Variational quantum algorithms

Abstract

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.