qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor

Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely on existing hardware using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wavefunction ansatz. Recently, an algorithm termed ADAPT-VQE was introduced to build system-adapted ansatze 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, which we term qubit-ADAPT. Through numerical simulations on $\text{H}_4$, LiH and $\text{H}_6$, we show that qubit-ADAPT reduces the circuit depth by an order of magnitude while maintaining the same accuracy as the original ADAPT-VQE. A key result of our approach is that the additional measurement overhead of qubit-ADAPT compared to fixed-ansatz variational algorithms scales only linearly with the number of qubits. Our work provides a crucial step forward in running algorithms on near-term quantum devices.