Robust analog quantum simulators by quantum error-detecting codes: Part I

Achieving noise resilience is an outstanding challenge in Hamiltonian-based quantum computation. To this end, energy-gap protection provides a promising approach, where the desired quantum dynamics are encoded into the ground space of a penalty Hamiltonian that suppresses unwanted noise processes. However, existing approaches either explicitly require high-weight penalty terms that are not directly accessible in current hardware, or utilize non-commuting 2-local Hamiltonians, which typically leads to an exponentially small energy gap. In this work, we introduce a general recipe for designing error-resilient Hamiltonian simulations, utilizing an excited encoding subspace stabilized by solely 2-local commuting Hamiltonians.

Part I of this talk introduces the general framework based on quantum error-detecting codes. We also describe how our approach overcomes a no-go theorem previously derived for ground-space encoding that prevents noise suppression schemes with solely 2-loca commuting Hamiltonians.