coulomb operator
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Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 208 ◽  
Author(s):  
Dominic W. Berry ◽  
Craig Gidney ◽  
Mario Motta ◽  
Jarrod R. McClean ◽  
Ryan Babbush

Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with O~(N3/2λ) T complexity, where N is number of orbitals and λ is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space.



2019 ◽  
Vol 42 (18) ◽  
pp. 6648-6659 ◽  
Author(s):  
Ramazan Ozarslan ◽  
Ahu Ercan ◽  
Erdal Bas




2016 ◽  
Vol 19 (1) ◽  
pp. 601-615
Author(s):  
Vittorio Coti Zelati ◽  
Margherita Nolasco


2014 ◽  
Vol 35 (28) ◽  
pp. 2056-2069
Author(s):  
Taweetham Limpanuparb ◽  
Josh Milthorpe ◽  
Alistair P. Rendell




2013 ◽  
Vol 9 (2) ◽  
pp. 863-867 ◽  
Author(s):  
Taweetham Limpanuparb ◽  
Josh Milthorpe ◽  
Alistair P. Rendell ◽  
Peter M. W. Gill
Keyword(s):  


2012 ◽  
Vol 46 (2) ◽  
pp. 025301 ◽  
Author(s):  
H Hogreve
Keyword(s):  


2012 ◽  
Vol 136 (10) ◽  
pp. 104102 ◽  
Author(s):  
Taweetham Limpanuparb ◽  
Joshua W. Hollett ◽  
Peter M. W. Gill
Keyword(s):  


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