Simulation of electronic structure Hamiltonians using quantum computers

By James D. Whitfield, Jacob D. Biamonte, Alán Aspuru-Guzik. 2010

523 citations recorded by the source corpus.

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, obtains the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule of how a chemical Hamiltonian can be simulated using a quantum computer.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/d305e1c556e50d45d5b74c575092e0c85f38d5df

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Physical and Theoretical Chemistry

Citations in the corpus

Elucidating reaction mechanisms on quantum computers (2016, methodology): “Conventional circuits, such as those in [13], break these terms in the Hamiltonian into a group of at most 8 commuting operators that act on the qubits in question.”
Quantum information processing with superconducting circuits: a review (2016, methodology): “A detailed analysis [389] shows that only the terms σxσxσyσy, σyσyσxσx, σyσxσxσy, σxσyσyσx need to be considered.”
Quantum algorithms to simulate many-body physics of correlated fermions. (2017, methodology): “(C10) commute with each other, and the first part can be implemented with only single-qubit gates with the JWT. 20”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “[36] James D Whitfield, Jacob Biamonte, and Alán AspuruGuzik, “Simulation of electronic structure Hamiltonians using quantum computers,” Mol.”
An adaptive variational algorithm for exact molecular simulations on a quantum computer (2018, methodology): “This was followed by several theoretical studies on VQE [7, 11–17] and demonstrations on other hardware such as superconducting qubits [7, 16, 18] and trapped ions [19, 20].”
Tapering off qubits to simulate fermionic Hamiltonians (2017, methodology): “[45] by working with four fermionic modes in a minimal basis.”