Efficient Parabolic Optimisation Algorithm for Adaptive VQE Implementations

Chemically Accurate Potential Curves for H2 Molecules Using Explicitly Correlated Qubit-ADAPT

“…At each iteration, the pool operators P̂ j ∈ scriptP are chosen from a complete minimal pool of size 2 n – 2, whose definition can be found in the Supporting Information. The question which selection criterion should be applied for picking the pool operators has been previously discussed, which includes considerations of utilizing the maximum gradient norm ,, or maximum impact on energy . While the latter approach was reported to show superior convergence properties, this work solely utilized the former one as in eq for the sake of comparability with the majority of previous studies.…”

“…The question which selection criterion should be applied for picking the pool operators has been previously discussed, which includes considerations of utilizing the maximum gradient norm ,, or maximum impact on energy . While the latter approach was reported to show superior convergence properties, this work solely utilized the former one as in eq for the sake of comparability with the majority of previous studies. The k th component of the energy gradient ∇ E can be rewritten as false( normal∇ E false) k = ∂ ∂ θ ⟨ ψ M | normale − i θ P̂ k † Ĥ normale i θ P̂ k | ψ M ⟩ false| θ = 0 = 2 R e { ⟨ ψ M | Ĥ P̂ k | ψ M ⟩ } …”

“…By featuring a repeated alteration of the ansatz and, correspondingly, its parameter landscape at each iteration, it acquires an intrinsic resilience to Barren plateaus . The combination of shallow circuits and systematic convergence properties renders this a particularly promising candidate for future NISQ applications and thus has been extensively studied in recent studies. − However, to the knowledge of the authors, so far, only the convergence (and by extension accuracy) of ADAPT has been established in terms of minimal basis sets using Slater-type orbitals approximated by linear combinations of three Gaussian functions (STO-3G). In order to study effects of electronic correlation, such basis sets are known to be insufficient and can only serve as a rough estimate, usually mostly at the Hartree–Fock level.…”

Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz

“…It is worth mentioning that the idea of parabola fitting has also been proposed in a recent work. 59 In each iteration, their method sets the optimization direction to the direction of the gradients and then employs parabola fitting to determine the minimum. Therefore, their method is gradient-based, while our method is gradient-free.…”

Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting

“…where s i (k) is the score of unitary U i (θ i ) at the k-th iteration and θ i,init is the initial guess θ i . However, a large gradient does not necessarily indicate a large contribution to the total energy as pointed out by Armaos et al 47 Therefore, using a full optimization instead of gradients, it can be observed that in most cases where UCCSD operator pool is sufficient to obtain chemical accuracy, ES-VQE can generate similar or even more compact ansatzes compared with ADAPT-VQE. However, one typical drawback of ES-VQE is its one-shot scoring strategy.…”