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