  In variational quantum optimization with particle-conserving quantum
circuits, it is often difficult to decide a priori which particle-conserving
gates and circuit ansatzes would be most efficient for a given problem. This is
important especially for noisy intermediate-scale quantum (NISQ) processors
with limited resources. While this may be challenging to answer in general,
deciding which particle-conserving gate would be most efficient is easier
within a specified circuit ansatz. In this paper, we show how to construct
efficient particle-conserving gates using some practical ideas from symmetric
tensor networks. We derive different types of particle-conserving gates,
including the generalized one. We numerically test the gates under the
framework of brick-wall circuits. We show that the general particle-conserving
gate with only four real parameters is generally best. In addition, we present
an algorithm to extend brick-wall circuit with two-qubit nearest-neighbouring
gates to non-nearest-neighbouring gates. We test and compare the efficiency of
the circuits with Heisenberg spin chain with and without
next-nearest-neighbouring interactions.
