Mutual information-assisted adaptive variational quantum eigensolver

Abstract

Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers on near-term quantum hardware. Those algorithms aim to build up optimal circuits for a certain problem and ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool. In this work, we propose a way to construct entangler pools with reduced size by leveraging classical algorithms. Our method uses mutual information between the qubits in classically approximated ground state to rank and screen the entanglers. The density matrix renormalization group method is employed for classical precomputation in this work. We corroborate our method numerically on small molecules. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We believe that our method paves a new way for adaptive construction of ansatz circuits for variational quantum algorithms.

A state-averaged orbital-optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states

“…While computing the ground state of a molecule gives information about the equilibrium geometries and transition states (essential to determine the energy barrier of a chemical reaction), several chemical reactions also depend on excited states (see for instance reference [21] and references therein). To date, most variational quantum algorithms have been specifically designed to prepare ground states [1,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] while excited state calculations have received less attention until only recently [23,[38][39][40][41][42][43][44][45][46][47][48][49]. It should be noted that some excited states can also be obtained as the lowest energy solutions of a given set of symmetries [50][51][52][53][54][55].…”

Variational Quantum Eigensolver with Reduced Circuit Complexity

“…Our previous work also demonstrated that an approximate MI is sufficient for the qubit rearrangement [38] for the reduction of circuit depth. The MI has also been used to construct a compact entangler pool for ADAPT-VQE [51]. According to quantum information theory, the MI between qubits i and j is defined as follows [49]:…”

The Variational Quantum Eigensolver: a review of methods and best practices

“…Research has also focused on addressing the wider question of operator pool optimization for adaptative ansätze. An interesting method that achieves up to nearly two orders of magnitude reduction in the operator pool size is the Mutual Information (MI) assisted Adaptive VQE [465] (it is worth noting that the method described below can be applied to any adaptive ansatz described above and below in this review).…”

“…In Ref. [465] Zhang et al suggest to cut off a certain percentage of operators with low correlation strength which they optimize numerically.…”