Variational Quantum Algorithms

2020/12/31 by M. Cerezo, Andrew Arrasmith, Ryan Babbush +8 · 418 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #cs.LG #quant-ph #stat.ML

paper · pdf · doi:10.1038/s42254-021-00348-9

published as Nature Reviews Physics 3, 625-644 (2021) · Review Article. 33 pages, 7 figures. Updated to published version

openalex created_date 2020/12/21 · crossref issued 2021/08/12 · crossref published 2021/08/12 · crossref published-online 2021/08/12 · openalex publication_date 2021/08/12 · crossref created 2021/08/12 · arxiv created 2021/10/04 · arxiv updated 2021/10/05 · crossref deposited 2023/02/05 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31

Abstract

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will likely not be available in the near future. Current quantum devices have serious constraints, including limited numbers of qubits and noise processes that limit circuit depth. Variational Quantum Algorithms (VQAs), which use a classical optimizer to train a parametrized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisioned for quantum computers, and they appear to the best hope for obtaining quantum advantage. Nevertheless, challenges remain including the trainability, accuracy, and efficiency of VQAs. Here we overview the field of VQAs, discuss strategies to overcome their challenges, and highlight the exciting prospects for using them to obtain quantum advantage.

Citations

• Simulated Quantum Computation of Molecular Energies
• Simulating Quantum Computation by Contracting Tensor Networks
• Quantum Machine Learning
• Error mitigation for short-depth quantum circuits
• Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision
• Quantum Computing in the NISQ era and beyond
• Quantum Computation and Quantum Information
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation
• Quantum computational advantage using photons
• Long-time simulations with high fidelity on quantum hardware

Cited by

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• Near-Optimal Parameter Tuning of Level-1 QAOA for Ising Models
• Ground State Energy of He molecule Using a Four-Qubit Photonic Processor with the Variational Quantum Eigensolver
• Continuous-Variable Quantum Encoding Techniques: A Comparative Study of Embedding Techniques and Their Impact on Machine Learning Performance
• Consensus-based qubit configuration optimization for variational algorithms on neutral atom quantum systems
• Applications of Hybrid Machine Learning Methods to Large Datasets: A Case Study
• Equating quantum imaginary time evolution, Riemannian gradient flows, and stochastic implementations