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The accurate computation of ground and excited states of many-fermion quantumsystems is one of the most consequential, contemporary challenges in thephysical and computational sciences whose solution stands to benefitsignificantly from the advent of quantum computing devices. Existingmethodologies using phase estimation or variational algorithms have potentialdrawbacks such as deep circuits requiring substantial error correction ornon-trivial high-dimensional classical optimization. Here we introduce aquantum solver of contracted eigenvalue equations, the quantum analogue ofclassical methods for the energies and reduced density matrices of ground andexcited states. The solver does not require deep circuits or difficultclassical optimization and achieves an exponential speed-up of the exactclassical algorithms. We demonstrate the algorithm though computations on botha quantum simulator and two IBM quantum processing units.

Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices