Qubit coherence decay down to threshold: influence of substrate dimensions

TL;DR

This paper investigates how reducing substrate dimensions affects the initial dephasing of solid-state qubits, aiming to maintain coherence above fault-tolerance thresholds crucial for quantum error correction.

Contribution

It provides explicit coherence dynamics in the independent-boson model and identifies minimal QEC rates considering substrate geometry, temperature, and coupling strength.

Findings

Reduced substrate dimensions can improve qubit coherence times.

Explicit coherence decay expressions enable systematic analysis.

Optimal substrate design enhances fault-tolerant quantum computing.

Abstract

Keeping single-qubit quantum coherence above some threshold value not far below unity is a prerequisite for fault-tolerant quantum error correction (QEC). We study the initial dephasing of solid-state qubits in the independent-boson model, which describes well recent experiments on quantum dot (QD) excitons both in bulk and in substrates of reduced geometry such as nanotubes. Using explicit expressions for the exact coherence dynamics, a minimal QEC rate is identified in terms of the error threshold, temperature, and qubit-environment coupling strength. This allows us to systematically study the benefit of a current trend towards substrates with reduced dimensions.