Quantum Algorithm Cuts Molecular Energy Calculations’ Costs with Streamlined Approach

Scientists are continually seeking improvements to variational quantum eigensolver algorithms for accurate molecular ground state energy calculations. Runhong He, Xin Hong (Key Laboratory of System Software, Chinese Academy of Sciences), and Qiaozhen Chai, alongside Ji Guan, Junyuan Zhou, and Arapat Ablimit, present a novel approach to enhance the adaptive derivative-assembled pseudo-trotter variational eigensolver (ADAPT-VQE). Their research introduces Param-ADAPT-VQE, an algorithm that intelligently selects excitation operators using a parameter-based criterion, effectively reducing redundancy and associated measurement costs. By combining this with a sub-Hamiltonian technique and a hot-start optimisation strategy, the authors demonstrate significant gains in computational accuracy and scalability, paving the way for more practical applications of ADAPT-VQE in molecular simulations. Parameter selection optimises variational quantum eigensolver performance for molecular simulations, leading to improved accuracy and efficiency Scientists have developed a new algorithm, Param-ADAPT-VQE, that significantly enhances the efficiency of molecular ground state energy calculations performed on quantum computers. This breakthrough addresses critical limitations in existing methods by reducing computational inaccuracies, minimising the size of the required quantum circuits, and dramatically lowering the number of measurements needed to achieve reliable results. The research introduces a parameter-based criterion for selecting excitation operators, a key component in building the quantum circuit, effectively avoiding the inclusion of redundant operators that hinder performance. This innovative approach moves beyond traditional gradient-based methods, offering a more robust and streamlined pathway to accurate molecular simulations. The core of this advancement lies in the optimisation of the adaptive derivative-assembled pseudo-trotter variational quantum eigensolver, or ADAPT-VQE, a hybrid quantum-classical algorithm widely used in quantum chemistry. While ADAPT-VQE has shown promise, its scalability has been limited by the proliferation of unnecessary excitation operators and the substantial measurement costs associated with determining the lowest energy state of a molecule. Param-ADAPT-VQE directly tackles these issues, introducing a novel strategy for operator selection that bypasses the pitfalls of relying solely on initial gradient values. By focusing on parameter-based criteria, the algorithm intelligently identifies and prioritises the most impactful operators, constructing a more concise and effective quantum circuit. Furthermore, the researchers integrated a sub-Hamiltonian technique alongside a hot-start VQE optimisation strategy, resulting in a substantial reduction in the overall measurement burden. Numerical experiments conducted on a range of molecular systems demonstrate that Param-ADAPT-VQE consistently outperforms the original ADAPT-VQE in terms of computational accuracy, the number of excitation operators required, and the associated measurement costs. This improved efficiency is crucial for extending the reach of quantum simulations to larger and more complex molecules, paving the way for advancements in materials science, drug discovery, and fundamental chemical understanding. Importantly, the new scheme maintains compatibility with existing modifications of ADAPT-VQE, allowing for further performance enhancements tailored to specific applications. This adaptability ensures that the benefits of Param-ADAPT-VQE can be seamlessly integrated into ongoing research efforts, accelerating progress in the field of molecular quantum chemistry and mitigating the obstacles that have previously hindered its practical implementation. The work represents a significant step towards harnessing the power of quantum computing to solve challenging problems in chemistry and beyond. Quantum computational methods for determining molecular ground state energies are increasingly sophisticated and accurate A 72-qubit superconducting processor forms the foundation of this work, utilized to implement the Param-ADAPT-VQE algorithm for calculating molecular ground state energies. The electronic Hamiltonian of molecules, expressed in atomic units, was first transformed into Pauli strings via the Jordan-Wigner transformation, enabling its evaluation on the quantum processor. This transformation facilitates the mapping of fermionic creation and annihilation operators into measurable quantum operators. The study employs the Variational Quantum Eigensolver (VQE) framework, minimizing the Hamiltonian expectation value with respect to variational parameters to derive an upper limit for the unknown ground-state energy. A moderately deep parameterized quantum circuit, U(θ), prepares the trial state |ψ(θ)⟩ from a reference Hartree-Fock state |HF⟩, with the expectation value calculated through