Circuit optimization of Hamiltonian simulation by simultaneous
diagonalization of Pauli clusters
- URL: http://arxiv.org/abs/2003.13599v2
- Date: Sat, 5 Sep 2020 23:54:08 GMT
- Title: Circuit optimization of Hamiltonian simulation by simultaneous
diagonalization of Pauli clusters
- Authors: Ewout van den Berg, Kristan Temme
- Abstract summary: Quantum circuits for exact time evolution of single Pauli operators are well known, and can be extended trivially to sums of commuting Paulis.
In this paper we reduce the circuit complexity of Hamiltonian simulation by partitioning the Pauli operators into mutually commuting clusters.
We show that the proposed approach can help to significantly reduce both the number of CNOT operations and circuit depth for Hamiltonians arising in quantum chemistry.
- Score: 1.0587959762260986
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Many applications of practical interest rely on time evolution of
Hamiltonians that are given by a sum of Pauli operators. Quantum circuits for
exact time evolution of single Pauli operators are well known, and can be
extended trivially to sums of commuting Paulis by concatenating the circuits of
individual terms. In this paper we reduce the circuit complexity of Hamiltonian
simulation by partitioning the Pauli operators into mutually commuting clusters
and exponentiating the elements within each cluster after applying simultaneous
diagonalization. We provide a practical algorithm for partitioning sets of
Paulis into commuting subsets, and show that the proposed approach can help to
significantly reduce both the number of CNOT operations and circuit depth for
Hamiltonians arising in quantum chemistry. The algorithms for simultaneous
diagonalization are also applicable in the context of stabilizer states; in
particular we provide novel four- and five-stage representations, each
containing only a single stage of conditional gates.
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