Hierarchical qubit maps and hierarchically implemented 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-to-logical qubits can be systematically structured. For concreteness, we estimate HI-QEC's impact on surface code resources in computing low-energy observables to fixed precision, finding up to approximately 60% reductions in qubit requirements plausible in early error-corrected simulations. Hierarchical qubit maps are also possible without error correction in qubit and qudit systems where fidelities are nonuniform, either unintentionally or by design. Hierarchical optimizations are another element in the codesign process of quantum computations, including quantum simulations for nuclear and particle physics.

Automated summary

Hierarchically implemented quantum error correction (HI-QEC) optimizes the fidelities of logical qubits to enhance the capabilities of quantum devices in scientific applications. It can reduce resource requirements for computing low-energy observables and impact the co-design process of quantum computations.