Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions

By P. Barkoutsos, J. Gonthier, Igor M. Sokolov, Nikolaj Moll, Gian Salis, Andreas Fuhrer, M. Ganzhorn, Daniel J. Egger, Matthias Troyer, Antonio Mezzacapo and 2 more. Physical Review A, 2018

312 citations recorded by the source corpus.

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward 'translation' of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9afe9b730a81ca0888313d614178db0c0c0d9cc3

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor (2019, methodology): “This problem was addressed by constructing particle-conserving entangling gates in-a stead of ordinary two-qubit gates [27, 28] and symmetry-preserving circuits [29].”
Warm-starting quantum optimization (2020, background): “For example, the particle-hole representation for VQE can be seen as a form of warm-start [89].”