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Hunting for quantum advantage in electronic structure calculations is a highly non-trivial task

Örs Legeza, Andor Menczer, Miklós Antal Werner, Sotiris S. Xantheas, Frank Neese, Martin Ganahl, Cole Brower, Samuel Rodriguez Bernabeu, Jeff Hammond, John Gunnels

Abstract

In light of major developments over the past decades in both quantum computing and simulations on classical hardware, it is a serious challenge to identify a real-world problem where quantum advantage is expected to appear. In quantum chemistry, electronic structure calculations of strongly correlated, i.e. multi-reference problems, are often argued to fall into such category because of their intractability with standard methods based on mean-field theory. Therefore, providing state-of-the-art benchmark data by classical algorithms is necessary to make a decisive conclusion when such competing development directions are compared. We report cutting-edge performance results together with high accuracy ground state energy for the Fe$_4$S$_4$ molecular cluster on a CAS(54,36) model space, a problem that has been included quite recently among the list of systems in the {\it Quantum Advantage Tracker} webpage maintained by IBM and RIKEN. Pushing the limits even further, we also present CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 89 electrons in 102 orbitals [CAS(89,102)] for the Fe$_5$S$_{12}$H$_4^{5-}$ molecular system comprising twenty five open shell orbitals in its sextet ground state and an active spaces size of 331 electrons in 451 orbitals. We have achieved our results via mixed-precision spin-adapted \textit{ab initio} Density Matrix Renormalization Group (DMRG) electronic structure calculations interfaced with the ORCA program package and utilizing the NVIDIA Blackwell graphics processing unit (GPU) platform. We argue that DMRG benchmark data should be taken as a classical reference when quantum advantage is reported. In addition, full exploitation of classical hardware should also be considered since even the most advanced DMRG implementations are still in a premature stage regarding utilization of all the benefits of GPU technology.

Hunting for quantum advantage in electronic structure calculations is a highly non-trivial task

Abstract

In light of major developments over the past decades in both quantum computing and simulations on classical hardware, it is a serious challenge to identify a real-world problem where quantum advantage is expected to appear. In quantum chemistry, electronic structure calculations of strongly correlated, i.e. multi-reference problems, are often argued to fall into such category because of their intractability with standard methods based on mean-field theory. Therefore, providing state-of-the-art benchmark data by classical algorithms is necessary to make a decisive conclusion when such competing development directions are compared. We report cutting-edge performance results together with high accuracy ground state energy for the FeS molecular cluster on a CAS(54,36) model space, a problem that has been included quite recently among the list of systems in the {\it Quantum Advantage Tracker} webpage maintained by IBM and RIKEN. Pushing the limits even further, we also present CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 89 electrons in 102 orbitals [CAS(89,102)] for the FeSH molecular system comprising twenty five open shell orbitals in its sextet ground state and an active spaces size of 331 electrons in 451 orbitals. We have achieved our results via mixed-precision spin-adapted \textit{ab initio} Density Matrix Renormalization Group (DMRG) electronic structure calculations interfaced with the ORCA program package and utilizing the NVIDIA Blackwell graphics processing unit (GPU) platform. We argue that DMRG benchmark data should be taken as a classical reference when quantum advantage is reported. In addition, full exploitation of classical hardware should also be considered since even the most advanced DMRG implementations are still in a premature stage regarding utilization of all the benefits of GPU technology.

Paper Structure

This paper contains 1 equation, 4 figures.

Figures (4)

  • Figure 1: Orbital occupation number profile obtained for the Fe$_4$S$_4$ cluster in a CAS(54,36) model space using DMRG with $D=8192$ and 20 sweeps, and the basis given in Ref. Sharma-2014c. $\langle n_\uparrow\rangle$ and $\langle n_\downarrow\rangle$ stand for occupation number of up- and down-spin electrons, respectively, while $\langle n\rangle=\langle n_\uparrow + n_\downarrow\rangle$. This latter quantity is also reproduced directly using $D_{SU(2)}=4096$ multiplets. Labels in the x-axis indicate the corresponding orbital index.
  • Figure 2: The ground state energy as a function of inverse DMRG bond dimension, $D_{SU(2)}\in\{1024,\ldots,12288\}$ for the Fe$_4$S$_4$ molecule in a CAS(54,36) model space Sharma-2014c (left panel) and as a function of truncation error $\varepsilon_{\rm tr}$ (right panel) obtained on a DGX B200 system via performant mode. Solid lines stand for second-order polynomial fits. The corresponding $U(1)$ bond dimension values are indicated by numbers next to the data points. Dashed line stands for reference energy obtained earlier with $D_{SU(2)}=4000$Sharma-2014c while dotted lines indicate 1.6 milliHa chemical accuracy with respect to the extrapolated ground state energy, $E_{\rm ext}$.
  • Figure 3: Orbital occupation number profile, $\langle n \rangle$, obtained for the DMRG-SCF optimized basis via $D_{SU(2)}=2048$ for (a) the singlet ground state of Fe$_4$S$_{10}$H$_4^{4-}$ cluster in a CAS(72,82) model space and for (b) the sextet ground state of the Fe$_5$S$_{12}$H$_4^{5-}$ cluster in a CAS(82,102) model space. The twenty and twenty-five open shell orbitals correspond to the four and five Fe atoms, respectively, while $\max(D)$ indicates the corresponding maximum $U(1)$ bond dimension.
  • Figure 4: Convergence of DMRG-SCF for the (a) singlet ground state of Fe$_4$S$_{10}$H$_4^{4-}$ cluster in a CAS(72,82) model space using various $D_{SU(2)}\in\{512,1024,2408\}$, $\varepsilon_{\rm sweep}=10^{-5}$, $\varepsilon_{\rm Lanczos}=10^{-6}$ and orca "tight" error setting. (b) The same but for the sextet ground state of Fe$_5$S$_{12}$H$_4^{5-}$ in a CAS(89,102) model space.