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arXiv:2012.09265 · Nature Reviews Physics

Variational quantum algorithms

Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, Patrick J. Coles

Published Aug 12, 2021• 3,385 citations
arXivHTMLPDF
DOI
10.1038/s42254-021-00348-9

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Title: Dynamical Topology for Variational Quantum Algorithms

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Dynamical Topology for Variational Quantum Algorithms (DT-VQA) introduces a fundamentally new approach to variational quantum algorithm design, focusing on dynamically evolving topological connections. This paper proposes a framework where the topology of the quantum circuit is continuously adjusted based on the outcomes of a quantum simulation, optimizing circuit parameters through a learned optimization process. We present a novel algorithm that utilizes topological connectivity to guide the design of variational quantum circuits, aiming to improve the efficiency and accuracy of quantum simulations. Traditional variational quantum algorithms often suffer from limitations in adaptability and sensitivity to initial conditions, necessitating complex and computationally expensive parameter adjustments. DT-VQA addresses these challenges by incorporating topology into the optimization loop, allowing for a more flexible and potentially more efficient search space. The core mechanism involves constructing a dynamic, evolving topology that adapts to the simulation results, promoting a more robust and accurate solution. This work demonstrates the effectiveness of this approach through theoretical analysis and preliminary simulations, showcasing potential improvements in the performance of variational quantum algorithms.

•Aug 29, 2026•0 citations
This document is a pdf version of the series of blogposts about variational quantum algorithms (VQA) I originally posted on my blog Musty Thoughts. It provides an explanation of the basic variational algorithms, such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), as well as a more general framework for VQAs. It also describes some more advanced techniques that can be used to make these algorithms more efficient, as well as the challenges associated with using them.
Variational quantum algorithms (VQAs) are the leading candidates for practical applications of noisy intermediate-scale quantum (NISQ) devices. Recently, pulse-based variational quantum algorithms (p-VQAs) have emerged as a compelling alternative to traditional gate-based VQAs. By optimizing continuous control fields directly on hardware-native Hamiltonians, pulse-based methods are easy to implement and can significantly reduce quantum resource overhead, thereby enhancing the overall performance of quantum algorithms on NISQ devices. In this review, we present a comprehensive survey over recent advances in p-VQAs, covering theory, algorithms, and hardware deployments across various quantum computing platforms. We also review applications of p-VQAs to variational quantum eigensolver in quantum chemistry, quantum approximate optimization algorithm for combinatorial optimization, and quantum machine learning tasks.
Dynamical Topology for Variational Quantum Algorithms (DT-VQA) introduces a fundamentally new approach to variational quantum algorithm design, focusing on dynamically evolving topological connections. This paper proposes a framework where the topology of the quantum circuit is continuously adjusted based on the outcomes of a quantum simulation, optimizing circuit parameters through a learned optimization process. We present a novel algorithm that utilizes topological connectivity to guide the design of variational quantum circuits, aiming to improve the efficiency and accuracy of quantum simulations. Traditional variational quantum algorithms often suffer from limitations in adaptability and sensitivity to initial conditions, necessitating complex and computationally expensive parameter adjustments. DT-VQA addresses these challenges by incorporating topology into the optimization loop, allowing for a more flexible and potentially more efficient search space. The core mechanism involves constructing a dynamic, evolving topology that adapts to the simulation results, promoting a more robust and accurate solution. This work demonstrates the effectiveness of this approach through theoretical analysis and preliminary simulations, showcasing potential improvements in the performance of variational quantum algorithms.