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Second-Quantized Fermionic Operators with Polylogarithmic Qubit and Gate Complexity
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DOI：10.1103/PRXQuantum.3.020351.png)
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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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BASIS-SET CONVERGENCE
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11
论文数:
919
被引数:
9.0K
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