A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive

Abstract

We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression which is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition metal complex ferrocene (Fe$({\mathrm{C}}_5{\mathrm{H}}_5{)}_2$), indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to CASSCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way towards a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

21 pages, 5 figures

References in corpus (11)

• Simulated Quantum Computation of Molecular Energies
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• The density matrix renormalization group for ab initio quantum chemistry
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo
• NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods
• The chromium dimer: closing a chapter of quantum chemistry
• The Bonsai algorithm: grow your own fermion-to-qubit mapping
• The Basics of Quantum Computing for Chemists
• A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions

Cited by in corpus (8)

• Which options exist for NISQ-friendly linear response formulations?
• Reducing the Resources Required by ADAPT-VQE Using Coupled Exchange Operators and Improved Subroutines
• Physically motivated improvements of Variational Quantum Eigensolvers
• A Hybrid Qubit Encoding: Splitting Fock Space into Fermionic and Bosonic Subspaces
• Divergences in classical and quantum linear response and equation of motion formulations
• Self-consistent Quantum Linear Response with a Polarizable Embedding environment
• Hyperfine Coupling Constants on Quantum Computers: Performance, Errors, and Future Prospects
• Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation