Exact electronic states with shallow quantum circuits from global optimisation

Quantum computers promise to revolutionise molecular electronic simulations by overcoming the exponential memory scaling. While electronic wave functions can be represented using a product of fermionic unitary operators, the best ansatz for strongly correlated electronic systems is far from clear. In this contribution, we construct universal wave functions from gate-efficient, spin symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits and provides a practical route for designing ansätze in the future. Numerical simulations for strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate the improved accuracy of gate-efficient quantum circuits for simulating strongly correlated chemistry

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Energy Landscapes for Electronic Structure.

Orbital-optimized multiple self-consistent-field (SCF) solutions are increasingly being interpreted as mean-field approximations of diabatic or excited electronic states. However, surprisingly little is known about the topology of the electronic energy landscape from which these multiple solutions emerge. In this contribution, we extend energy landscape methods, developed for investigating molecular potential energy surfaces, to investigate and understand the structure of the electronic SCF energy surface. Using analytic gradients and Hessians, we systematically identify every real SCF minimum for the prototypical H4 molecule with the 3-21G basis set, and the index-1 saddles that connect these minima. The resulting SCF energy landscape has a double-funnel structure, with no high-energy local minima. The effect of molecular symmetry on the pathways is analyzed, and we demonstrate how the SCF energy landscape changes with the basis set, SCF potential, molecular structure, and spin state. These results provide guiding principles for the future development of algorithms to systematically identify multiple SCF solutions from an orbital optimization perspective