FLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuits

Abstract

When compared to fault-tolerant quantum computational strategies, variational quantum algorithms stand as one of the candidates with the potential of achieving quantum advantage for real-world applications in the near term. However, the optimization of the circuit parameters remains arduous and is impeded by many obstacles such as the presence of barren plateaus, many local minima in the optimization landscape, and limited quantum resources. A non-random initialization of the parameters seems to be key to the success of the parametrized quantum circuits (PQC) training. Drawing and extending ideas from the field of meta-learning, we address this parameter initialization task with the help of machine learning and propose FLIP: a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters from a family of related problems which are used as the training set. The flexibility advocated to FLIP hinges in the possibility of predicting the initialization of parameters in quantum circuits with a larger number of parameters from those used in the training phase. This is a critical feature lacking in other meta-learning parameter initializing strategies proposed to date. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.

arXiv comment15 pages, 11 figures. Figures revised and minor changes for clarification throughout the main text

References in corpus (22)

• Correlated Electrons in High Temperature Superconductors
• 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
• Adiabatic Quantum Computing
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Meta-SGD: Learning to Learn Quickly for Few-Shot Learning
• Towards Practical Quantum Variational Algorithms
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Differentiable Learning of Quantum Circuit Born Machine
• Quantum Approximate Optimization of the Long-Range Ising Model with a Trapped-Ion Quantum Simulator
• The one-dimensional Hubbard model: A reminiscence
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Estimating the gradient and higher-order derivatives on quantum hardware
• Quantum Optimization with a Novel Gibbs Objective Function and Ansatz Architecture Search
• Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem
• Learning to learn with quantum neural networks via classical neural networks
• For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances
• Abrupt Transitions in Variational Quantum Circuit Training
• An application benchmark for fermionic quantum simulations

Cited by in corpus (11)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Graph neural network initialisation of quantum approximate optimisation
• Molecular Quantum Circuit Design: A Graph-Based Approach
• Quantum algorithm for credit valuation adjustments
• Hyperparameter Importance of Quantum Neural Networks Across Small Datasets
• ORQVIZ: Visualizing High-Dimensional Landscapes in Variational Quantum Algorithms
• Generative flow-based warm start of the variational quantum eigensolver
• Optimizing Quantum Variational Circuits with Deep Reinforcement Learning