Perturbative gadgets

[babbush]

Perturbative gadgets are techniques for manipulating representations of qubit Hamiltonians which would be very useful in some contexts. They are particularly interesting in the context of quantum simulation and multiple papers have explored their application to electronic structure specifically. One can use perturative gadgets to reduce the many-body order of a QubitHamiltonian, or change the connectivity graph, or change the types of terms in the Hamiltonian, in a way that leaves the low energy portion of the "gadgetized" Hamiltonian spectra invariant. A few relevant papers in this area would be:

For electronic structure https://arxiv.org/abs/1311.3967 https://arxiv.org/abs/1706.03637

Various other papers with important gadget constructions https://arxiv.org/abs/quant-ph/0406180 https://arxiv.org/abs/quant-ph/0504050 https://arxiv.org/abs/0802.1874 https://arxiv.org/abs/1311.2555 https://arxiv.org/abs/1311.3161 https://arxiv.org/abs/1709.02705

Any code to implement these gadgets would be a welcome addition to OpenFermion. @yudongcao , a member of the OpenFermion community, is an expert in this topic in case people have questions.

[babbush]

Papers that provide diagonal representations of the electronic structure Hamiltonian may also be of interest since this makes the gadgetization much easier: https://arxiv.org/abs/1706.00023 https://arxiv.org/abs/1709.08059

Likewise, for certain systems, such as the Hubbard model, fermion to qubit mappings of constant locality may also be important: https://arxiv.org/abs/cond-mat/0508353 https://arxiv.org/abs/1712.00446