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The ability to perform classically intractable electronic structurecalculations is often cited as one of the principal applications of quantumcomputing. A great deal of theoretical algorithmic development has beenperformed in support of this goal. Most techniques require a scheme for mappingelectronic states and operations to states of and operations upon qubits. Thetwo most commonly used techniques for this are the Jordan-Wigner transformationand the Bravyi-Kitaev transformation. However, comparisons of these schemeshave previously been limited to individual small molecules. In this paper wediscuss resource implications for the use of the Bravyi-Kitaev mapping scheme,specifically with regard to the number of quantum gates required forsimulation. We consider both small systems which may be simulatable onnear-future quantum devices, and systems sufficiently large for classicalsimulation to be intractable. We use 86 molecular systems to demonstrate thatthe use of the Bravyi-Kitaev transformation is typically at least approximatelyas efficient as the canonical Jordan-Wigner transformation, and results insubstantially reduced gate count estimates when performing limited circuitoptimisations.

A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry