Simulated Quantum Computation of Molecular Energies

Aspuru‐Guzik, Alán; Dutoi, Anthony D.; Love, Peter J.; Head‐Gordon, Martin

doi:10.1126/science.1113479

Cited by 1,254 publications

(1,561 citation statements)

References 14 publications

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“…A quantum Fourier transform [22] (QFT) is used to retrieve the phase in a binary expansion and thus obtain the eigenenergy. This scheme has been proposed to simulate quantum systems, especially Fermion systems, on a quantum computer [5,9,19,20]. If the Hamiltonian can be decomposed by means of a split-operator technique [6,8,11,18], the quantum computational cost is polynomial, it can provide an exponential speed increase over its classical counterpart.…”

Section: Implementation Of CI Scheme On a Quantum Computermentioning

confidence: 99%

Quantum algorithm for obtaining the energy spectrum of molecular systems

Wang

Kais

Aspuru‐Guzik

et al. 2008

Phys. Chem. Chem. Phys.

119

143

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Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the wellknown result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multi-configurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible; Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.

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Section: Implementation Of CI Scheme On a Quantum Computermentioning

confidence: 99%

Quantum algorithm for obtaining the energy spectrum of molecular systems

Wang

Kais

Aspuru‐Guzik

et al. 2008

Phys. Chem. Chem. Phys.

119

143

View full text Add to dashboard Cite

show abstract

“…One may also perform first quantized calculations in a basis of slater determinants. This was introduced as a representation of the electronic wavefunction by qubits in [7] (the compact mapping) and the efficiency of time evolution in this basis was recently shown [35]. The second quantized approach places the antisymmetry requirements on the operators.…”

Section: Second Quantized Hamiltonianmentioning

confidence: 99%

“…al. showed that these approaches might be particularly promising for quantum chemistry [7]. There have been many developments both in theory [8][9][10] and experimental realization [11][12][13] of quantum chemistry on quantum computers.…”

Section: Introductionmentioning

confidence: 99%

Exploiting Locality in Quantum Computation for Quantum Chemistry

McClean

Babbush

Love

et al. 2014

J. Phys. Chem. Lett.

Self Cite

127

190

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Accurate prediction of chemical and material properties from first principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route towards highly accurate solutions with polynomial cost, however this solution still carries a large overhead. In this perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provide numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.

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“…Quantum chemical state preparation is important in both the VQE approach, where it ultimately determines the state, energy, and properties measured, and in QPE, where it determines the success probability of the energy measurement 9,21,22 . Hence an understanding of the general effect of errors on state preparation is crucial to the success of both algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…The first uses the quantum phase estimation (QPE) algorithm [9][10][11][12][13] to evolve an initial state toward the molecular ground state. The second approach is the variational quantum eigensolver (VQE) [14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

Sawaya

Smelyanskiy

McClean

et al. 2016

J. Chem. Theory Comput.

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Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHi PSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated eighteen 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure- * To whom correspondence should be addressed † Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA ‡ Parallel Computing Lab, Intel Corporation, Santa Clara, CA 95054, USA ¶ Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.

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Simulated Quantum Computation of Molecular Energies

Cited by 1,254 publications

References 14 publications

Quantum algorithm for obtaining the energy spectrum of molecular systems

Quantum algorithm for obtaining the energy spectrum of molecular systems

Exploiting Locality in Quantum Computation for Quantum Chemistry

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

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