Hierarchical Qubit Maps and Hierarchical Quantum Error Correction

We consider hierarchically implemented quantum error correction (HI-QEC) in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications. By employing qubit representations that propagate hierarchies in simulated systems to those in logical qubit noise sensitivities, heterogeneity in the distribution of physical qubits among logical qubits can be systematically structured. For concreteness, we estimate HI-QEC’s impact on surface code resources in computing low-energy observables to a fixed precision, finding up to ~60% reductions in qubit requirements possible in early error corrected simulations. This heterogeneous distribution of physical-to-logical qubits is identified as another element that can be optimized in the co-design process of quantum simulations of Standard Model physics.