Quantum Information Driven Ansatz (QIDA): shallow-depth empirical quantum circuits from Quantum Chemistry

Abstract

Hardware-efficient empirical variational ansätze for Variational Quantum Eigensolver simulations of Quantum Chemistry suffer from the lack of a direct connection to classical Quantum Chemistry methods. In the present work, we propose a method to fill this gap by introducing a new approach for constructing variational quantum circuits, leveraging quantum mutual information associated with classical Quantum Chemistry states to design simple yet effective heuristic ansätze with a topology that reflects the correlations of the molecular system. As first step, Quantum Chemistry calculations, such as Møller-Plesset (MP2) perturbation theory, firstly provide an approximate Natural Orbitals basis, which has been recently shown to be the best candidate one-electron basis for developing compact empirical wavefunctions (Ratini, et al 2023). Secondly, throughout the evaluation of quantum mutual information matrices, they provide information about the main correlations between qubits of the quantum circuit, enabling the development of a direct design of entangling blocks for the circuit. The resulting ansatz is then utilized with a Variational Quantum Eigensolver (VQE) to obtain a short depth variational groundstate of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis by simulations over various molecular systems ($H_2,LiH,H_{2}O$) and apply it to the more complex $N{H}_3$ molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, surpassing the standard empirical ladder-entangler ansatz in performance. Overall, our approach can be used as effective state preparation providing a promising route for designing efficient variational quantum circuits for large molecular systems.

arXiv comment18 pages, 9 figures

References in corpus (23)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Noisy intermediate-scale quantum (NISQ) algorithms
• Recent developments in the PySCF program package
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Fermionic quantum computation
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Quantum Computing for Finance: State of the Art and Future Prospects
• Measuring orbital interaction using quantum information theory
• Quantum computing enhanced computational catalysis
• Tapering off qubits to simulate fermionic Hamiltonians
• Resource-Efficient Quantum Algorithm for Protein Folding
• The Delicate Balance of Static and Dynamic Electron Correlation
• Concept of orbital entanglement and correlation in quantum chemistry
• Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE
• Mutual information-assisted Adaptive Variational Quantum Eigensolver
• The Landscape of the Quantum Start-up Ecosystem
• Natural orbitals and sparsity of quantum mutual information
• Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study

Cited by in corpus (4)

• Quantum Information reveals that orbital-wise correlation is essentially classical in Natural Orbitals
• Mitigating decoherence in molecular spin qudits
• Compact Multi-Threshold Quantum Information Driven Ansatz For Strongly Interactive Lattice Spin Models
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions