The adaptive derivative-assembled pseudotrotter variational quantum eigensolver (ADAPT-VQE) is a promising hybrid quantum-classical algorithm for molecular ground-state energy calculation, yet its practical scalability is hampered by redundant excitation operators and excessive measurement costs. To address these challenges, we propose Param-ADAPT-VQE, a novel improved algorithm that selects excitation operators based on a parameter-based criterion instead of a traditional gradient-based metric. This strategy effectively avoids redundant operators. We further developed a sub-Hamiltonian technique and integrated a hot-starting VQE optimization strategy, achieving a significant reduction in measurement costs. Numerical experiments on typical molecular systems demonstrate that Param-ADAPT-VQE outperforms the original ADAPT-VQE in ansatz size, computational accuracy, and measurement costs. Furthermore, our scheme retains the fundamental framework of ADAPT-VQE and is thus fully compatible with its various modified versions, enabling further performance improvements in specific aspects. This work presents an efficient and scalable enhancement to ADAPT-VQE, mitigating the core obstacles that impede its practical implementation in molecular quantum chemistry.
The adaptive derivative-assembled pseudotrotter variational quantum eigensolver (ADAPT-VQE) is a promising hybrid quantum-classical algorithm for molecular ground-state energy calculation, yet its practical scalability is hampered by redundant excitation operators and excessive measurement costs. To address these challenges, we propose Param-ADAPT-VQE, a novel improved algorithm that selects excitation operators based on a parameter-based criterion instead of a traditional gradient-based metric. This strategy effectively avoids redundant operators. We further developed a sub-Hamiltonian technique and integrated a hot-starting VQE optimization strategy, achieving a significant reduction in measurement costs. Numerical experiments on typical molecular systems demonstrate that Param-ADAPT-VQE outperforms the original ADAPT-VQE in ansatz size, computational accuracy, and measurement costs. Furthermore, our scheme retains the fundamental framework of ADAPT-VQE and is thus fully compatible with its various modified versions, enabling further performance improvements in specific aspects. This work presents an efficient and scalable enhancement to ADAPT-VQE, mitigating the core obstacles that impede its practical implementation in molecular quantum chemistry.
The adaptive derivative-assembled pseudo-trotter variational quantum eigensolver (ADAPT-VQE) is a promising hybrid quantum-classical algorithm for molecular ground state energy calculation, yet its practical scalability is hampered by redundant excitation operators and excessive measurement costs. To address these challenges, we propose Param-ADAPT-VQE, a novel improved algorithm that selects excitation operators based on a parameter-based criterion instead of the traditional gradient-based metric. This strategy effectively eludes redundant operators. We further develop a sub-Hamiltonian technique and integrate a hot-start VQE optimization strategy, achieving a significant reduction in measurement costs. Numerical experiments on typical molecular systems demonstrate that Param-ADAPT-VQE outperforms the original ADAPT-VQE in computational accuracy, ansatz size, and measurement costs. Furthermore, our scheme retains the fundamental framework of ADAPT-VQE and is thus fully compatible with its various modified versions, enabling further performance improvements in specific aspects. This work presents an efficient and scalable enhancement to ADAPT-VQE, mitigating the core obstacles that impede its practical implementation in the field of molecular quantum chemistry.
Designing compact ansätze in Variational Quantum Eigensolver (VQE) is crucial for solving energetic problems of practical molecules on near-term quantum devices. However, existing Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansätze face two challenges: improper operator selection and accumulation of degraded operators. In this paper, we propose the Hamiltonian-Aware (HA) ADAPT-VQE algorithm to address these issues. First, we establish a novel excitation operator selection criterion. It breaks the local constraint of existing criteria by incorporating Hamiltonian information, prioritizes physically meaningful excitation operators, and incurs no extra classical or quantum computational overhead. Furthermore, we develop a problem-adaptive method for discriminating and pruning redundant excitation operators stemming from improper selection and inevitable degradation. This method balances redundant operator pruning and convergence guarantee, and is applicable to ansätze with arbitrary scales. Systematic numerical experiments on typical strongly correlated molecular systems demonstrate that our HA-ADAPT-VQE avoids energy plateaus and outperforms baseline algorithms in terms of energy error, ansatz size, and measurement cost. This work offers an efficient, robust ansatz construction paradigm, facilitating the development and practical deployment of large-scale VQE in quantum chemistry.
