Quantum optimization using variational algorithms on near-term quantum devices

By Nikolaj Moll, P. Barkoutsos, Lev S. Bishop, Jerry M. Chow, Andrew W. Cross, Daniel J. Egger, Stefan Filipp, Andreas Fuhrer, Jay M. Gambetta, M. Ganzhorn and 8 more. Quantum Science and Technology, 2017

764 citations recorded by the source corpus.

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fa8079f389756c88a3221bdf489f833e2ea91d3f

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Citations in the corpus

Variational Quantum Computation of Excited States (2018, methodology): “Here we study hybrid quantum-classical algorithms, which dramatically reduce the required gate depth to run and somewhat mitigate errors, by closely integrating classical and quantum subroutines [2, 9, 14, 15, 21, 23, 26, 40].”
Variational quantum algorithms (2020, background): “Here we discuss a different possibility where one employs a VQA to solve a classical optimization problem [105].”
Quantum simulation and computing with Rydberg-interacting qubits (2020, methodology): “= − 1 / 2 , following the convention in Moll et al. 212 .”
Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices (2018, background): “[4] Nikolaj Moll, Panagiotis Barkoutsos, Lev S Bishop, Jerry M Chow, Andrew Cross, Daniel J Egger, Stefan Filipp, Andreas Fuhrer, Jay M Gambetta, Marc Ganzhorn, Abhinav Kandala, Antonio Mezzacapo, Peter Müller, Walter Riess, Gian Salis, John Smolin, Ivano Tavernelli, and Kristan Temme, “Quantum opti”
Barren plateaus in quantum neural network training landscapes (2018, methodology): “Since then, the quantum approximate optimization algo-rithm was developed in a similar context to address hard optimization problems [5, 17–19].”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, methodology): “The variational method has shown huge potentials in applications such as quantum machine learning [4], [7], [56], [63], numerical analysis [37], [39], quantum simulation [30], [31], [52], and optimizations [18], [47].”