Fast gradient-free optimization of excitations in variational quantum eigensolvers

Abstract

Finding molecular ground states and energies with variational quantum eigensolvers is central to chemistry applications on quantum computers. Physically motivated ansätze based on excitation operators respect physical symmetries, but existing quantum-aware optimizers, such as Rotosolve, have been limited to simpler operator types. To fill this gap, we introduce ExcitationSolve, a fast quantum-aware optimizer that is globally-informed, gradient-free, and hyperparameter-free. ExcitationSolve extends these optimizers to parameterized unitaries with generators $G$ of the form $G^3=G$ exhibited by excitation operators in approaches such as unitary coupled cluster. ExcitationSolve determines the global optimum along each variational parameter using the same quantum resources that gradient-based optimizers require for one update step. We provide optimization strategies for both fixed and adaptive variational ansätze, along with generalizations for simultaneously selecting and optimizing multiple excitations. On molecular ground state energy benchmarks, ExcitationSolve outperforms state-of-the-art optimizers by converging faster, achieving chemical accuracy for equilibrium geometries in a single parameter sweep, yielding shallower adaptive ansätze and remaining robust to real hardware noise. By uniting physical insight with efficient optimization, ExcitationSolve paves the way for scalable quantum chemistry calculations.

56 pages, 16 figures. Updated version as published

References in corpus (27)

• A variational eigenvalue solver on a quantum processor
• Quantum Circuit Learning
• Evaluating analytic gradients on quantum hardware
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Quantum algorithms for quantum chemistry and quantum materials science
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Training variational quantum algorithms is NP-hard
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Structure optimization for parameterized quantum circuits
• Sequential minimal optimization for quantum-classical hybrid algorithms
• Quantum simulations of materials on near-term quantum computers
• Hardware-efficient variational quantum algorithms for time evolution
• Qubit-excitation-based adaptive variational quantum eigensolver
• A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
• Reducing qubit requirements for quantum simulation using molecular point group symmetries
• An efficient quantum algorithm for the time evolution of parameterized circuits
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Minimum Hardware Requirements for Hybrid Quantum-Classical DMFT
• Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
• A basis-set error correction based on density-functional theory for strongly correlated molecular systems
• Simulating Time Evolution with Fully Optimized Single-Qubit Gates on Parameterized Quantum Circuits
• Here comes the SU(N): multivariate quantum gates and gradients
• Sequential optimal selection of a single-qubit gate and its relation to barren plateau in parameterized quantum circuits

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