quantum measurement. The initial ansatz considered was the Unitary Coupled Cluster Singles and Doubles (UCCSD), containing approximately O(N 2 ) single and O(N 4 ) double excitation operators for a system with N spin orbitals. To mitigate the complexity of UCCSD, the adaptive derivative-assembled pseudo-trotter (ADAPT-VQE) method was initially implemented, constructing the ansatz incrementally by selecting excitation operators with the maximum initial gradient from a predefined operator pool. The novel Param-ADAPT-VQE algorithm then replaced this gradient-based criterion with a parameter-based selection, aiming to reduce ansatz redundancy. A sub-Hamiltonian technique was developed to suppress measurement cost during operator pool scanning, while a hot-start VQE optimization strategy further reduced the overall measurement cost. Benchmark experiments were conducted on six typical molecules at varying bond lengths to assess performance improvements in operator count, computational accuracy, and measurement cost. BeH2 optimisation demonstrates improved operator selection and convergence with Param-ADAPT-VQE, yielding more accurate results The Param-ADAPT-VQE algorithm achieved an energy error of 10−4 Hartree for the BeH2 molecule after 50 iterations, requiring only 39 excitation operators. This represents a 28% reduction in the number of operators compared to the original ADAPT-VQE, which needed 54 operators to reach the same error level. Detailed analysis of the BeH2 molecule, with symmetrically stretched bonds at a distance of 2.6Å, revealed that the gradient-based selection criterion in ADAPT-VQE is not consistently effective. The parameter-based criterion in Param-ADAPT-VQE demonstrably avoids the introduction of redundant operators during the iterative process. ADAPT-VQE exhibited three distinct error plateaus between iterations 13-16, 25-32, and 37-42, indicating periods of minimal energy reduction despite adding new operators. Conversely, Param-ADAPT-VQE consistently reduced energy error with each iteration, avoiding these plateaus and demonstrating more efficient operator selection. Initial gradient magnitudes of newly added operators in ADAPT-VQE were substantial even during flat regions of negligible performance improvement. In comparison, Param-ADAPT-VQE selected operators with smaller initial gradient magnitudes around the 25th iteration, yet achieved a more significant reduction in energy error. Further benchmark studies were conducted on LiH, H2O, and NH3 to assess scalability and effectiveness across diverse molecular systems. These studies focused on three key metrics: energy error, parameter count, and measurement cost. The research utilized the STO-3G basis set and the BFGS algorithm for optimization procedures. Electronic integrals and molecular point groups were computed using PySCF, while second quantization and quantum circuit simulations were performed via MindSpore Quantum. The Hamiltonian-Informed UCCSD ansatz was employed to reduce the number of excitation operators without compromising expressibility. All simulations were performed under idealized conditions, excluding sampling and hardware-related noise. Optimised excitation selection for scalable variational quantum eigensolver calculations reduces computational cost Researchers have developed an enhanced algorithm, Param-ADAPT-VQE, to improve the efficiency of molecular ground state energy calculations. This new approach addresses limitations in the original ADAPT-VQE algorithm, specifically the issue of redundant excitation operators and high measurement costs that hinder its scalability for complex molecular systems. Param-ADAPT-VQE achieves this by selecting excitation operators using a parameter-based criterion, effectively avoiding unnecessary calculations. The algorithm further incorporates a sub-Hamiltonian technique and a hot-start VQE optimization strategy, leading to substantial reductions in the computational resources required. Numerical tests on various molecular systems demonstrate that Param-ADAPT-VQE surpasses the original ADAPT-VQE in terms of computational accuracy, the size of the required quantum circuit, and the number of measurements needed. Importantly, the new scheme maintains compatibility with existing modifications of ADAPT-VQE, allowing for potential future improvements. The authors acknowledge that the performance of the algorithm is dependent on the chosen basis set, such as the minimal STO-3G, and that further investigation into optimal parameter selection criteria could yield additional gains. Future research may focus on exploring the algorithm’s performance with larger, more complex molecular systems and integrating it with other advanced quantum computational techniques to further enhance its capabilities and broaden its applicability in the field of molecular physics and chemistry. 👉 More information 🗞 Constructing Compact ADAPT Unitary Coupled-Cluster Ansatz with Parameter-Based Criterion 🧠 ArXiv: https://arxiv.org/abs/2602.04253 Tags: