Variational quantum algorithms

By M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio and 1 more. Nature Reviews Physics, 2020

3,982 citations recorded by the source corpus.

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers, owing to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will probably 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 parameterized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisaged for quantum computers, and they appear to be 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. The advent of commercial quantum devices has ushered in the era of near-term quantum computing. Variational quantum algorithms are promising candidates to make use of these devices for achieving a practical quantum advantage over classical computers. Variational quantum algorithms (VQAs) are the leading proposal for achieving quantum advantage using near-term quantum computers. VQAs have been developed for a wide range of applications, including finding ground states of molecules, simulating dynamics of quantum systems and solving linear systems of equations. VQAs share a common structure, where a task is encoded into a parameterized cost function that is evaluated using a quantum computer, and a classical optimizer trains the parameters in the VQA. The adaptive nature of VQAs is well suited to handle the constraints of near-term quantum computers. Trainability, accuracy and efficiency are three challenges that arise when applying VQAs to large-scale applications, and strategies are currently being developed to address these challenges. Variational quantum algorithms (VQAs) are the leading proposal for achieving quantum advantage using near-term quantum computers. VQAs have been developed for a wide range of applications, including finding ground states of molecules, simulating dynamics of quantum systems and solving linear systems of equations. VQAs share a common structure, where a task is encoded into a parameterized cost function that is evaluated using a quantum computer, and a classical optimizer trains the parameters in the VQA. The adaptive nature of VQAs is well suited to handle the constraints of near-term quantum computers. Trainability, accuracy and efficiency are three challenges that arise when applying VQAs to large-scale applications, and strategies are currently being developed to address these challenges.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c1cf657d1e13149ee575b5ca779e898938ada60a

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Citations in the corpus

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “The relation of QAOA and other variational algorithms [125] to QOCT is a lot closer, though [141, 276, 639].”
Training Variational Quantum Algorithms Is NP-Hard. (2021, neutral): “[4] for a review.”
Error mitigation with Clifford quantum-circuit data (2020, methodology): “It also includes variational quantum algorithms [3, 10, 18, 34, 40], some of which can be used to remove the eﬀects of in-coherent noise [9, 29–31 , 42].”
Quantum computing with Qiskit (2024, background): “For example, a common pattern is to iteratively generate new circuits that depend on the results obtained from a previous batch of circuits, which can be seen as a loop around the last three steps above [29].”
Quantum variational algorithms are swamped with traps (2022, neutral): “VQAs have found numerous applications 18 , and a countless number of VQA instances have been proposed for various quantum learning tasks.”
Ising machines as hardware solvers of combinatorial optimization problems (2022, methodology): “Hybrid Quantum-Classical Algorithms The aim of variational quantum algorithms 158 is to solve classical and quantum optimization problems by combining a parametrized quantum circuit with a classical optimizer to obtain the variational parameters.”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “In Section III we present the theoretical framework for VQAs, which FIG.”
Connecting ansatz expressibility to gradient magnitudes and barren plateaus (2021, methodology): “Variational quantum algorithms have gathered attention as a computational strategy that is well suited to the constraints imposed by NISQ devices [3–20].”
Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control (2020, background): “A connection between optimal control theory and variational quantum algorithms [150] has been established in [151].”
VQE method: a short survey and recent developments (2021, methodology): “Several comprehensive reviews covering VQE have been published recently.[21, 22, 23, 24] The goal of this work is to present recent advances in methods that produce shorter VQE circuits or provide higher accuracy.”
Quantum convolutional neural network for classical data classification (2021, methodology): “The PQC models—also known as variational quantum circuits (Cerezo et al. 2021)—are attractive since they are expected to be suitable for Noisy Intermediate-Scale Quantum (NISQ) hardware (Preskill 2018; Bharti et al. 2021).”
Challenges and opportunities in quantum machine learning (2022, background): “These involve a sequence of unitary gates acting on the quantum data states | ψ j (cid:105) , some of which have free parameters θ that will be trained to solve the problem at hand [38].”
Distributed Quantum Computing: a Survey (2022, neutral): “These paradigms include the Quantum Fourier Transform (QFT) [51], the Grover Operator (GO) [52], the Harrow/Hassidim/Lloyd (HHL) method for linear systems [53], Variational Quantum Algorithms (VQA) [54], and direct Hamiltonian simulation (SIM).”
The randomized measurement toolbox (2022, background): “95 , Springer Nature Ltd. compressing quantum circuits 113 .”
Noise-induced barren plateaus in variational quantum algorithms (2020, background): “At the heart of this discussion are Variational Quantum Algorithms (VQAs), which are believed to be the best hope for near-term quantum advantage [2–4].”