Hierarchical Qubit Maps and Hierarchical Quantum Error Correction

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 physicalto-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 ∼ 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.

Quantum Error Correction with Gauge Symmetries

“…With the long-time goal of performing quantum simulation of LGT on fault-tolerant protocols, an intriguing possibility is to tailor general purpose error correction schemes to best exploit the structural properties of these theories in order to reduce the resource requirements for early explorations (see e.g. [18] for a recent attempt in this direction using the surface code). The physical intuition behind the approach followed in this work is that error correcting codes can be seen as artificial gauge theories where the logical Hilbert space is determined by states that satisfy a suitable local symmetry.…”

Real-time dynamics of Plaquette Models using NISQ Hardware

“…Schemes for addressing depolarising errors have been investigated in 50 , and readout errors in [51][52][53] . Proposals of correcting depolarizing noise in a hierarchical fashion in quantum circuits depending on whether they contribute to the UV or IR physics have been put forward in 54 , and would allow targeted improvements in scientific applications in appropriate energy windows.…”