Abstract
Quantum chemistry provides key applications for near-term quantum computing, but these are greatly complicated by the presence of noise. In this work we present an efficient ansatz for the computation of two-electron atoms and molecules within a hybrid quantum-classical algorithm. The ansatz exploits the fundamental structure of the two-electron system, and treating the nonlocal and local degrees of freedom on the quantum and classical computers, respectively. Here the nonlocal degrees of freedom scale linearly with respect to basis-set size, giving a linear ansatz with only $\mathcal{O}(1)$ circuit preparations required for reduced state tomography. We implement this benchmark with error mitigation on two publicly available quantum computers, calculating accurate dissociation curves for 4- and 6- qubit calculations of ${\rm H}_\textrm{2}^{}$ and ${\rm H}_\textrm{3}^+$.
Highlights
Quantum computers possess a natural affinity for quantum simulation and can transform exponentially scaling problems into polynomial ones [1,2,3]
Even if we model a two-electron system on a quantum computer and construct the state through the above tomography, we may find that the occupations ni and ni do not match for a given i, which implies a violation of the fermion statistics
In this work we present an ansatz for two-electron quantum systems which can be implemented on near-term and future quantum computers
Summary
Quantum computers possess a natural affinity for quantum simulation and can transform exponentially scaling problems into polynomial ones [1,2,3]. The twin goals of the work are (i) to present a quantum-computing benchmark based on the correlated but polynomial scaling two-electron problem, solvable on classical computers, that can be used to assess the accuracy of quantum computers and (ii) to develop an efficient ansatz for solving the twoelectron problem on quantum computers, based on an effective partitioning of the computational work between classical and quantum computers that is applicable to more general N-electron molecular systems. The two-electron density matrix (2DM) of any twoelectron system can be expressed as a functional of its oneelectron reduced density matrix (1RDM) and a set of phase factors This representation of the 2DM has important connections to natural-orbital functional theories and geminalbased theories in quantum chemistry [9,10,11,12,13,14,15,16].
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