An adaptive variational algorithm for exact molecular simulations on a quantum computer

Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin; Mayhall, Nicholas J.

doi:10.1038/s41467-019-10988-2

Cited by 797 publications

(967 citation statements)

References 52 publications

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“…the inclusion of noise and momentum terms in the optimization procedure, the simplification of the function landscape by increase of the model size [46] or the computation of higher order gradients. Moreover, schemes that were developed in the context of VQE algorithms, such as adaptive initialization [47], could help to circumvent this issue.…”

Section: Discussionmentioning

confidence: 99%

Quantum Generative Adversarial Networks for learning and loading random distributions

2019

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Quantum algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best known methods require O (2 n ) gates to load an exact representation of a generic data structure into an n-qubit state. This scaling can easily predominate the complexity of a quantum algorithm and, thereby, impair potential quantum advantage.Our work presents a hybrid quantum-classical algorithm for efficient, approximate quantum state loading. More precisely, we use quantum Generative Adversarial Networks (qGANs) to facilitate efficient learning and loading of generic probability distributions -implicitly given by data samples -into quantum states. Through the interplay of a quantum channel, such as a variational quantum circuit, and a classical neural network, the qGAN can learn a representation of the probability distribution underlying the data samples and load it into a quantum state.The loading requires O (poly (n)) gates and can, thus, enable the use of potentially advantageous quantum algorithms, such as Quantum Amplitude Estimation.We implement the qGAN distribution learning and loading method with Qiskit and test it using a quantum simulation as well as actual quantum processors provided by the IBM Q Experience. Furthermore, we employ quantum simulation to demonstrate the use of the trained quantum channel in a quantum finance application.

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Section: Discussionmentioning

confidence: 99%

Quantum Generative Adversarial Networks for learning and loading random distributions

2019

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“…However, this comes at the cost of an increased number of measurements, and the introduction of a wavefunction ansatz that can limit the accuracy of the simulation (although our recent approach, ADAPT-VQE, can remove the ansatz error). 8 The initial demonstration of VQE 7 was followed by several theoretical studies [9][10][11][12][13][14][15] and demonstrations on other hardware such as superconducting qubits 10,14,16 and trapped ions. 17,18 A key ingredient in VQE is the ansatz, which is implemented as a quantum circuit which constructs trial wavefunctions that are measured and then updated in a classical optimization loop.…”

Section: Introductionmentioning

confidence: 99%

“…To answer this question, we perform classical simulations with randomly shuffled operators using a custom code built with OpenFermion 28 and Psi4, 29 which utilizes the gradient algorithm described in the Appendix of Ref. 8. The results using various operator orderings are compared to both UCCSD and Full CI (FCI).…”

Section: Introductionmentioning

confidence: 99%

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Grimsley

Claudino

Economou

et al. 2019

J. Chem. Theory Comput.

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144

148

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The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact k-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a "model chemistry", in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.

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“…Hybrid quantum-classical algorithms with a variational eigenvalue solver are among the most promising algorithms for near-term applications [6,[29][30][31]. For our approach we utilize a variational eigensolver on the quantum device but apply it only to the optimization of the 2DM in the naturalorbital basis set.…”

Section: B Variational Hybrid Algorithmmentioning

confidence: 99%

Efficient two-electron ansatz for benchmarking quantum chemistry on a quantum computer

Smart

Mazziotti

2020

Phys. Rev. Research

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Quantum chemistry provides key applications for near-term quantum computing, but these are greatly complicated by the presence of noise. In this work we present an efficient ansatz for the computation of twoelectron atoms and molecules within a hybrid quantum-classical algorithm. The ansatz exploits the fundamental structure of the two-electron system, treating the nonlocal and local degrees of freedom on the quantum and classical computers, respectively. Here the nonlocal degrees of freedom scale linearly with respect to basis-set size, giving a linear ansatz with only O(1) circuit preparations required for reduced state tomography. We implement this benchmark with error mitigation on two publicly available quantum computers, calculating accurate dissociation curves for four-and six-qubit calculations of H 2 and H 3 + .

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An adaptive variational algorithm for exact molecular simulations on a quantum computer

Cited by 797 publications

References 52 publications

Quantum Generative Adversarial Networks for learning and loading random distributions

Quantum Generative Adversarial Networks for learning and loading random distributions

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Efficient two-electron ansatz for benchmarking quantum chemistry on a quantum computer

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