The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) provides a promising approach for simulating highly correlated quantum systems on quantum devices, as it strikes a balance between hardware efficiency, trainability, and accuracy. Although ADAPT-VQE avoids many of the shortcomings of other VQEs, it is sometimes hindered by a phenomenon known as gradient troughs. This refers to a non-monotonic convergence of the gradients, which may become very small even though the minimum energy has not been reached. This results in difficulties finding the right operators to add to the ansatz, due to the limited number of shots and statistical uncertainties, leading to stagnation in the circuit structure optimization. In this paper, we propose ways to detect and mitigate this phenomenon. Leveraging the non-commutative algebra of the ansatz, we develop heuristics for determining where to insert new operators into the circuit. We find that gradient troughs are more likely to arise when the same locations are used repeatedly for new operator insertions. Our novel protocols, which add new operators in different ansatz positions, allow us to escape gradient troughs and thereby lower the measurement cost of the algorithm. This approach achieves an effective balance between cost and efficiency, leading to faster convergence without compromising the low circuit depth and gate count of ADAPT-VQE.
The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) provides a promising approach for simulating highly correlated quantum systems on quantum devices, as it strikes a balance between hardware efficiency, trainability, and accuracy. Although ADAPT-VQE avoids many of the shortcomings of other VQEs, it is sometimes hindered by a phenomenon known as gradient troughs. This refers to a non-monotonic convergence of the gradients, which may become very small even though the minimum energy has not been reached. This results in difficulties finding the right operators to add to the ansatz, due to the limited number of shots and statistical uncertainties, leading to stagnation in the circuit structure optimization. In this paper, we propose ways to detect and mitigate this phenomenon. Leveraging the non-commutative algebra of the ansatz, we develop heuristics for determining where to insert new operators into the circuit. We find that gradient troughs are more likely to arise when the same locations are used repeatedly for new operator insertions. Our novel protocols, which add new operators in different ansatz positions, allow us to escape gradient troughs and thereby lower the measurement cost of the algorithm. This approach achieves an effective balance between cost and efficiency, leading to faster convergence without compromising the low circuit depth and gate count of ADAPT-VQE.
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.
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 variational quantum eigensolvers (ADAPT-VQE) represent one of the most promising approaches for quantum chemistry on near-term quantum devices. However, their optimization is slow and may stall due to vanishing parameters and redundant operators in the ansatz. In this work, we propose a simple strategy of operator elimination that removes non-contributing operators from the pool once they are detected, enabling the optimization to continue progressing toward convergence. We examine two variants, with and without pool restoration after elimination, and find that the former converges more smoothly and faster than the latter and the standard ADAPT-VQE. To capture dynamical correlations between the active space and its environment, we combine ADAPT-VQE with our recently developed downfolding approach, the one-body downfolding framework (OBDF). In OBDF, the bare molecular Hamiltonian in the active space is replaced by a correlated effective Hamiltonian that incorporates dynamical correlation effects outside the active space. We benchmark our implementation on a linear \ce{H_6} chain, an \ce{H_6} lattice, an \ce{H_6} ring, and the \ce{N_2} molecule using the OpenFermion simulator. Our results show that operator elimination significantly reduces circuit depth and iteration count, and that OBDF-ADAPT-VQE yields energies closer to the full configuration interaction (FCI) reference than the standard approach within the same active space.
Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this paper, we introduce an algorithm called TETRIS-ADAPT-VQE (tiling efficient trial circuits with rotations implemented simultaneously adaptive derivative-assembled problem-tailored variational quantum eigensolver), which iteratively builds up variational a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm, in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of controlled- gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared with ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware. Published by the American Physical Society 2024
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.