Tranter, A; Love, PJ; Mintert, F; Coveney, PV; (2018) A Comparison of the Bravyi-Kitaev and Jordan-Wigner Transformations for the Quantum Simulation of Quantum Chemistry. Journal of Chemical Theory and Computation , 14 (11) pp. 5617-5630. 10.1021/acs.jctc.8b00450.

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Abstract

The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper, we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems, which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation and results in substantially reduced gate count estimates when performing limited circuit optimizations.

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