Hardware-efficient empirical variational ansätze for Variational Quantum Eigensolver (VQE) simulations of quantum chemistry often lack a direct connection to classical quantum chemistry methods. In this work, we propose a method to bridge this gap by introducing a novel approach to constructing a starting point for variational quantum circuits, leveraging quantum mutual information from classical quantum chemistry states to design simple yet effective heuristic ansätze with a topology reflecting the molecular system’s correlations. As a first step, we make use of quantum chemistry calculations, such as Mo̷ller–Plesset (MP2) perturbation theory, to initially provide approximate Natural Orbitals, which have been shown to be the best candidate one-electron basis for developing compact empirical wave functions. 1 Second, we evaluate the quantum mutual information matrix, which provides insights about the main correlations between qubits of the quantum circuit, and enables a direct design of entangling blocks for the circuit. The resulting ansatz is then used with a VQE to obtain a short-depth variational ground state of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis through simulations of various molecular systems ( H 2, LiH, H 2 O ) and apply it to the more complex NH 3 molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, outperforming the standard empirical ladder-entangler ansatz. Overall, our approach can be used as an effective state preparation, providing a promising route for designing efficient variational quantum circuits for large molecular systems.
Hardware-efficient empirical variational ansätze for Variational Quantum Eigensolver (VQE) simulations of quantum chemistry often lack a direct connection to classical quantum chemistry methods. In this work, we propose a method to bridge this gap by introducing a novel approach to constructing a starting point for variational quantum circuits, leveraging quantum mutual information from classical quantum chemistry states to design simple yet effective heuristic ansätze with a topology reflecting the molecular system’s correlations. As a first step, we make use of quantum chemistry calculations, such as Mo̷ller–Plesset (MP2) perturbation theory, to initially provide approximate Natural Orbitals, which have been shown to be the best candidate one-electron basis for developing compact empirical wave functions. 1 Second, we evaluate the quantum mutual information matrix, which provides insights about the main correlations between qubits of the quantum circuit, and enables a direct design of entangling blocks for the circuit. The resulting ansatz is then used with a VQE to obtain a short-depth variational ground state of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis through simulations of various molecular systems ( H 2, LiH, H 2 O ) and apply it to the more complex NH 3 molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, outperforming the standard empirical ladder-entangler ansatz. Overall, our approach can be used as an effective state preparation, providing a promising route for designing efficient variational quantum circuits for large molecular systems.
The variational quantum eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers.However, the circuit depth is expected to grow significantly with the problem size.Increased depth can both degrade the accuracy of the results and reduce trainability.In this work, we propose an approach to reduce ansatz circuit depth.Our approach, called "PermVQE," adds an additional optimization loop to the VQE that permutes qubits in order to solve for the qubit Hamiltonian that maximally localizes correlations in the ground state.The choice of permutations is based on mutual information, which is a measure of interaction between electrons and/or holes in spin-orbitals.Encoding strongly entangled spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state.For representative molecular systems, LiH, H 2 , (H 2 ) 2 , H = 4 , H + 3 , and N 2 , we demonstrate that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy.The approach is designed for hardware-efficient ansatz of any qubit connectivity, and examples are demonstrated for linear and twodimensional grid architectures.The main ideas can also be applied to simulate molecules with other ansatz as well as variational quantum algorithms beyond the VQE.In particular, we demonstrate the beneficial effect of qubit permutations to build fermionic-adaptive derivative assembled pseudo-Trotter ansatz on a linear qubit connectivity architecture with nearly a twofold reduction of the number of controlled NOT gates.
In this work, we present a comprehensive comparative study between two different Ansatz quantum circuits , specifically the Unitary Vibrational Coupled Cluster (UVCC) and the Compact Heuristic Circuit (CHC) with use in computational chemistry . By incorporating these circuits into the Variational Quantum Eigensolver (VQE), we aim to find the vibrational ground state energy of small molecules. Our results, obtained using both the UVCC and CHC ansatzes with and without quantum hardware noise, are benchmarked against classical computational methods for energy state determination. We emphasize the efficiency and accuracy of the CHC Ansatz , which significantly reduces circuit complexity without sacrificing the fidelity of the results. This characteristic demonstrates the potential of the CHC Ansatz for scalable quantum chemistry applications, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era. Furthermore, we employ the CHC Ansatz in conjunction with the Variational Quantum Deflation (VQD) algorithm to determine the excited vibrational state energies, which is compared against the reliable method of quantum Equation of Motion(qEOM). Through this comparative study, we aim to provide valuable insights into the practical applications of these Ansatz in quantum simulations of molecular systems, highlighting their respective advantages and potential for future quantum chemistry research.
