The zero-energy variance principle can be exploited in variational quantum eigensolvers for solving general eigenstates but its capacity for obtaining a specified eigenstate,such as ground state,is limited as all eige...The zero-energy variance principle can be exploited in variational quantum eigensolvers for solving general eigenstates but its capacity for obtaining a specified eigenstate,such as ground state,is limited as all eigenstates are of zero energy variance.We propose a variance-based variational quantum eigensolver for solving the ground state by searching in an enlarged space of wavefunction and Hamiltonian.With a mutual variance-Hamiltonian optimization procedure,the Hamiltonian is iteratively updated to guild the state towards to the ground state of the target Hamiltonian by minimizing the energy variance in each iteration.We demonstrate the performance and properties of the algorithm with numeral simulations.Our work suggests an avenue for utilizing guided Hamiltonian in hybrid quantum-classical algorithms.展开更多
The original variational quantum eigensolver(VQE)typically minimizes energy with hybrid quantum-classical optimization that aims to find the ground state.Here,we propose a VQE based on minimizing energy variance and c...The original variational quantum eigensolver(VQE)typically minimizes energy with hybrid quantum-classical optimization that aims to find the ground state.Here,we propose a VQE based on minimizing energy variance and call it the variance-VQE,which treats the ground state and excited states on the same footing,since an arbitrary eigenstate for a Hamiltonian should have zero energy variance.We demonstrate the properties of the variance-VQE for solving a set of excited states in quantum chemistry problems.Remarkably,we show that optimization of a combination of energy and variance may be more efficient to find low-energy excited states than those of minimizing energy or variance alone.We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling,which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12005065)the Guangdong Basic and Applied Basic Research Fund(Grant No.2021A1515010317)。
文摘The zero-energy variance principle can be exploited in variational quantum eigensolvers for solving general eigenstates but its capacity for obtaining a specified eigenstate,such as ground state,is limited as all eigenstates are of zero energy variance.We propose a variance-based variational quantum eigensolver for solving the ground state by searching in an enlarged space of wavefunction and Hamiltonian.With a mutual variance-Hamiltonian optimization procedure,the Hamiltonian is iteratively updated to guild the state towards to the ground state of the target Hamiltonian by minimizing the energy variance in each iteration.We demonstrate the performance and properties of the algorithm with numeral simulations.Our work suggests an avenue for utilizing guided Hamiltonian in hybrid quantum-classical algorithms.
基金supported by the National Natural Science Foundation of China(Grant No.12005065)the Guangdong Basic and Applied Basic Research Fund(Grant No.2021A1515010317)
文摘The original variational quantum eigensolver(VQE)typically minimizes energy with hybrid quantum-classical optimization that aims to find the ground state.Here,we propose a VQE based on minimizing energy variance and call it the variance-VQE,which treats the ground state and excited states on the same footing,since an arbitrary eigenstate for a Hamiltonian should have zero energy variance.We demonstrate the properties of the variance-VQE for solving a set of excited states in quantum chemistry problems.Remarkably,we show that optimization of a combination of energy and variance may be more efficient to find low-energy excited states than those of minimizing energy or variance alone.We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling,which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.
