  Variational wavefunction ans\"{a}tze are at the heart of solving quantum
many-body problems in physics and chemistry. Previous designs of
hardware-efficient ansatz (HEA) on quantum computers are largely based on
heuristics and lack rigorous theoretical foundations. In this work, we
introduce a physics-constrained approach for designing HEA with rigorous
theoretical guarantees by imposing a few fundamental 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 overlooked in previous designs of HEA. We extend
the notion of size-consistency to HEA, and present a concrete realization of
HEA that satisfies all these fundamental constraints while only requiring
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.
