Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver

Yoshikawa, Takeshi; Takanashi, Tomoya; Nakai, Hiromi

doi:10.1021/acs.jctc.2c00602

Cited by 4 publications

(2 citation statements)

References 85 publications

(111 reference statements)

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“…Research has also focused on incorporating problem decomposition techniques developed for classical quantum chemistry applications − into quantum algorithms to further improve the efficiency of simulations on near-term quantum and FTQC devices. − Problem decomposition techniques offer the advantage of decomposing the full electronic structure problem of a molecule into smaller subproblems that can be solved with fewer qubits and qubit gates, and the aforementioned preprocessed Hamiltonians can be easily combined. Such approaches have a long history, originating from the application of the Bethe–Goldstone equation in quantum chemistry in the 1960s. − It has been shown that, by decomposing the correlation energy of the molecular system into n -body subsystems (increments) through the expansion of occupied − or virtual ,, orbitals, correlation energies close to the FCI accuracy can be recovered at low values of n in an embarrassingly parallel computation.…”

Section: Introductionmentioning

confidence: 99%

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation

Xu,

Shimomoto,

Ten-no

et al. 2024

J. Phys. Chem. A

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In this work, we utilize the framework of many-body expansion (MBE) to decompose electronic structures into fragments by incrementing virtual orbitals, aiming to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. While our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and its generalization, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bondbreaking processes of the ground state of two molecules (H 2 O and N 2 ) and calculate the ground and excited state energies of three molecules (LiH, CH + , and H 2 O). The results demonstrate that our approach can, in principle, provide reliable descriptions in all the tests including strongly correlated systems when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.

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Section: Introductionmentioning

confidence: 99%

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation

Xu,

Shimomoto,

Ten-no

et al. 2024

J. Phys. Chem. A

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“…Employing the random subspace technique in a quantum machine learning setting would parallel the various quantum circuit splitting techniques (c.f. for example [19]), and divide-and-conquer approaches, that have been utilized in the field of quantum chemistry [20] and quantum optimization [21].…”

Section: Introductionmentioning

confidence: 99%

Resource Saving via Ensemble Techniques for Quantum Neural Networks

Incudini¹,

Grossi²,

Ceschini³

et al. 2023

Preprint

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Quantum neural networks hold significant promise for numerous applications, particularly as they can be executed on the current generation of quantum hardware. However, due to limited qubits or hardware noise, conducting large-scale experiments often requires significant resources. Moreover, the output of the model is susceptible to corruption by quantum hardware noise. To address this issue, we propose the use of ensemble techniques, which involve constructing a single machine learning model based on multiple instances of quantum neural networks. In particular, we implement bagging and AdaBoost techniques, with different data loading configurations, and evaluate their performance on both synthetic and real-world classification and regression tasks. To assess the potential performance improvement under different environments, we conduct experiments on both simulated, noiseless software and IBM superconducting-based QPUs, suggesting these techniques can mitigate the quantum hardware noise. Additionally, we quantify the amount of resources saved using these ensemble techniques. Our findings indicate that these methods enable the

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Resource saving via ensemble techniques for quantum neural networks

Incudini,

Grossi,

Ceschini

et al. 2023

Quantum Mach. Intell.

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Quantum neural networks hold significant promise for numerous applications, particularly as they can be executed on the current generation of quantum hardware. However, due to limited qubits or hardware noise, conducting large-scale experiments often requires significant resources. Moreover, the output of the model is susceptible to corruption by quantum hardware noise. To address this issue, we propose the use of ensemble techniques, which involve constructing a single machine learning model based on multiple instances of quantum neural networks. In particular, we implement bagging and AdaBoost techniques, with different data loading configurations, and evaluate their performance on both synthetic and real-world classification and regression tasks. To assess the potential performance improvement under different environments, we conducted experiments on both simulated, noiseless software and IBM superconducting-based QPUs, suggesting these techniques can mitigate the quantum hardware noise. Additionally, we quantify the amount of resources saved using these ensemble techniques. Our findings indicate that these methods enable the construction of large, powerful models even on relatively small quantum devices.

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Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver

Cited by 4 publications

References 85 publications

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation

Resource Saving via Ensemble Techniques for Quantum Neural Networks

Resource saving via ensemble techniques for quantum neural networks

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