Variational wavefunction ans\"{a}tze are at the heart of solving quantum
many-body problems in physics and chemistry. Here, we propose a
physics-constrained approach for designing hardware-efficient ansatz (HEA) with
rigorous theoretical guarantees on quantum computers by satisfying a few
fundamental constraints, which is inspired by the remarkably successful way to
design exchange-correlation functionals in density functional theories by
satisfying exact constraints. Specifically, we require that the target HEA to
be universal, systematically improvable, and size-consistent, which is an
important concept in quantum many-body theories for scalability, but has been
largely overlooked in previous designs of HEA by heuristics. We extend the
notion of size-consistency to HEA, and present a concrete realization of HEA
that satisfies all these fundamental constraints and only requires linear qubit
connectivity. The developed physics-constrained HEA is superior to other
heuristically designed HEA in terms of both accuracy and scalability, as
demonstrated numerically for the Heisenberg model and some typical molecules.
In particular, we find that restoring size-consistency can significantly reduce
the number of layers needed to reach certain accuracy. In contrast, the failure
of other HEA to satisfy these constraints severely limits their scalability to
larger systems with more than ten qubits. Our work highlights the importance of
incorporating physical constraints into the design of HEA for efficiently
solving many-body problems on quantum computers.Comment: 21 pages, 4 figure