Qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansätze on a quantum processor

Abstract

Quantum simulation, being one of the most promising applications of a quantum computer, has been realised on current noisy intermediate-scale quantum (NISQ) devices using different algorithms. Among these, the variational quantum eigensolver is extensively used for finding the ground state energy of molecular Hamiltonians. The feasibility and performance of this algorithm depend critically on the number of variational parameters in the wavefunction ansatz and on the depths of the state preparation circuits that create the ansatz on the quantum processor. Recently, an algorithm termed ADAPT-VQE was introduced to build system-adapted ansätze with substantially fewer variational parameters compared to other approaches. However, deep state preparation circuits remain a challenge. Here, we present a hardware-efficient variant of this algorithm called qubit-ADAPT. By numerical simulations on H4, LiH and H6, we show that with a well-designed operator pool, qubit-ADAPT can reduce the circuit depth by one order of magnitude while maintaining the same accuracy as the original ADAPT-VQE. Addressing the high measurement cost which is proportional to the size of the operator pool, we show the possibility to construct a sufficient pool with size growing linearly in the number of qubits. This result highlights the promise of adaptive simulation algorithms on near-term quantum devices.