The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

Miháliková, Ivana; Pivoluska, Matej; Plesch, Martin; Friák, Martin; Nagaj, Daniel; Šob, Mojmı́r

doi:10.3390/nano12020243

Cited by 14 publications

(16 citation statements)

References 52 publications

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“…Only two circuits (which we will call Circuits 0 and 1 below) were needed in our case. Numerous runs (so-called shots) and measurements of the probabilities of the basis states were needed to obtain reliable expectation values for these two circuits (we used 4096 shots, unless specified otherwise) [ 53 ].…”

Section: Methodsmentioning

confidence: 99%

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

et al. 2022

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Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi–Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder–Mead and Powell methods. The results obtained when using the Ry variational form were better than those obtained when the RyRz form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight.

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Section: Methodsmentioning

confidence: 99%

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

et al. 2022

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“…The parametric R y -linear entangling circuit has been used successfully as a shallow yet effective hardware-efficient ansatz in finding the ground-state energies of various molecules via VQE. 37,38 The final evolved state |ψ(θ)⟩ = U ̂(θ)|ψ(0)⟩ can be used to evaluate the expectation value E(θ) on a classical computer, which the variational principle implies must be greater than or equal to…”

Section: Methodsmentioning

confidence: 99%

“…We evolve an initial Hartree–Fock state |ψ(0)⟩ with a suitable hardware-efficient ansatz for unitary operator Û ( θ ) and L layers by means of a quantum computer with the R y -parametrized rotation gates taking on the standard form Each L component is composed of a parametric layer equipped with R y rotation gates for each qubit and a linear entangling layer , where CNOT gates are arranged in a linear fashion from the first to the N th qubit setting for the recursive case. The parametric R y -linear entangling circuit has been used successfully as a shallow yet effective hardware-efficient ansatz in finding the ground-state energies of various molecules via VQE. , …”

Section: Methodsmentioning

confidence: 99%

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Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing

Choy

Wales

2023

J. Chem. Theory Comput.

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Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardwareefficient ansaẗze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.

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“…Only two circuits (that we will call circuit 0 and 1 below) are needed in our case. Numerous runs (so-called shots) and measurements of probabilities of basis states are needed to get reliable expectation values for these two circuits (we have used 4096 shots unless specified differently) [32].…”

Section: Methodsmentioning

confidence: 99%

Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule

Miháliková,

Friák,

Pivoluska

et al. 2021

Preprint

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Quantum computers are reaching one crucial milestone after another. Motivated by their 1 progress in quantum chemistry, we have performed an extensive series of simulations of quantum-2 computer runs that were aimed at inspecting best-practice aspects of these calculations. In order to 3 compare the performance of different set-ups, the ground-state energy of hydrogen molecule has 4 been chosen as a benchmark for which the exact solution exists in literature. Applying variational 5 quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi-Kitaev transformation 6 we have analyzed the impact of various computational technicalities. These include (i) the choice 7 of optimization methods, (ii) the architecture of quantum circuits, as well as (iii) different types 8 of noise when simulating real quantum processors. On these we eventually performed a series 9 of experimental runs as a complement to our simulations. The SPSA and COBYLA optimization 10 methods have clearly outperformed the Nelder-Mead and Powell methods. The results obtained when 11 using the R y variational form were better than those obtained when the R y R z form was used. The 12 choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization 13 method. The circular entangling layer has been found to worsen the performance of the COBYLA 14 method while the full entangling layer improved it. All four optimization methods sometimes lead 15 to an energy that corresponds to an excited state rather than the ground state. We also show that a 16 similarity analysis of measured probabilities can provide a useful insight.

show abstract

The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

Cited by 14 publications

References 52 publications

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing

Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule

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