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.
Highlights
Quantum computing holds promise for a number of applications that have motivated the decades-long quest to build the necessary physical hardware
Variational Quantum Algorithms (VQAs) have been proposed for essentially all applications that researchers have envisioned for quantum computers, and they appear to the best hope for obtaining quantum advantage
VQAs leverage the toolbox of classical optimization, since VQAs use parametrized quantum circuits to be run on the quantum computer, and outsource the parameter optimization to a classical optimizer
Summary
Quantum computing holds promise for a number of applications that have motivated the decades-long quest to build the necessary physical hardware. Variational Quantum Algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantage on NISQ devices. VQAs leverage the toolbox of classical optimization, since VQAs use parametrized quantum circuits to be run on the quantum computer, and outsource the parameter optimization to a classical optimizer This approach has the added advantage of keeping the quantum circuit depth shallow and mitigating noise, in contrast to quantum algorithms developed for the fault-tolerant era. VQAs have already been considered for a plethora of applications (see Figure 3), covering essentially all of the applications that researchers had envisioned for quantum computers They may be the key to obtaining near-term quantum advantage, VQAs still face important challenges, including their trainability, accuracy, and effi-. In this Review, we discuss the exciting prospects for VQAs, and we highlight the challenges that must be overcome to obtain the ultimate goal of quantum advantage
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