Sequence of penalties method to study excited states using VQE
arXiv:2304.05262 · doi:10.1088/2058-9565/acd1a9
Abstract
We propose an extension of the Variational Quantum Eigensolver (VQE) that leads to more accurate energy estimations and can be used to study excited states. The method is based on the introduction of a sequence of increasing penalties in the cost function. This approach does not require circuit modifications and thus can be applied with no additional depth cost. Through numerical simulations, we show that we are able to produce variational states with desired physical properties, such as total spin and charge. We assess its performance both on classical simulators and on currently available quantum devices, calculating the potential energy curves of small molecular systems in different physical configurations. Finally, we compare our method to the original VQE and to another extension, obtaining a better agreement with exact simulations for both energy and targeted physical quantities.
arXiv comment11 pages, 9 figures, published in IOP Quantum Science and Technology
References in corpus (39)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- The theory of variational hybrid quantum-classical algorithms
- A Quantum Approximate Optimization Algorithm
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum Chemistry in the Age of Quantum Computing
- Error mitigation for short-depth quantum circuits
- Evaluating analytic gradients on quantum hardware
- The Variational Quantum Eigensolver: a review of methods and best practices
- Fermionic quantum computation
- State preservation by repetitive error detection in a superconducting quantum circuit
- Extending the computational reach of a noisy superconducting quantum processor
- Validating quantum computers using randomized model circuits
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Efficient variational quantum simulator incorporating active error minimisation
- The Bravyi-Kitaev transformation for quantum computation of electronic structure
- Variational Quantum Computation of Excited States
- Robust determination of molecular spectra on a quantum processor
- 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
- Subspace-search variational quantum eigensolver for excited states
- Variational quantum algorithms for discovering Hamiltonian spectra
- Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits
- Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
- Tapering off qubits to simulate fermionic Hamiltonians
- Digital zero noise extrapolation for quantum error mitigation
- Sequential minimal optimization for quantum-classical hybrid algorithms
- Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
- Estimating the gradient and higher-order derivatives on quantum hardware
- An efficient quantum algorithm for the time evolution of parameterized circuits
- Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition
- Lipkin model on a quantum computer
- Penalty methods for variational quantum eigensolver
- Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer
- Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver
- Accelerating lattice quantum field theory calculations via interpolator optimization using NISQ-era quantum computing
- Addressing hard classical problems with Adiabatically Assisted Variational Quantum Eigensolvers