Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers
arXiv:2109.11759 · doi:10.1103/PhysRevA.105.052415
Abstract
Variational quantum eigensolver (VQE), which attracts attention as a promising application of noisy intermediate-scale quantum devices, finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum circuits called ansatz. Since the difficulty of the optimization depends on the complexity of the problem Hamiltonian and the structure of the ansatz, it has been difficult to analyze the performance of optimizers for the VQE systematically. To resolve this problem, we propose a technique to construct a benchmark problem whose ground state is guaranteed to be achievable with a given ansatz by using the idea of parent Hamiltonian of low-depth parameterized quantum circuits. We compare the convergence of several optimizers by varying the distance of the initial parameters from the solution and find that the converged energies showed a threshold-like behavior depending on the distance. This work provides a systematic way to analyze optimizers for VQE and contribute to the design of ansatz and its initial parameters.
arXiv comment5 pages, 4 figures
References in corpus (19)
- Quantum Computing in the NISQ era and beyond
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Barren plateaus in quantum neural network training landscapes
- Quantum Circuit Learning
- Simulated Quantum Computation of Molecular Energies
- Evaluating analytic gradients on quantum hardware
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Variational ansatz-based quantum simulation of imaginary time evolution
- Quantum Natural Gradient
- Training variational quantum algorithms is NP-hard
- Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
- Sequential minimal optimization for quantum-classical hybrid algorithms
- Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
- Methodology for replacing indirect measurements with direct measurements
- An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
- Quantum Analytic Descent
- Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems