Hierarchical Qubit Maps and Hierarchical Quantum Error Correction

TL;DR

This paper introduces hierarchical quantum error correction (HI-QEC) and hierarchical qubit maps, which optimize logical qubit fidelities and reduce resource requirements in quantum simulations, especially for scientific applications.

Contribution

It presents a novel hierarchical approach to quantum error correction and qubit mapping that enhances efficiency and fidelity in quantum computing systems.

Findings

Up to 60% reduction in qubit requirements for certain simulations

Hierarchical qubit maps enable non-uniform fidelities without error correction

Potential applications in nuclear and particle physics simulations

Abstract

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 $\sim 60\%$ 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 non-uniform, either unintentionally or by design. Hierarchical optimizations are another element in the co-design process of quantum simulations for nuclear and particle physics.