Ground-state energy estimation of the water molecule on a trapped ion quantum computer

Nam, Yoonsu; Chen, Jwo-Sy; Pisenti, Neal C.; Wright, Kenneth; Delaney, Conor P.; Maslov, Dmitri; Brown, Kenneth R.; Allen, Stewart; Amini, Jason M.; Apisdorf, Joel; Beck, Kristin M.; Blinov, Aleksey; Chaplin, V.; Chmielewski, Mika; Collins, Coleman; Debnath, Shantanu; Ducore, Andrew M.; Hudek, Kai; Keesan, Matthew; Kreikemeier, Sarah M.; Mizrahi, Jonathan; Solomon, Phil; Williams, M.; Wong-Campos, J. D.; Monroe, Christopher; Kim, Jungsang

doi:10.48550/arxiv.1902.10171

Cited by 51 publications

(85 citation statements)

References 33 publications

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“…5. (a), (b), (c), and (d) shows convergence results in the case of ( 2), ( 3), ( 5), and (6).Tabu search contribute to stabilize the convergence of energy levels. As shown in Fig.…”

Section: Iii1 the Effect Of Constrained And Tabu Search Term On Calcu...mentioning

confidence: 93%

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Effect of constraint and Tabu Search term on Variational Quantum Eigensolver and Subspace-Search Variational Quantum Eigensolver

Wakaura

Tomono

2021

Preprint

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Subspace-Search Variational Quantum Eigensolver(SSVQE) is searching method of multiple states and relies on the unitarity of transformations to ensure the orthogonality of output states for multiple states. Therefore, this method is thought to be promising method for quantum chemistry because ordinary Variational Quantum Eigensolver (VQE) can only calculate the excited states step by step from ground state based on Variational Quantum deflation (VQD). We compare the advantage of VQE, SSVQE with/without the constraint term and/or Tabu search term, that are added by Lagrange's multiplier method so as to calculate the desired energy levels. We evaluated the advantage by calculating each energy levels of H2 and HeH, respectively. As there simulation results, the accuracy calculated by constrained VQE with Tabu search indicates higher accuracy than that of our other algorithm, for analysis on H2. The accuracy calculated by constrained SSVQE indicate higher that of the constrained VQE with Tabu search. We found it is beneficial for enhance the accuracy to use constraint terms decreasing convergence times to use Tabu search terms according to the nature of molecules. We demonstrate that constraint and Tabu search terms contribute to the accuracy and convergence time on quantum chemical calculating.

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“…5. (a), (b), (c), and (d) shows convergence results in the case of ( 2), ( 3), ( 5), and (6).Tabu search contribute to stabilize the convergence of energy levels. As shown in Fig.…”

Section: Iii1 the Effect Of Constrained And Tabu Search Term On Calcu...mentioning

confidence: 93%

“…FIG.3. Diatomic bond length( Å) of hydrogen molecule v.s.the energy levels (Hartree) of each state calculated by VQE method of the case (1), (2), (3), (4), (5), and(6). Solid line on each state is connecting average points by ten sampling data.…”

mentioning

confidence: 99%

Effect of constraint and Tabu Search term on Variational Quantum Eigensolver and Subspace-Search Variational Quantum Eigensolver

Wakaura

Tomono

2021

Preprint

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“…14 A recent advance has even enabled a postquantum classical correction from perturbation theory to enhance the accuracy of the method. 15 VQE and its extensions have been deployed on physical quantum hardware to simulate the ground and excited-state energies of small molecules and magnetic systems, including deployment on superconducting 1,6,12 and ion-trap 16 quantum hardware.…”

Section: Introductionmentioning

confidence: 99%

A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization

Parrish¹,

Iosue²,

Ozaeta³

et al. 2019

Preprint

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“…Hamiltonians in second-quantization are ubiquitous in quantum chemistry, many-body physics, and quantum field theory, all of which are target applications for quantum simulation. Fermionic Hamiltonians with fixed particle number admit simple encodings in the Pauli basis [1][2][3], and these have been the focus of many quantum simulation experiments to date [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. However, second-quantized Hamiltonians are sparse -they have only polynomiallymany nonzero entries per row or column -as long as they have polynomially-many terms.…”

mentioning

confidence: 99%

Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding

Kirby,

Hadi,

Kreshchuk

et al. 2021

Preprint

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We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the φ 4 -theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

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Ground-state energy estimation of the water molecule on a trapped ion quantum computer

Cited by 51 publications

References 33 publications

Effect of constraint and Tabu Search term on Variational Quantum Eigensolver and Subspace-Search Variational Quantum Eigensolver

Effect of constraint and Tabu Search term on Variational Quantum Eigensolver and Subspace-Search Variational Quantum Eigensolver

A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization

Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding

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