constrained ansatz free from barren plateaus.

arXiv comment13+12 pages, 7 figures; Accepted for publication in Quantum

References in corpus (50)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• An introduction to quantum machine learning
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Complexity and Shock Wave Geometries
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Towards Practical Quantum Variational Algorithms
• Efficient variational quantum simulator incorporating active error minimisation
• Quantum mechanical evolution towards thermal equilibrium
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Quantum Computation as Geometry
• A rigorous and robust quantum speed-up in supervised machine learning
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Chaos and complexity by design
• Theory of variational quantum simulation
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• The Second Law of Quantum Complexity
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Out-of-Time-Order Correlation for Many-Body Localization
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Equilibration of quantum systems and subsystems
• Real- and imaginary-time evolution with compressed quantum circuits
• Quantum Complexity and Negative Curvature
• Linear growth of quantum circuit complexity
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• Large gradients via correlation in random parameterized quantum circuits
• Classically optimized Hamiltonian simulation
• Finite-size scaling of out-of-time-ordered correlators at late times
• Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Graph neural network initialisation of quantum approximate optimisation
• Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems
• Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits

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• Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver
• Resource-efficient quantum algorithm for linear systems of equations
• Exploiting many-body localization for scalable variational quantum simulation
• A coherent approach to quantum-classical optimization
• Estimates of loss function concentration in noisy parametrized quantum circuits
• Global optimization in variational quantum algorithms via dynamic tunneling method
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization
• Numerical investigation of the quantum inverse algorithm on small molecules
• Learning complexity gradually in quantum machine learning models
• Gradient Scalability and Taylor Surrogation of Quantum Cost Landscapes
• Qubit encodings for lattices of dipolar planar rotors
• Preparation of the single-spinon wave function on a quantum computer
• Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation