A size-extensive scheme for variational quantum ansatzes without Trotter approximation

One of the most promising applications for quantum computers is simulating the low-energy states of complex quantum systems. In the near-term, this can be done with variational ansatzes. Such ansatzes should follow physical principles to ensure high performance, one of the key principles being size-extensivity. Unfortunately, digitizing such ansatzes into standard operations generally requires the use of the inexact Trotter expansion, which constrains the expected accuracy of the ansatz.

In this work, we resolve this conflict by developing a framework for physically motivated ansatzes, which is fundamentally digital and thereby involves no Trotter errors. Using the stabilizer formalism, we construct a family of digital ansatzes that provably cover the entire Hilbert space with a minimal number of parameters. We show how to compress such parent ansatzes into practical child ansatzes that target specific systems, following the principle of size-extensivity. For this purpose, we develop a convenient diagrammatic approach. We apply our method numerically to the quantum Ising chain, with good convergence outside the critical regime.