Quantum Algorithms for Open Lattice Field Theories

Certain aspects of unitary quantum systems are well-described by non-Hermitian effective Hamiltonians, as in the Wigner-Weisskopf (WW) theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian can be embedded in a unital quantum channel via a generalization of the WW theory. This existence demonstrates the physical relevance of novel features like exceptional points in quantum dynamics and opens avenues for studying many-body systems in the complex plane of couplings. In the case of lattice field theory (LFT), locality/sparsity lends these channels the promise of efficient simulation on standard quantum hardware. We thus consider quantum operations that correspond to Suzuki-Lee-Trotter approximation of LFTs undergoing non-Hermitian dynamics, with potential applicability to spin or gauge models at finite temperature, and/or chemical potential, to quantum phase transitions, and a class of theories with sign problems. We explore these channels on a benchmark, the 1D quantum transverse Ising model with an imaginary longitudinal magnetic field, showing that observables can probe the Lee-Yang edge singularity. Our channels can resolve this despite quantum jumps, and potentially other noise, making a coarse implementation viable for NISQ era technologies