The theory of variational hybrid quantum-classical algorithms

By Jarrod R. McClean, Jonathan Romero, Ryan Babbush, Alán Aspuru-Guzik. 2015

2,424 citations recorded by the source corpus.

Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘the quantum variational eigensolver’ was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c78988d6c8b3d0a0385164b372f202cdeb4a5849

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Citations in the corpus

Transfer learning in hybrid classical-quantum neural networks (2019, background): “One of the possible quantum generalizations of feedforward neural networks can be given in terms of variational quantum circuits [17, 24, 30, 30, 33, 34, 39, 41, 43].”
Circuit-centric quantum classifiers (2018, background): “Hybrid approaches called “variational algorithms” [2, 13, 14] are much more suited to near term quantum computing and are rapidly getting popularity in the quantum research community in recent months.”
Strawberry Fields: A Software Platform for Photonic Quantum Computing (2018, methodology): “Popular techniques include variational quantum eigensolvers [5, 6], quantum approximate optimization algorithms [7, 8], sampling from computationally hard probability distributions [9–17], and quantum annealing [18, 19].”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “[31] Jarrod McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,” New Journal of Physics 18, 023023 (2016).”
Harnessing the Power of the Second Quantum Revolution (2020, background): “Currently, hybrid quantum-classical models in which measurements on quantum states are inputs to a classical processor are seen as a promising arena for NISQ implementations of algorithms such as the VQE [84] and the quantum approximate-optimization algorithm (QAOA) [119].”
Scalable Quantum Simulation of Molecular Energies (2015, background): “While the unitary variant has no efficient preparation scheme on a classical computer, scalable methods of preparation for a fixed set of parameters on a quantum device have now been documented several times [19,20,22,23].”
Theory of variational quantum simulation (2018, methodology): “For solving static problems, the Rayleigh-Ritz variational method can be naturally generalised to the quantum regime, such as the variational quantum eigensolver (VQE) [29–40] and the quantum approximate optimisation algorithm (QAOA) [28].”
A Practical Quantum Instruction Set Architecture (2016, neutral): “0.20170217”
Effect of data encoding on the expressive power of variational quantum-machine-learning models (2020, background): “This approach is known by different names such as variational circuits [1, 2], quantum circuit learning [3], quantum neural networks [4, 5], or parametrised quantum circuits [6].”
Quantum technology for military applications (2021, background): “Simulating Molecules using VQE.”
Variational quantum algorithms for nonlinear problems (2019, background): “We achieve this by maximizing F = ⟨ψexact∣ψMPS⟩ as well as F = ⟨ψexact∣ψQA⟩ using standard tensor network optimization techniques [20, 21].”