An adaptive scheme is used to reduce the cost of molecular excited states and increase their feasibility in Noisy Intermediate-Scale Quantum (NISQ) computers
In a collaboration that started at Imperial College led by MSc student Hans Chan (now a PhD student at Oxford), the Variational Quantum Deflation (VQD) algorithm[1] is combined with the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) scheme[2] to compute molecular excited states with an emulator based on the Quantum Variational Eigensolver (VQE).[3]
The main goal is to reduce the size of the Hilbert space spanned by the molecular wave function, reducing resource requirements in quantum computers and thus in principle making molecular excited state simulations more feasible in these novel devices. This is effectively accomplished in our emulations by using the ADAPT scheme to create truncated (smaller) wave functions with only a few Unitary Coupled-Cluster (UCC) amplitudes that nevertheless accrue most of the electron correlation achieving chemical accuracy.
Our work, now available in arXiv,[4] aims to bridge the gap between the more traditional aspects in quantum chemistry and the novel concepts employed in quantum information theory and applied in quantum computers. To do this the Quantum Eigensolver Building on Achievements of Both quantum computing and quantum chemistry (QEBAB) package was developed, which is readily available in an online repository.[5] A white paper with pseudo-code is also provided in the supporting information of the manuscript to walk the reader through the different methods and how these are implemented in the package.[4]
The work was being written as the implementation of ADAPT-VQD by Aspuru-Guzik and co-workers was published.[6] Our study adds to this by comparing different UCC schemes available in the literature and provides further support for this technique by assessing the computational gains, as well as the errors incurred, throughout the dissociation curve of LiH.
These are our first steps into this novel and exciting field!
References
[1] O. Higgott, D. Wang and S. Brierley, "Variational Quantum Computation of Excited States", Quantum, 2019, 3, 156.
[2] H. R. Grimsley, S. E. Economou, E. Barnes and N. J. Mayhall,"An adaptive variational algorithm for exact molecular simulations on a quantum computer", Nature Communications, 2019, 10, 1–11.
[3] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik and Jeremy L. O’Brien, "A variational eigenvalue solver on a photonic quantum processor", Nature Communications, 2014, 5, 4213.
[4] Hans H. S. Chan, Nathan Fitzpatrick, Javier Segarra-Martí, Michael J. Bearpark and David P. Tew, "Molecular Excited State Calculations with Adaptive Wavefunctions on a Quantum Eigensolver Emulation: Reducing Circuit Depth and Separating Spin States", arXiv:2105.10275 [quant-ph]
[5] Hans H. S. Chan, 2021, https://github. com/hanschanhs/QEBAB.
[6] Jakob S. Kottmann, Abhinav Ananda and Alán Aspuru-Guzik, "A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers", Chemical Science, 2021, 12, 3497.
Comments