Improving the trainability of VQE on NISQ computers for solving portfolio optimization using convex interpolation

Abstract

Solving combinatorial optimization problems using variational quantum algorithms (VQAs) might be a promise application in the NISQ era. However, the limited trainability of VQAs could hinder their scalability to large problem sizes. In this paper, we improve the trainability of variational quantum eigensolver (VQE) by utilizing convex interpolation to solve portfolio optimization. Based on convex interpolation, the location of the ground state can be evaluated by learning the property of a small subset of basis states in the Hilbert space. This enlightens naturally the proposals of the strategies of close-to-solution initialization, regular cost function landscape, and recursive ansatz equilibrium partition. The successfully implementation of a $40$-qubit experiment using only $10$ superconducting qubits demonstrates the effectiveness of our proposals. Furthermore, the quantum inspiration has also spurred the development of a prototype greedy algorithm. Extensive numerical simulations indicate that the hybridization of VQE and greedy algorithms achieves a mutual complementarity, combining the advantages of both global and local optimization methods. Our proposals can be extended to improve the trainability for solving other large-scale combinatorial optimization problems that are widely used in real applications, paving the way to unleash quantum advantages of NISQ computers in the near future.

References in corpus (34)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Ising formulations of many NP problems
• Efficient classical simulation of slightly entangled quantum computations
• Barren plateaus in quantum neural network training landscapes
• Noisy intermediate-scale quantum (NISQ) algorithms
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• The Variational Quantum Eigensolver: a review of methods and best practices
• Challenges and Opportunities in Quantum Machine Learning
• Quantum computing for finance: overview and prospects
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• A Review on Quantum Approximate Optimization Algorithm and its Variants
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Simulating Large Quantum Circuits on a Small Quantum Computer
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Effect of barren plateaus on gradient-free optimization
• Improving Variational Quantum Optimization using CVaR
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Distributed Quantum Computing: a Survey
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• Large gradients via correlation in random parameterized quantum circuits
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Performance of hybrid quantum/classical variational heuristics for combinatorial optimization
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks
• Expressibility of the alternating layered ansatz for quantum computation
• Benchmarking of Different Optimizers in the Variational Quantum Algorithms for Applications in Quantum Chemistry
• Efficient classical algorithms for simulating symmetric quantum systems
• Doubly optimal parallel wire cutting without ancilla qubits
• Classical Splitting of Parametrized Quantum Circuits
• Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance