Second-Quantized Fermionic Operators with Polylogarithmic Qubit and Gate Complexity by William Kirby, Bryce Fuller, Charles Hadfield, Antonio Mezzacapo

“…When the number F of fermions is much smaller than the number M of modes, this symmetry reduces the number of information-theoretically required qubits from Θ(M) to O(Flog⁡M). In this limit, our encoding requires O(F^{2}log^{4}⁡M) qubits, while encoded fermionic creation and annihilation operators have cost O(F^{2}log^{5}⁡M) in two-qubit gates. …”
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