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11 Dec 2024

Quantum Fault Tolerance Threshold Plots

Title slide: Quantum fault tolerance thresholds -- your simple guide to interpreting threshold plots, with a sample plot

Three important ideas: 1. Hardware imperfections, 2. Logical qubit errors, 3. Logical qubit size

Hardware imperfections: photos illustrating depolarizing noise, leakage, scattering, and optical loss in qubits

Threshold plot with labeled x-axis: any hardware imperfection can be put on the x-axis

Threshold plot with labeled y-axis: the effective error rate for logical qubits goes on the y-axis

Logical qubit errors: physical qubit errors propagate to the logical level, and the logical error rate is what matters

Logical qubit size: larger logical qubits use more physical qubits, and different sizes have different performance

Threshold plot with qubit grid diagrams showing code sizes 3, 5, and 7 each produce a distinct curve

Question slide: So why is it called a threshold plot?

The fault tolerance threshold: the crossing point where all code-size curves meet on the plot

Above threshold: increasing logical qubit size makes the error rate worse (size up, logical errors up)

Below threshold: increasing logical qubit size reduces errors -- that's where the magic happens

Key takeaway: the fault tolerance threshold is where a quantum system can correct errors faster than they occur

Plaquette makes threshold plots easy: diagram showing a qubit lattice processed by Plaquette into a threshold plot

Learn more about Plaquette: contact QC Design on LinkedIn or at qc.design

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