High Resolution Image Download MS PowerPoint Slide The variational quantum eigensolver (VQE) algorithm has positioned quantum chemistry calculation methods as promising applications for noisy intermediate-scale quantum (NISQ) devices. In NISQ devices, where the quantum noise is considerable, it is desirable to have an ansatz for the quantum circuit that is practical to implement and capable of achieving high chemical accuracy. Hardware-efficient Ansätze (HEA), such as the RyRz linear ansatz (RLA) and its modified form that preserves physical quantities─the symmetry preserving ansatz (SPA)─are constructed using quantum gates that can be implemented easily on a quantum computer. However, the extent to which HEA can accurately yield the electronic state energies of actual molecules and the number of quantum gates required to achieve chemical accuracy─which, in practical cases, should be within 1 kcal/mol of the exact energy value─are not well understood. In this study, we aimed to gain a detailed understanding of these aspects by performing noiseless simulations to obtain the ground and low-lying excited state using high-depth HEA quantum circuits for several molecules, including LiH, H 2 O, BeH 2, CH 4, and N 2 . From the results, we demonstrated that symmetry preserving HEA, such as SPA, can achieve accurate computational results that maintain CCSD-level chemical accuracy by increasing the number of layers. We quantitatively analyze how the expressibility and entangling capability of RLA and SPA quantum circuits evolve with circuit depth. Our results reveal that while increased layers generally expand accessible Hilbert space and entanglement, differences in their limitations highlight the importance of considering physically allowed entanglement for performance of a parametric quantum circuit in VQE. We also studied the potential energy surface of the dissociation of these molecules and found that quantum circuits using SPA can capture static electron correlation, which is challenging to address with classical single-reference quantum chemistry methods such as CCSD. These results from SPA demonstrate its potential to represent electronic states, as it achieves highly accurate results with fewer gate operations compared to physically inspired quantum circuits such as the Unitary Coupled Cluster (UCC) method. This study establishes a possible path for the application of quantum devices in solving quantum chemistry problems.
The use of the variational quantum eigensolver (VQE) for quantum chemistry is one of the most promising applications for noisy intermediate-scale quantum (NISQ) devices. A major limitation is represented by the need to build compact and shallow circuit ansatzes having the variational flexibility to catch the complexity of the electronic structure problem. To alleviate this drawback, we introduce a modified VQE scheme in which the form of the molecular Hamiltonian is adapted to the circuit ansatz through an optimization procedure. Exploiting the invariance of the Hamiltonian by molecular orbital rotations, we can optimize it using gradients that can be calculated without significant computational overload. The proposed method, named Wavefunction Adapted Hamiltonian Through Orbital Rotation (WAHTOR), has been applied to small molecules in numerical state vector simulations. The results demonstrate that, at variance with standard VQE, the method is less dependent on circuit topology and less prone to be trapped into high-energy local minima. It is able to recover a significant amount of electron correlation even with only empirical ansatzes with shallow circuit depth. Noisy calculations demonstrate the robustness and feasibility of the proposed methodology and indicate the hardware requirements to effectively apply the procedure using forthcoming NISQ devices.
Abstract Quantum algorithms based on the variational principle have found applications in diverse areas with a huge flexibility. But as the circuit size increases the variational landscapes become flattened, causing the so-called Barren plateau phenomena. This will lead to an increased difficulty in the optimization phase, due to the reduction of the cost function parameters gradient. One of the possible solutions is to employ shallower circuits or adaptive ansätze. We introduce a systematic procedure for ansatz building based on approximate Quantum Mutual Information (QMI) with improvement on each layer obtained by repeated applications of the previously defined Quantum Information Driven Ansatz (QIDA) approach. The objective is to recover the correlation that is discarded by the standalone QIDA method, including it in additional layers. Our approach generates a layered-structured ansatz, where each layer entangler map is defined on the qubit couples selected based on their QMI values. Following the rationale that shallower circuits may mitigate the phenomenon of barren plateaus, the Multi-QIDA ansatz partitions the optimization landscape into smaller steps. The method employs an iterative construction and optimization strategy, progressively extending the circuit depth to guide the optimization towards the appropriate potential well. We benchmarked our approach on various configurations of the Heisenberg model Hamiltonian, ranging between 9 and 12 qubits, demonstrating significant improvements in the accuracy of the ground state energy calculations, in terms of deviation from the best results and convergence, compared to traditional heuristic ansatz methods. Our results show that the Multi-QIDA method reduces the computational complexity while maintaining high precision, making it a promising tool for quantum simulations in lattice spin models.
In recent years, the Variational Quantum Eigensolver (VQE) has emerged as one of the most popular algorithms for solving the electronic structure problem on near-term quantum computers. The utility of VQE is often hindered by the limitations of current quantum hardware, including, but not limited to, short qubit coherence times and low gate fidelities. These limitations become particularly pronounced when VQE is used along with deep quantum circuits, such as those required by the ”Unitary Coupled Cluster Singles and Doubles” (UCCSD) ansatz, often resulting in significant errors. To address these issues, we propose a low-depth ansatz based on parallelized Givens rotations, which can recover substantial correlation energy while drastically reducing circuit depth and two-qubit gate counts for an arbitrary active space (AS). Also, considering the current hardware architectures with low qubit counts, we introduce a systematic way to select molecular orbitals to define active spaces (ASs) that retain significant electron correlation. We validate our approach by computing bond dissociation profiles of water and strongly correlated systems, such as molecular nitrogen and oxygen, across various ASs. Noiseless simulations using the new ansatz yield ground-state energies comparable to those from the UCCSD ansatz while reducing circuit depth by 50–70%. Moreover, in noisy simulations, our approach achieves energy error rates an order of magnitude lower than that of UCCSD. Considering the efficiency and practical usage of our ansatz, we hope that it becomes a potential choice for performing quantum chemistry calculations on near-term quantum devices.