Session 08 - Syndrome Extraction and Hardware Constraints

Status: planned.

Prerequisites And Diagnostics

Ask:

1. What is a stabilizer measurement circuit for one check?
2. In a surface code, why are checks easy to measure locally?
3. What changes when a Tanner check is not geometrically local?
4. What does bisection width measure on the hardware side?

Lesson Scope

• Stabilizer measurement circuit for a concrete CSS check.
• Hardware graph as the native two-qubit gate constraint.
• SWAP-only routing as the minimal compilation model.
• Congestion as cross-cut resource overload.
• Dilation as path-length overhead.
• CD(T_n,G) as the product-style routing functional.
• Static 2D Omega(sqrt(n)) lower bound and what model it has already been proved in.
• Space-depth tradeoff: why extra physical qubits can buy depth.

Source Anchors

• cross-cut-gate-service-lower-bounds-stabilizer-cut-rank.md
• stabilizer-cut-rank-functional.md
• expansion-cut-to-syndrome-depth.md
• 2d-local-clifford-syndrome-space-depth-tradeoff.md
• 2d-syndrome-depth-from-code-parameters.md
• weighted-separator-function-to-syndrome-depth.md

Active Recall

• Draw a one-check measurement circuit and identify where hardware nonlocality appears.
• Explain congestion and dilation using one nonlocal Tanner edge routed on a grid.
• State what the current static 2D theorem proves and what it does not prove about the full CD conjecture.

Next-Step Handoff

After this session, the learner should be ready to read the Conjecture 3 map as a chain of reductions rather than as a list of unfamiliar nodes.