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Variational wavefunction ans\"{a}tze are at the heart of solving quantummany-body problems in physics and chemistry. Previous designs ofhardware-efficient ansatz (HEA) on quantum computers are largely based onheuristics and lack rigorous theoretical foundations. In this work, weintroduce a physics-constrained approach for designing HEA with rigoroustheoretical guarantees by imposing a few fundamental constraints. Specifically,we require that the target HEA to be universal, systematically improvable, andsize-consistent, which is an important concept in quantum many-body theoriesfor scalability, but has been overlooked in previous designs of HEA. We extendthe notion of size-consistency to HEA, and present a concrete realization ofHEA that satisfies all these fundamental constraints while only requiringlinear qubit connectivity. The developed physics-constrained HEA is superior toother heuristically designed HEA in terms of both accuracy and scalability, asdemonstrated numerically for the Heisenberg model and some typical molecules.In particular, we find that restoring size-consistency can significantly reducethe number of layers needed to reach certain accuracy. In contrast, the failureof other HEA to satisfy these constraints severely limits their scalability tolarger systems with more than ten qubits. Our work highlights the importance ofincorporating physical constraints into the design of HEA for efficientlysolving many-body problems on quantum computers.

Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers that is Universal, Systematically Improvable, and Size-consistent