OpenFermion: The Electronic Structure Package for Quantum Computers

Babbush, Ryan; McClean, Jarrod R.; Kivlichan, Ian D.; Steiger, Damian S.; Sung, Kevin J.; Cao, Yudong; Fried, Eliot; Gidney, Craig; Haener, Thomas; Havlíček, Vojtěch; Zhang, Jiang; Neeley, M.; Romero, Jhonathan; Rubin, Nicholas C.; Sawaya, Nicholas; Setia, Kanav; Sim, Sukim; Sun, W.

doi:10.48550/arxiv.1710.07629

Cited by 115 publications

(154 citation statements)

References 61 publications

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“…The depth of Hamiltonian and cluster terms are set to n, which in the following discussions is 2. It is expressed as U (θ i ) = l k exp(−iθ i l c l k P l k ) by the index of the variable l and the index of terms belongs to variable l transformed into Pauli words k [13] [14]. We use Unitary Coupled Cluster(UCC) [15] ansatz to calculate the derivatives.…”

Section: Methodsmentioning

confidence: 99%

Genetic-Multi-initial Generalized VQE: Advanced VQE method using Genetic Algorithms then Local Search

Wakaura,

Tomono

2021

Preprint

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Variational-Quantum-Eigensolver(VQE) method has been known as the method of chemical calculation using quantum computers and classical computers. This method also can derive the energy levels of excited states by Variational-Quantum-Deflation(VQD) method. Although, parameter landscape of excited state have many local minimums that the results are tend to be trapped by them. Therefore, we apply Genetic Algorithms then Local Search(GA then LS) as the classical optimizer of VQE method. We performed the calculation of ground and excited states and their energies on hydrogen molecule by modified GA then LS.Here we uses Powell, Broyden-Fletcher-Goldferb-Shanno, Nelder-Mead, and Newton's method as an optimizer of LS. We obtained the result that Newton's method can derive ground and excited states and their energies in higher accuracy than others. we are predicting that newton method is more effective for speedup and be more accurate.

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Section: Methodsmentioning

confidence: 99%

Genetic-Multi-initial Generalized VQE: Advanced VQE method using Genetic Algorithms then Local Search

Wakaura,

Tomono

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The depth of Hamiltonian and cluster terms are set to n, which in the following discussion is 2. It is expressed as U (θ j ) = l k exp(−iθ j l c l k P l k ) by the index of the variable l and the index of terms belongs to variable l transformed into Pauli words k [15] [16]. We use Unitary Coupled Cluster(UCC) [17] ansatz to calculate the derivatives.…”

Section: Methodsmentioning

confidence: 99%

Tangent Vector Variational Quantum Eigensolver: A Robust Variational Quantum Eigensolver against the inaccuracy of derivative

Wakaura¹,

Suksmono²

2021

Preprint

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Observing rapid developments of both the number of qubits and quantum volume, especially with recent advances in ion-trap quantum computers, it is no doubt that Fault-Tolerant-Quantum-Computer (FTQC) will be realized in the near future. Since FTQC requires 10,000 physical qubits for every 100 logical ones, it will be used as the first large-scale Noisy-Intermediate-Scale-Quantum (NISQ) . The Variational Quantum Eigensolver (VQE) method will be used until large-scale FTQC with more than 100 logical qubits are realized. Therefore, the VQE method must be improved with respect to both accuracy and time to solution using large resource of the near FTQC . In this paper, we propose Tangent-Vector VQE (TVVQE) method to manage these issues. The method optimizes the norm of tangent vector of trial energy. We demonstrate the calculation of energy levels on Hydrogen molecule, Hubbard model, and Lithium Hydride molecule and reveal that TVVQE has a potential to calculate ground and excited energy levels more accurately than other VQE methods.

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“…The depth of U n/2 j→k and U n/2 +→− are both 4. All datas are calculated by blueqat SDK and openfermion [20].…”

Section: Methodsmentioning

confidence: 99%

Frame Superposition Cluster: The method to derive the transition matrices in high accuracy

Wakaura¹,

Tomono²

2021

Preprint

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Variational Quantum Eigensolver (VQE) method is the way to derive the wave functions from their eigenenergies using quantum computers. But, the methods to utilize the superposition states between them haven't been developed yet. The method to calculate the off-diagonal element of observables between two states derived by VQE method requires large numbers of gate operations for Noisy-Intermediate-Scale-Quantum (NISQ) devices. We propose the novel method to derive the superposition state between the states derived by VQE method. We call it Frame Superposition Cluster (FSC) method. Using the method, we confirmed that dipole transition moment could be calculated with the highest accuracy compared to other methods.

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OpenFermion: The Electronic Structure Package for Quantum Computers

Cited by 115 publications

References 61 publications

Genetic-Multi-initial Generalized VQE: Advanced VQE method using Genetic Algorithms then Local Search

Genetic-Multi-initial Generalized VQE: Advanced VQE method using Genetic Algorithms then Local Search

Tangent Vector Variational Quantum Eigensolver: A Robust Variational Quantum Eigensolver against the inaccuracy of derivative

Frame Superposition Cluster: The method to derive the transition matrices in high accuracy

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