Quantum variational optimization: The role of entanglement and problem hardness

2021/03/31 by Pablo Díez-Valle, Diego Porras, Juan José García‐Ripoll +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Mathematical optimization #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #quant-ph

paper · pdf · doi:10.1103/physreva.104.062426

published as Phys. Rev. A 104, 062426 (2021) · 12 pages, 10 figures, close to published version

openalex created_date 2021/04/13 · openalex publication_date 2021/12/16 · arxiv created 2021/12/28 · arxiv updated 2021/12/30 · openalex updated_date 2026/08/05

Abstract

The authors investigate the ability of variational quantum algorithms to solve a combinatorial optimization problem, and demonstrate an advantage when the entanglement structure in the algorithm is chosen to mimic the structure of the problem. Notably, they find that when a certain cost function is used the depth of variational circuits is only moderately relevant, which suggests that new classical methods using product states may outperform existing quantum architectures.

Citations

• How "Quantum" is the D-Wave Machine?
• A Quantum Approximate Optimization Algorithm
• A Limited Memory Algorithm for Bound Constrained Optimization
• Conditioning of quasi-Newton methods for function minimization
• A family of variable-metric methods derived by variational means
• A new approach to variable metric algorithms
• An efficient method for finding the minimum of a function of several variables without calculating derivatives
• Bootstrap Methods: Another Look at the Jackknife
• A variational eigenvalue solver on a photonic quantum processor
• A Simplex Method for Function Minimization
• Quantum Computing in the NISQ era and beyond
• Addressing hard classical problems with Adiabatically Assisted Variational Quantum Eigensolvers
• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Variational Quantum Algorithms
• Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing

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