Solving the electronic many-body Schrödinger equation for strongly correlated systems is a significant challenge in physics, materials science, and chemistry. Classical numerical simulations of these systems are limited by the exponential scaling of the many-body basis. Quantum computers can efficiently represent and manipulate quantum states. Therefore, they could enable exponential speedup in the simulation of many-body problems. Over the past decade, advances in quantum hardware engineering have played a critical role in reinvigorating interest in algorithm development, with most efforts being dedicated phase estimation and the variational quantum eigensolver. These two techniques have been successfully applied to solve small molecular problems using quantum simulators and near-term noisy quantum computers. The field has recently witnessed the emergence of new quantum algorithms that introduce alternative strategies to solve many-body problems. This talk will cover developments in quantum subspace diagonalization and projective algorithms. In the first part, I will discuss quantum algorithms analogous to Krylov subspace methods. I will consider a multireference selected quantum Krylov (MRSQK) approach. This method uses quantum measurement to identify a set of important zeroth-order states, from which we generate a set of Krylov sequences using the real-time propagator. The MRSQK method is tested on several molecular systems that display strong correlation effects and compared to classical selected configuration interaction and adaptive quantum variational algorithms. In the second part, I will discuss an alternative approach to realize unitary coupled-cluster via quantum computers using a projective formalism.

Quantum algorithms for strongly correlated molecular electronic states

ACS Spring Meeting 2021

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