Observable-Conditioned Backaction in Dynamic Circuits: A Higher-Order Context-Conditioned Kernel for Local Dynamics

Abstract

Mid-circuit measurements are essential primitives for dynamic circuits and quantum error correction, yet characterizing their induced disturbance on spectator qubits remains a central practical problem. Device-level benchmarking often compresses this disturbance into low-order proxy metrics such as $T_1$, $T_2$, readout assignment error, and pairwise crosstalk. We argue that these proxies can be operationally incomplete for multiscale dynamic circuits. We introduce a higher-order context-conditioned kernel, $Γ_{\mathrm{eff}}[Y,O] = Γ_{\mathrm{loc}}[O] + Γ_{\mathrm{proxy}}[O] + Γ_{\mathrm{rel}}[Y,O]$, where $Y$ is a global context label and $O$ a local observable. The term $Γ_{\mathrm{rel}}[Y,O]$ is a phenomenological compression ansatz isolating residual context dependence unexplained by standard proxies. To avoid impossibility issues of quantum partial-information decompositions on non-commuting algebras, the Möbius weights entering this ansatz are evaluated operationally on classical measurement outcomes. We present evidence in three steps. First, earlier GHZ-versus-clock hardware results motivate an observable-class split. Second, we present dynamical evidence using the A6 synthetic hardware harness. A6 injects a pure higher-order context dependence via a programmed conditional interaction. Because the $(C_0,C_1,C_2)$ parity context is invisible to singles and pairs by construction, standard low-order diagnostics are fundamentally blind to the source of the probe's disturbance. Third, we demonstrate coherent controllability through the A6.2 quantum-eraser experiment. Programmable MARK interactions suppress unconditional fringes while eraser-basis conditioning restores them, consistent with complementarity bounds. These results validate a context-conditioned description of backaction over proxy-only null models.

Figures (3)

• Figure 1: Updated conceptual geometry of the paper. The higher-order structure lives in the context$Y$, not in the size of the local probe itself. In A6, the parity label on $(C_0,C_1,C_2)$ is pairwise matched by construction, while the measured probe is the local witness $E_{X,\mathrm{mean}}$ on $(A,B)$. In A6.2, a separate marker $M$ is used to study programmable which-path tagging and conditional interference restoration.
• Figure 2: A6v23 hardware evidence for context-dependent local dynamics on ibm_boston. Panel (a) shows the lane-balanced parity effect $\Delta E=E_{\mathrm{even}}-E_{\mathrm{odd}}$ in the XX basis as a function of the programmed interaction angle $\theta$. The data (blue points with SEM error bars across 8 lanes) are overlaid with a theoretical fit $\Delta E(\theta) = a(1-\cos\theta)+b$ (red dashed line), yielding an $R^2=1.000$ and a reduced $\chi^2 = 0.249$, confirming the exact expected functional form of the synthetic harness. Panel (b) resolves the corresponding lane-balanced branch values $E_{\mathrm{even}}$ and $E_{\mathrm{odd}}$. Panel (c) shows the passive controls PASSIVE1 and PASSIVE2; while PASSIVE1 shows a statistically resolvable drift, the SEM error bars strictly bound the magnitude to the order of $\sim 10^{-3}$, which is completely dwarfed by the active signal, proving the compute/uncompute scaffold alone does not induce the massive context-dependent effect. Panel (d) shows the CTXONLY lane-quality screen, confirming the cleanliness of the pairwise-matched parity context.SramekA6Context2026
• Figure 3: A6.2 MARK/ERASE results, tag diagnostics, and complementarity bounds on ibm_boston. Panel (a) plots the probe-fringe magnitude $V(\lambda)$ versus marker strength $\lambda$, showing strong suppression of the unconditional marginal (MARK) while the conditional average (ERASE) remains large. The LOCAL curve is a hardware reference (not an optimized local-dephasing null). Panel (b) tracks the global-tag observable $C_3(\lambda)=\langle XXX\rangle$ for the MARK branch and a local-matched reference as an auxiliary diagnostic of the applied marker interaction. Panel (c) resolves the conditional visibilities by eraser-basis outcome ($m=0, 1$). Panel (d) directly tests the Englert--Greenberger--Yasin complementarity bound; as marker distinguishability $\mathcal{D}$ (red squares) increases, unconditional visibility $V$ (blue circles) drops, maintaining the structural bound $V^2 + \mathcal{D}^2 \le 1$ (green triangles) across the sweep. The supported claim is the textbook quantum-eraser one: unconditional interference is exported into system--marker correlations by MARK, while eraser-basis conditioning restores large fringes.Scully1982Kim2000SramekA62Erasure2026Englert1996