  Application of the adiabatic model of quantum computation requires efficient
encoding of the solution to computational problems into the lowest eigenstate
of a Hamiltonian that supports universal adiabatic quantum computation.
Experimental systems are typically limited to restricted forms of 2-body
interactions. Therefore, universal adiabatic quantum computation requires a
method for approximating quantum many-body Hamiltonians up to arbitrary
spectral error using at most 2-body interactions. Hamiltonian gadgets,
introduced around a decade ago, offer the only current means to address this
requirement. Although the applications of Hamiltonian gadgets have steadily
grown since their introduction, little progress has been made in overcoming the
limitations of the gadgets themselves. In this experimentally motivated
theoretical study, we introduce several gadgets which require significantly
more realistic control parameters than similar gadgets in the literature. We
employ analytical techniques which result in a reduction of the resource
scaling as a function of spectral error for the commonly used subdivision, 3-
to 2-body and $k$-body gadgets. Accordingly, our improvements reduce the
resource requirements of all proofs and experimental proposals making use of
these common gadgets. Next, we numerically optimize these new gadgets to
illustrate the tightness of our analytical bounds. Finally, we introduce a new
gadget that simulates a $YY$ interaction term using Hamiltonians containing
only $\{X,Z,XX,ZZ\}$ terms. Apart from possible implications in a theoretical
context, this work could also be useful for a first experimental implementation
of these key building blocks by requiring less control precision without
introducing extra ancillary qubits.

Quantum Physics