Early faulttolerant simulations of the Hubbard model
Abstract
Simulation of the Hubbard model is a leading candidate for the first useful applications of a faulttolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan \textit{et al.} Quantum 4 296 (2019)] found that the lowest resource costs were achieved by splitoperator Trotterization combined with the fastfermionic Fourier transform (FFFT) on an $L \times L$ lattice with length $L=2^k$. On lattices with length $L \neq 2^k$, Givens rotations can be used instead of the FFFT but lead to considerably higher resource costs. We present a new analytic approach to bounding the simulation error due to Trotterization that provides much tighter bounds for the splitoperator FFFT method, leading to $16 \times$ improvement in error bounds. Furthermore, we introduce plaquette Trotterization that works on any size lattice and apply our improved error bound analysis to show competitive resource costs. We consider a phase estimation task and show plaquette Trotterization reduces the number of nonClifford gates by a factor $5.5\times$ to $9 \times$ (depending on the parameter regime) over the best previous estimates for $8 \times 8$ and $16 \times 16$ lattices and a much larger factor for other lattice sizes not of the form $L=2^k$. In conclusion, we find there is a potentially useful application for faulttolerant quantum computers using around one million Toffoli gates.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.09238
 arXiv:
 arXiv:2012.09238
 Bibcode:
 2020arXiv201209238C
 Keywords:

 Quantum Physics
 EPrint:
 Some typos corrected since V1 with gate counts slightly adjusted. V2 more polished