Second-quantized fermionic Hamiltonians for quantum simulation with polylogarithmic qubit and gate complexity.
Year: 2021
Type: preprint
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. This is the first second-quantized encoding of fermions in qubits whose costs in qubits and gates are both polylogarithmic in $M$, which will permit studying fermionic systems in the high-precision regime of many modes.
Source: arXiv (Cornell University)
Authors: William Kirby, Bryce Fuller, Charles Hadfield, Antonio Mezzacapo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3203203249