Hierarchical Qubit Maps and Hierarchical Quantum Error Correction
- URL: http://arxiv.org/abs/2109.01953v1
- Date: Sun, 5 Sep 2021 00:40:02 GMT
- Title: Hierarchical Qubit Maps and Hierarchical Quantum Error Correction
- Authors: Natalie Klco and Martin J. Savage
- Abstract summary: We consider hierarchically implemented quantum error correction (HI-QEC)
We estimate HI-QEC's impact on surface code resources in computing low-energy observables to fixed precision.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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