Second-quantized fermionic operators with polylogarithmic qubit and gate complexity

• URL: http://arxiv.org/abs/2109.14465v4
• Date: Mon, 6 Jun 2022 23:07:27 GMT
• Title: Second-quantized fermionic operators with polylogarithmic qubit and gate complexity
• Authors: William Kirby, Bryce Fuller, Charles Hadfield, and Antonio Mezzacapo
• Abstract summary: We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved. This is the first second-quantized encoding of fermions in qubits whose costs in qubits and gates are both polylogarithmic in $M$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. 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 $\Theta(M)$ to $O(F\log M)$. 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. When incorporated into randomized simulation methods, this permits simulating time-evolution with only polylogarithmic explicit dependence on $M$. This is the first second-quantized encoding of fermions in qubits whose costs in qubits and gates are both polylogarithmic in $M$, which permits studying fermionic systems in the high-accuracy regime of many modes.

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