A coherent approach to quantum-classical optimization
arXiv:2409.13924 · doi:10.1038/s42005-025-02111-3
Abstract
Hybrid quantum-classical optimization techniques, which incorporate the pre-optimization of Variational Quantum Algorithms (VQAs) using Tensor Networks (TNs), have been shown to allow for the reduction of quantum computational resources. In the particular case of large optimization problems, commonly found in real-world use cases, this strategy is almost mandatory to reduce the otherwise unfathomable execution costs and improve the quality of the results. We identify the coherence entropy as a crucial metric in determining the suitability of quantum states as effective initialization candidates. Our findings are validated through extensive numerical tests for the Quantum Approximate Optimization Algorithm (QAOA), in which we find that the optimal initialization states are pure Gibbs states. Further, these results are explained with the inclusion of a simple and yet novel notion of expressivity adapted to classical optimization problems. Based on this finding, we propose a quantum-classical optimization protocol that significantly improves on previous approaches for such tasks, with specific focus on its effectiveness.
14 pages, 10 figures
References in corpus (31)
- Quantum Machine Learning
- Variational Quantum Algorithms
- Supervised learning with quantum enhanced feature spaces
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum computational chemistry
- Quantum Chemistry in the Age of Quantum Computing
- Time-evolution methods for matrix-product states
- Classical simulation of quantum many-body systems with a tree tensor network
- Quantum advantage in learning from experiments
- Hybrid quantum-classical algorithms and quantum error mitigation
- Principal Component Analysis: A Natural Approach to Data Exploration
- An initialization strategy for addressing barren plateaus in parametrized quantum circuits
- Time-evolving a matrix product state with long-ranged interactions
- Variational quantum algorithms for nonlinear problems
- Towards Quantum Machine Learning with Tensor Networks
- Warm-starting quantum optimization
- Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
- Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
- Equivalence of quantum barren plateaus to cost concentration and narrow gorges
- Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
- Barren plateaus preclude learning scramblers
- Quantum Optimization with a Novel Gibbs Objective Function and Ansatz Architecture Search
- Tensor operators: constructions and applications for long-range interaction systems
- Hamiltonian variational ansatz without barren plateaus
- Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
- Thermodynamics as a Consequence of Information Conservation
- Dimensional Expressivity Analysis of Parametric Quantum Circuits
- Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
- Variational quantum simulation: a case study for understanding warm starts
- Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits
- Automatic quantum circuit encoding of a given arbitrary quantum state