Quantum simulation of the generalized chiral-fermion Hamiltonian with an MPO norm

Develop a quantum-simulation method for the generalized Hamiltonian dynamics i \tilde{N} d|\phi(t)\rangle/dt = \tilde{H} |\phi(t)\rangle of interacting chiral fermions on a lattice endowed with a matrix product operator (MPO) semi-definite norm, and ascertain whether such a simulation can be implemented on a quantum simulator or quantum computer without coupling the edge theory to a higher-dimensional bulk or introducing long-range interactions via the similarity transformation \tilde{N}^{-1/2} \tilde{H} \tilde{N}^{-1/2}.

Background

The paper introduces a Hamiltonian formalism for interacting chiral fermions on a lattice in which the physical inner product is determined by a semi-definite matrix product operator (MPO) norm \tilde{N}. Dynamics are governed by a generalized Schrödinger equation i \tilde{N} d|\phi\rangle/dt = \tilde{H} |\phi\rangle, and observables are computed within this non-orthogonal framework.

Classical tensor-network methods (e.g., MPS/DMRG and TDVP) can be adapted to this generalized setting, but implementing analogous dynamics on quantum hardware is nontrivial because \tilde{H} does not admit a simple Trotter decomposition and because mapping to a standard inner product via \tilde{N}^{-1/2} \tilde{H} \tilde{N}^{-1/2} typically introduces long-range interactions. The authors explicitly identify the feasibility of such a quantum simulation—without resorting to a higher-dimensional bulk embedding or long-range interactions—as an unresolved issue.