Google Research

Variational Quantum Algorithms

  • Marco Cerezo
  • Andrew Arrasmith
  • Ryan Babbush
  • Simon Benjamin
  • Suguro Endo
  • Keisuke Fujii
  • Jarrod Ryan McClean
  • Kosuke Mitarai
  • Xiao Yuan
  • Lukasz Cincio
  • Patrick Coles
Nature Reviews Physics (2021)


Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications, although fault-tolerant quantum computers will likely not be available for several years. Currently available quantum devices have serious constraints, including limited qubit numbers and noise processes that limit circuit depth. Variational Quantum Algorithms (VQAs), which employ 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. In this review article we present an overview of the field of VQAs. Furthermore, we discuss strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage.

Research Areas

Learn more about how we do research

We maintain a portfolio of research projects, providing individuals and teams the freedom to emphasize specific types of work