English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The quantum simulation of quantum chemistry is a promising application ofquantum computers. However, for N molecular orbitals, the $\mathcal{O}(N^4)$gate complexity of performing Hamiltonian and unitary Coupled Cluster Trottersteps makes simulation based on such primitives challenging. We substantiallyreduce the gate complexity of such primitives through a two-step low-rankfactorization of the Hamiltonian and cluster operator, accompanied bytruncation of small terms. Using truncations that incur errors below chemicalaccuracy, we are able to perform Trotter steps of the arbitrary basiselectronic structure Hamiltonian with $\mathcal{O}(N^3)$ gate complexity insmall simulations, which reduces to $\mathcal{O}(N^2 \log N)$ gate complexityin the asymptotic regime, while our unitary Coupled Cluster Trotter step has$\mathcal{O}(N^3)$ gate complexity as a function of increasing basis size for agiven molecule. In the case of the Hamiltonian Trotter step, these circuitshave $\mathcal{O}(N^2)$ depth on a linearly connected array, an improvementover the $\mathcal{O}(N^3)$ scaling assuming no truncation. As a practicalexample, we show that a chemically accurate Hamiltonian Trotter step for a 50qubit molecular simulation can be carried out in the molecular orbital basiswith as few as 4,000 layers of parallel nearest-neighbor two-qubit gates,consisting of fewer than 100,000 non-Clifford rotations. We also apply ouralgorithm to iron-sulfur clusters relevant for elucidating the mode of actionof metalloenzymes.

Low rank representations for quantum simulation of electronic structure