Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz

Abstract

A large ongoing research effort focuses on Variational Quantum Algorithms (VQAs), representing leading candidates to achieve computational speed-ups on current quantum devices. The scalability of VQAs to a large number of qubits, beyond the simulation capabilities of classical computers, is still debated. Two major hurdles are the proliferation of low-quality variational local minima, and the exponential vanishing of gradients in the cost function landscape, a phenomenon referred to as barren plateaus. Here we show that by employing iterative search schemes one can effectively prepare the ground state of paradigmatic quantum many-body models, circumventing also the barren plateau phenomenon. This is accomplished by leveraging the transferability to larger system sizes of iterative solutions, displaying an intrinsic smoothness of the variational parameters, a result that does not extend to other solutions found via random-start local optimization. Our scheme could be directly tested on near-term quantum devices, running a refinement optimization in a favorable local landscape with non-vanishing gradients.

5 + 9 pages, 4 + 12 figures, comments are welcome

References in corpus (8)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Evenly distributed unitaries: on the structure of unitary designs
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Avoiding barren plateaus using classical shadows
• Random quantum circuits are approximate unitary $t$-designs in depth $O\left(n{t}^{5+o(1)}\right)$
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Two-dimensional ${\mathbb{Z}}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
• Accelerated variational algorithms for digital quantum simulation of many-body ground states

Cited by in corpus (39)

• Barren Plateaus in Variational Quantum Computing
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Barren plateaus in quantum tensor network optimization
• Hamiltonian variational ansatz without barren plateaus
• Quantum approximate optimization via learning-based adaptive optimization
• Challenges of variational quantum optimization with measurement shot noise
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Variational quantum simulation: a case study for understanding warm starts
• Engineered dissipation to mitigate barren plateaus
• Neural network encoded variational quantum algorithms
• Lie-algebraic classical simulations for quantum computing
• Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainability
• Diabatic Quantum Annealing for the Frustrated Ring Model
• EHA: Entanglement-variational Hardware-efficient Ansatz for Eigensolvers
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets
• Convergence of Digitized-Counterdiabatic QAOA: circuit depth versus free parameters
• Symmetry-informed transferability of optimal parameters in the Quantum Approximate Optimization Algorithm
• Hybrid quantum learning with data re-uploading on a small-scale superconducting quantum simulator
• Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations
• Characterization of variational quantum algorithms using free fermions
• Equivalence of cost concentration and gradient vanishing for quantum circuits: An elementary proof in the Riemannian formulation
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Beyond Quantum Annealing: Optimal control solutions to MaxCut problems
• Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver
• Sketching phase diagrams using low-depth variational quantum algorithms
• SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation
• Reusability Report: Comparing gradient descent and monte carlo tree search optimization of quantum annealing schedules
• Efficient quantum-enhanced classical simulation for patches of quantum landscapes
• Tensor-Programmable Quantum Circuits for Solving Differential Equations
• Pitfalls when tackling the exponential concentration of parameterized quantum models
• Perturbative gadgets for gate-based quantum computing: Non-recursive constructions without subspace restrictions
• Syndrome decoding by quantum approximate optimization
• Efficient Online Quantum Circuit Learning with No Upfront Training
• Exploiting many-body localization for scalable variational quantum simulation
• Generative flow-based warm start of the variational quantum eigensolver
• Learning complexity gradually in quantum machine learning models
• Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization