Materials design stands to be one of the most promising applications of quantum computing. However, the presence of noise in near-term quantum devices restricts quantum simulations of materials to shallow circuits. In this work, we present circuit-efficient variational quantum eigensolver (VQE) simulations of periodic materials using qubit-encoded wave functions based on Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) VQE. To iteratively construct accurate wave functions for periodic systems, we introduce operator pools comprising a complete set of anti-Hermitian one- and two-body qubit excitation/flipping operators. Numerical results demonstrate that these qubit-encoded algorithms can accurately predict the ground-state energy of periodic systems while significantly reducing circuit depth compared to Fermion-encoded algorithms. Additionally, we integrate the variance extrapolation technique with ADAPT-VQE algorithms to enhance the accuracy of ground-state energy estimations. This strategy further reduces the required circuit depth, enabling scalable and precise simulations of periodic systems.
Materials design stands to be one of the most promising applications of quantum computing. However, the presence of noise in near-term quantum devices restricts quantum simulations of materials to shallow circuits. In this work, we present circuit-efficient variational quantum eigensolver (VQE) simulations of periodic materials using qubit-encoded wave functions based on Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) VQE. To iteratively construct accurate wave functions for periodic systems, we introduce operator pools comprising a complete set of anti-Hermitian one- and two-body qubit excitation/flipping operators. Numerical results demonstrate that these qubit-encoded algorithms can accurately predict the ground-state energy of periodic systems while significantly reducing circuit depth compared to Fermion-encoded algorithms. Additionally, we integrate the variance extrapolation technique with ADAPT-VQE algorithms to enhance the accuracy of ground-state energy estimations. This strategy further reduces the required circuit depth, enabling scalable and precise simulations of periodic systems.
The adaptive derivative-assembled pseudo-trotter (ADAPT) variational quantum eigensolver (VQE) is an appealing framework for iteratively constructing accurate representations of ground- and excited-state wave functions as products of exponentialized one- and two-body operators acting on a reference state. In this work, we propose a CNOT-efficient circuit for implementing exponentialized two-body qubit-excitation-based (QEB) operators, enabling the construction of the low-depth wave function Ansätze. Our proposed circuit architecture employs a 2-qubit-controlled rotation gate flanked by two layers of CNOT gates, requiring only 9 CNOT gates per two-body QEB operator while preserving essential symmetries, including particle number and the Z -component of spin. By integrating these optimized circuits into the ADAPT–VQE framework, we achieve a reduction in circuit depth of approximately 28% compared to the original QEB ADAPT–VQE method, without sacrificing accuracy in simulating ground- and excited-state properties of small molecules. Numerical simulations validate the improved performance of our approach, demonstrating its potential as an efficient tool for quantum simulations of electronic structures.
Abstract Reducing circuit depth is essential for implementing quantum simulations of electronic structure on near-term quantum devices. In this work, we propose a variational quantum eigensolver (VQE) based perturbation theory (PT) algorithm to accurately simulate electron correlation of periodic materials with shallow ansatz circuits, which are generated from adaptive derivative-assembled pseudo-trotter or qubit-excitation-based VQE calculations using a loose convergence criteria. Here, the major part of the electron correlation is described using the VQE ansatz circuit and the remaining correlation energy is described by either multireference or similarity transformation-based PT. Numerical results demonstrate that the new algorithms are able to accurately describe electron correlation of the LiH crystal with only one circuit parameter, in contrast with ~30 parameters required in the adaptive VQE to achieve the same accuracy. Meanwhile, for fixed-depth ansätze, e.g. unitary coupled cluster, we demonstrate that the VQE-based PT provides an appealing scheme to improve their accuracy.
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.
Recently, adaptive variational quantum algorithms, e.g., Adaptive Derivative-Assembled Pseudo-Trotter-Variational Quantum Eigensolver (ADAPT-VQE) and Iterative Qubit-Excitation Based-Variational Quantum Eigensolver (IQEB-VQE), have been proposed to optimize the circuit depth, while a huge number of additional measurements make these algorithms highly inefficient. In this work, we reformulate the ADAPT-VQE with reduced density matrices (RDMs) to avoid additional measurement overhead. With Valdemoro's reconstruction of the three-electron RDM, we present a revised ADAPT-VQE algorithm, termed ADAPT-V, without any additional measurements but at the cost of increasing variational parameters compared to the ADAPT-VQE. Furthermore, we present an ADAPT-Vx algorithm by prescreening the anti-Hermitian operator pool with this RDM-based scheme. ADAPT-Vx requires almost the same variational parameters as ADAPT-VQE but a significantly reduced number of gradient evaluations. Numerical benchmark calculations for small molecules demonstrate that ADAPT-V and ADAPT-Vx provide an accurate description of the ground- and excited-state potential energy curves. In addition, to minimize the quantum resource demand, we generalize this RDM-based scheme to circuit-efficient IQEB-VQE algorithm and achieve significant measurement reduction.
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the noisy intermediate-scale quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various well known strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides an assessment of current quantum algorithms for molecular modeling on real quantum hardware, highlighting the impact of noise and hardware limitations on the achievable accuracy.
Approximating the ground states of strongly interacting electron systems in quantum chemistry and condensed matter physics is expected to be one of the earliest applications of quantum computers. In this paper, we prepare highly accurate ground states of the Fermi-Hubbard model for small grids up to 6 sites (12 qubits) by using an interpretable, adaptive variational quantum eigensolver(VQE) called ADAPT-VQE. In contrast with non-adaptive VQE, this algorithm builds a system-specific ansatz by adding an optimal gate built from one-body or two-body fermionic operators at each step. We show this adaptive method outperforms the non-adaptive counterpart in terms of fewer variational parameters, short gate depth, and scaling with the system size. The fidelity and energy of the prepared state appear to improve asymptotically with ansatz depth. We also demonstrate the application of adaptive variational methods by preparing excited states and Green functions using a proposed ADAPT-SSVQE algorithm. Lower depth, asymptotic convergence, noise tolerance of a variational approach, and a highly controllable, system-specific ansatz make the adaptive variational methods particularly well-suited for NISQ devices.