%0 Generic %1 wang2018accelerated %A Wang, Daochen %A Higgott, Oscar %A Brierley, Stephen %D 2018 %K quantumcomputing %R 10.1103/PhysRevLett.122.140504 %T Accelerated Variational Quantum Eigensolver %U http://arxiv.org/abs/1802.00171 %X The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE requires $O(1)$ repetitions of circuits with depth $O(1/\epsilon)$, whereas each expectation estimation subroutine within VQE requires $O(1/\epsilon^2)$ samples from circuits with depth $O(1)$. We propose a generalised VQE algorithm that interpolates between these two regimes via a free parameter $\alphaın0,1$ which can exploit quantum coherence over a circuit depth of $O(1/\epsilon^\alpha)$ to reduce the number of samples to $O(1/\epsilon^2(1-\alpha))$. Along the way, we give a new routine for expectation estimation under limited quantum resources that is of independent interest.

@misc{wang2018accelerated, abstract = {The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE requires $O(1)$ repetitions of circuits with depth $O(1/\epsilon)$, whereas each expectation estimation subroutine within VQE requires $O(1/\epsilon^{2})$ samples from circuits with depth $O(1)$. We propose a generalised VQE algorithm that interpolates between these two regimes via a free parameter $\alpha\in[0,1]$ which can exploit quantum coherence over a circuit depth of $O(1/\epsilon^{\alpha})$ to reduce the number of samples to $O(1/\epsilon^{2(1-\alpha)})$. Along the way, we give a new routine for expectation estimation under limited quantum resources that is of independent interest.}, added-at = {2020-03-12T11:14:57.000+0100}, author = {Wang, Daochen and Higgott, Oscar and Brierley, Stephen}, biburl = {https://www.bibsonomy.org/bibtex/2821ff3bffa67a80e837923c8f71c7331/cmcneile}, description = {Accelerated Variational Quantum Eigensolver}, doi = {10.1103/PhysRevLett.122.140504}, interhash = {73e63187a611ca063b5b2910ac72d241}, intrahash = {821ff3bffa67a80e837923c8f71c7331}, keywords = {quantumcomputing}, note = {cite arxiv:1802.00171Comment: 11 pages}, timestamp = {2020-03-12T11:14:57.000+0100}, title = {Accelerated Variational Quantum Eigensolver}, url = {http://arxiv.org/abs/1802.00171}, year = 2018 }