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Quantum computers have the potential to be a profoundly transformativetechnology, particularly in the context of quantum chemistry. However, runninga chemistry application that is demonstrably useful currently requires aprohibitive number of logical operations. For example, the canonical estimateof the number of operations required to simulate the molecule FeMoco, the keycomponent in biological nitrogen fixation, requires around $10^{15}$ logicalgates. A quantum computer that is capable of applying logical operations at 1Mhz rates would require more than 30 years to complete such a calculation. Itis imperative to reduce this prohibitive runtime, by better understanding andoptimising quantum algorithms, if the technology is to have commercial utility.The purpose of this paper is to introduce such an optimisation. The gadget thatwe introduce below affords a 6x improvement in runtime for Trotterized quantumchemistry employing the Jordan-Wigner transformation, without altering therequired number of qubits.

A Jordan-Wigner gadget that reduces T count by more than 6x for quantum chemistry applications