The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) is one of the most widely used algorithms for electronic structure calculations in quantum computers. It adaptively selects operators based on their gradient, constructing ansätze that continuously evolve to match the energy landscape, helping avoid local traps and barren plateaus. However, this flexibility in reoptimization can lead to the inclusion of redundant or inefficient operators that have almost zero parameter value, barely contributing to the ansatz. We identify three phenomena responsible for the appearance of these operators: poor operator selection, operator reordering, and fading operators. In this work, we propose an automated, cost-free refinement method that removes unnecessary operators from the ansatz without disrupting convergence. Our approach evaluates each operator after ADAPT-VQE optimization by using a function that considers both its parameter value and position in the ansatz, striking a balance between eliminating low-coefficient operators while preserving the natural reduction of coefficients as the ansatz grows. Additionally, a dynamic threshold based on the parameters of recent operators enables efficient convergence. We apply this method to several molecular systems and find that it reduces ansatz size and accelerates convergence, particularly in cases with flat energy landscapes. The refinement process incurs, at most, a small additional computational cost and consistently improves or maintains ADAPT-VQE performance.
The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) is one of the most widely used algorithms for electronic structure calculations in quantum computers. It adaptively selects operators based on their gradient, constructing ansätze that continuously evolve to match the energy landscape, helping avoid local traps and barren plateaus. However, this flexibility in reoptimization can lead to the inclusion of redundant or inefficient operators that have almost zero parameter value, barely contributing to the ansatz. We identify three phenomena responsible for the appearance of these operators: poor operator selection, operator reordering, and fading operators. In this work, we propose an automated, cost-free refinement method that removes unnecessary operators from the ansatz without disrupting convergence. Our approach evaluates each operator after ADAPT-VQE optimization by using a function that considers both its parameter value and position in the ansatz, striking a balance between eliminating low-coefficient operators while preserving the natural reduction of coefficients as the ansatz grows. Additionally, a dynamic threshold based on the parameters of recent operators enables efficient convergence. We apply this method to several molecular systems and find that it reduces ansatz size and accelerates convergence, particularly in cases with flat energy landscapes. The refinement process incurs, at most, a small additional computational cost and consistently improves or maintains ADAPT-VQE performance.
Adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) stands out as a robust algorithm for constructing compact ansätze for molecular simulation. It enables to significantly reduce the circuit depth with respect to other methods, such as unitary coupled cluster singles and doubles, while achieving higher accuracy and not suffering from so-called barren plateaus that hinder the variational optimization of many hardware-efficient ansätze. In its standard implementation, however, it introduces a considerable measurement overhead in the form of gradient evaluations through estimations of many commutator operators. In this work, we mitigate this measurement overhead by exploiting a recently introduced method for energy evaluation relying on adaptive informationally complete generalized measurements (AIMs). Besides offering an efficient way to measure the energy itself, informationally complete (IC) measurement data can be reused to estimate all the commutators of the operators in the operator pool of ADAPT-VQE, using only classically efficient postprocessing. The framework is generic for any IC positive operator-valued measures (POVMs) implementation, and in this work, we demonstrate it’s effectiveness with dilation POVMs. We present the AIM-ADAPT-VQE scheme in detail, and investigate its performance with H 4 , N 2 , and 1,3,5,7-octatetraene Hamiltonians and several operator pools. Our numerical simulations indicate that the measurement data obtained to evaluate the energy can be reused to implement ADAPT-VQE with no additional measurement overhead for the systems considered here. In addition, we show that, if the energy is measured within chemical precision, the count in the resulting circuits is close to the ideal one. With scarce measurement data, AIM-ADAPT-VQE still converges to the ground state with high probability, albeit with an increased circuit depth in some cases.
In order to answer the problem of Quantum Phase Estimation Algorithm been not suitable for NISQ devices, and allows one to outperform classical computers, Variational Quantum Algorithms (VQAs) were designed. Our subject of interest is the so-called Variational Quantum Eigensolver (VQE) algorithm and was originally designed to simulate electronic structures and to compute the ground state of a given molecule. VQE is made of two main components : an ansatz and a classical optimizer. The ansatz runs on the quantum device and aims to simulate the wavefunction, the parameters of the ansatz will be optimized until the expectation value is minimum. The very first ansatz that has originally been used is called UCCSD and it is based on Coupled Cluster Theory. The main issue considering UCCSD is the large amount of parameters to optimize and this leads us to the introduction of Adaptive Derivative-Assembled Pseudo-Trotter ansatz VQE (ADAPT-VQE) which determines a quasi-optimal ansatz with a minimal number of parameters. The key point of ADAPT-VQE is to grow the ansatz at every step, by adding operators chosen from a pre-determined pool of operators one-at-a-time, assuring that the maximal amount of correlation energy is recovered at each step. There exists different kind of ADAPT-VQE depending on the starting pool of operators as the fermionic-ADAPT, the qubit-ADAPT or even the qubit excitation based (QEB). Our goal is to implement the different types of ADAPT-VQE mentioned before. After a quick review of the theoretical background under all of these concepts, we will implement each algorithm using quiskit. We will also compare all of these algorithms on different criterions such as the number of parameters, the accuracy or the number of CNOT gate used on H2 and LiH molecules. Then we will have a small discussion about the results we obtained.