Counterdiabatic ADAPT-VQE for molecular simulation

TL;DR

This work introduces CD-ADAPT, a hybrid quantum–classical approach that unites ADAPT-VQE with counterdiabatic driving to accelerate adiabatic-state preparation for molecular Hamiltonians. By mapping the molecular problem to an adiabatic form and constructing an operator pool from approximate adiabatic gauge potentials via nested commutators, the method enables adaptive selection of Pauli-string generators that efficiently approximate the counterdiabatic flow. Numerical results on LiH, HF, and BeH_2 show that higher-order AGP-derived pools dramatically improve ground-state energies while reducing circuit depth, outperforming digitized counterdiabatic optimization and fermionic ADAPT-VQE in both accuracy and CNOT counts. The approach offers a scalable route toward accurate, shallow-vorticity quantum simulations of chemistry on NISQ and early fault-tolerant hardware, with the operator-pool size and performance tunable through the order of the AGP expansion and the schedule parameter t'.

Abstract

Among variational quantum algorithms designed for NISQ devices, ADAPT-VQE stands out for its robustness against barren plateaus, particularly in estimating molecular ground states. On the other hand, counterdiabatic algorithms have shown advantages in both performance and circuit depth when compared to standard adiabatic approaches. In this work, we propose a hybrid method that integrates the ADAPT-VQE framework with counterdiabatic driving within an adiabatic evolution scheme. Specifically, we map the molecular Hamiltonian to a qubit representation and construct an adiabatic Hamiltonian, from which an approximate adiabatic gauge potential is computed using nested commutators. The resulting operator terms define the operator pool, and the ADAPT-VQE algorithm is applied to iteratively select the most relevant elements for the ansatz. Our results demonstrate improvements in performance and reductions in circuit depth compared to using either counterdiabatic algorithms or ADAPT-VQE with fermionic excitation operators, thus supporting the effectiveness of combining both paradigms in molecular simulations.

Figures (5)

• Figure 1: Number of operators in the operator pool $\{ \hat{G}_j \}_{j=1}^{\eta}$ for: a) LiH, HF and BeH$_2$ in function of $l$-th order of approximation of AGP and: b) for LiH with time-dependent approximation for $l=1,2$.
• Figure 2: Ground state energy and corresponding error for LiH calculated via CD-ADAPT. (a) Energy dissociation curve compared to the FCI. (b) Absolute error as a function of interatomic distance for first ($l=1$) and second-order ($l=2$) approximations with time parameters $t'=0.25$ and $t'=0.75$.
• Figure 3: Ground state energy and corresponding error for HF calculated via CD-ADAPT. (a) Energy dissociation curve compared to the FCI. (b) Absolute error as a function of interatomic distance for first ($l=1$) and second-order ($l=2$) approximations with time parameters $t'=0.25$ and $t'=0.75$.
• Figure 4: Ground state energy and corresponding error for BeH$_2$ calculated via CD-ADAPT. (a) Energy dissociation curve compared to the FCI. (b) Absolute error as a function of interatomic distance for first ($l=1$) and second-order ($l=2$) approximations with time parameters $t'=0.25$ and $t'=0.75$.
• Figure 5: Absolute error calculated for CD-ADAPT, ADAPT-VQE and DCQO vs interatomic distance. (a) For LiH (b) For BeH$_2$.