Simulated Quantum Computation of Molecular Energies

By A. Aspuru‐Guzik, A. Dutoi, Peter J. Love, M. Head‐Gordon. Science, 2005

1,477 citations recorded by the source corpus.

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a08ce3537b626e01277ef5fce0f331b941e90aee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Theory and Mathematics

Citations in the corpus

Qudits and High-Dimensional Quantum Computing (2020, methodology): “To give some examples, a quantum simulator utilizing the PEA algorithm has been used to calculate the molecular ground-state energies [8] and to obtain the energy spectra of molecular systems [13, 41, 42, 84, 154].”
Quantum error correction: an introductory guide (2019, methodology): “Example: The [[4,2,2]] detection code The [[4, 2, 2]] detection code is the smallest stabilizer code to offer protection against a quantum noise model in which the qubits are susceptible to bothX- and Z-errors [38,39].”
Variational Quantum Computation of Excited States (2018, methodology): “Quantum computers have the potential to solve these and other problems significantly faster than any known methods using classical computers [1, 11, 19, 36].”
Simulating chemistry using quantum computers. (2010, methodology): “We applied adiabatic state preparation (ASP) to the case of the hydrogen molecule H2 in the STO-3G basis at various bond lengths (10).”
Variational quantum algorithms (2020, methodology): “Previous quantum algorithms to find the ground state of a given Hamiltonian H were based on adiabatic state preparation and quantum phase estimation subroutines [87, 88], both of which have circuit depth requirements beyond those available in the NISQ era.”
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, background): “[7], the idea that one should use phase estimation and adiabatic state preparation [8 – 10] to extract quantum chemistry ground-state energies became especially popular.”
Scalable Quantum Simulation of Molecular Energies (2015, background): “We also report an experimental demonstration of the original quantum algorithm for chemistry [2].”
Quantum error correction below the surface code threshold (2024, positive): “Quantum computing promises computational speedups in quantum chemistry [5], quantum simulation [6], cryptography [7], and optimization [8].”
Quantum Chemistry in the Age of Quantum Computing. (2018, methodology): “Equation 44 is equivalent to the following local Hamiltonian in the Jordan-Wigner representation: H= X p Tpq+ Up 2 + X q Vpq 2 ! Zp+ X p6=q VpqZpZq+ X p6=q Tpq 2 (XpZp+1 :::Zq 1Xq+ YpZp+1 :::Zq 1Yq): (45) Notice that this Hamiltonian also encompasses the Fermi-Hubbard Hamiltonian and can be readily ”
Cloud Quantum Computing of an Atomic Nucleus. (2018, methodology): “These ground-breaking quantum computing experiments used phase estimation algorithms [14] and the variational quantum eigensolver (VQE) [11, 15].”
Quantum simulation of the Dirac equation (2009, background): “A natural route for the near future will be to move theoretically and experimentally towards the simulation of dynamics that are impossible (or difficult) to calculate in real systems, such as in quantum chemistry [27] or quantized Dirac fields in a quantum field theory context [1].”