Reaction depth of two anticommuting π/8 PPRs parallelized via a bridge qubit in the active-volume architecture

Reaction depth of two anticommuting π/8 PPRs parallelized via a bridge qubit in the active-volume architecture Ask Question Asked today Modified today Viewed 6 times 1 In the active volume architecture (https://arxiv.org/pdf/2211.15465) (Litinski 2022), reaction depth is defined as the number of sequential reactive measurement layers, where a layer is added whenever the pending Pauli correction from a previous reactive measurement anticommutes with the next measurement's basis. I have two anticommuting π/8 PPRs acting on q1 and q2: ( X 1 ⊗ Z 2 )π/8and( X 1 ⊗ X 2 )π/8 ( 𝑋 1 ⊗ 𝑍 2 ) 𝜋 / 8 and ( 𝑋 1 ⊗ 𝑋 2 ) 𝜋 / 8 I want to parallelize them so they fit into a single logical cycle. Since both PPRs touch q1, true parallelism requires a bridge qubit: I use a Bell pair (|00⟩+|11⟩)/ 2 – √ ( | 00 ⟩ + | 11 ⟩ ) / 2 , with one half acting as a bridge to teleport q1's state to a second location so the two PPMs can be set up concurrently. Each PPR is implemented as a joint Pauli product measurement (PPM) with an auxiliary magic state, followed by a reactive cleanup measurement on the stale magic state. My confusion: By the standard Litinski rule, two anticommuting PPRs in sequence give reaction depth = 2 (each PPR's PPM is in its own reactive layer because the basis depends on the previous outcome). But I'm unsure how the bridge-qubit Bell measurement affects this: Naive view: the Bell measurement has a fixed basis (XX, ZZ), so it doesn't add a reactive layer on its own — reaction depth stays at 2. Alternative view: the pending X-type Pauli correction from PPR_1 anticommutes with the XX component of the Bell measurement basis, so the Bell measurement is itself reactive on PPR_1's outcome — reaction depth becomes 3. Question: What is the correct reaction depth of this parallelized PPR-bridge-PPR construction — 2 or 3? And what is the principled criterion? error-correctionmeasurement-based-qc Share Improve this question Follow asked 1 hour ago next dimension 112 2 bronze badges New contributor Add a comment Know someone who can answer? Share a link to this question via email, Twitter, or Facebook. Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions error-correctionmeasurement-based-qc See similar questions with these tags. 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