Phase accumulation during idle intervals in superconducting qubits is well known, and virtual Z (Rz) gates are routinely used for correction. However, the distinction between unconditional (static) and conditional (timing-aware) phase correction has received limited experimental attention. Here we present experimental results on IBM Quantum superconducting processors showing that unconditional phase correction can systematically degrade fidelity in timing-misaligned regimes, specifically for Bell-type superposition under ZZ-dominated evolution. On ibm_kingston (Heron r2), unconditional correction yields GPS = -0.201 ± 0.007 (z = -27.9σ) while conditional MCM feedforward achieves GPS = +0.345 ± 0.007 (z = +47.96σ), a gap of ΔGPS = +0.546. GPS = F_ff - F_ref isolates the incremental effect of correction by removing baseline decoherence. This result does not invalidate static phase correction globally; the effect emerges only under timing-misaligned stochastic phase regimes. The physical mechanism is derived from H = ξ_ZZ|11⟩⟨11|: applying Rz(-φ*) unconditionally to one qubit of a Bell pair adds φ* to the relative phase rather than canceling it, doubling the phase error at τ*. Density matrix simulation with Kraus operators confirms GPS_static = -0.39 (model). These results demonstrate that phase correction effectiveness is strongly regime-dependent, and identify conditional phase correction as a synchronization primitive between stochastic phase evolution and control application. AI assistance (Claude, Anthropic) disclosed.Data: IBM Quantum Cloud, 2026-03-22, job d6vqgtov5rlc73f5a7kg.Code: https://github.com/okudat9/Quantum-6502
Phase accumulation during idle intervals in superconducting qubits is well known, and virtual Z (Rz) gates are routinely used for correction. However, the distinction between unconditional (static) and conditional (timing-aware) phase correction has received limited experimental attention. Here we present experimental results on IBM Quantum superconducting processors showing that unconditional phase correction can systematically degrade fidelity in timing-misaligned regimes, specifically for Bell-type superposition under ZZ-dominated evolution. On ibm_kingston (Heron r2), unconditional correction yields GPS = -0.201 ± 0.007 (z = -27.9σ) while conditional MCM feedforward achieves GPS = +0.345 ± 0.007 (z = +47.96σ), a gap of ΔGPS = +0.546. GPS = F_ff - F_ref isolates the incremental effect of correction by removing baseline decoherence. This result does not invalidate static phase correction globally; the effect emerges only under timing-misaligned stochastic phase regimes. The physical mechanism is derived from H = ξ_ZZ|11⟩⟨11|: applying Rz(-φ*) unconditionally to one qubit of a Bell pair adds φ* to the relative phase rather than canceling it, doubling the phase error at τ*. Density matrix simulation with Kraus operators confirms GPS_static = -0.39 (model). These results demonstrate that phase correction effectiveness is strongly regime-dependent, and identify conditional phase correction as a synchronization primitive between stochastic phase evolution and control application. AI assistance (Claude, Anthropic) disclosed.Data: IBM Quantum Cloud, 2026-03-22, job d6vqgtov5rlc73f5a7kg.Code: https://github.com/okudat9/Quantum-6502
We derive analytically that the optimal feedforward phase for ZZ-coupling correction in superconducting qubits is given by the argument of the first circular moment of the accumulated phase distribution: φ* = arctan(S/C), where C = ⟨cos φ⟩ and S = ⟨sin φ⟩. A negative second derivative proves this is always a maximum. We measure GPS = P_ff − P_ref on IBM Heron r2 processors (ibm_kingston, ibm_marrakesh; five qubit pairs) and IQM Garnet (Crystal 20). A robust empirical invariant is observed: π ν_ZZ τ* ≈ const ≈ 0.873 rad, confirmed across five independent IBM configurations (π ν_ZZ τ* = 0.873 ± 0.001 rad). A preliminary τ-scan on IQM Garnet shows a GPS sign reversal consistent with a zero-crossing near φ = 0.873 rad. The result establishes a robust empirical invariant within superconducting architectures, enabling feedforward calibration without full phase tomography. Related work:- EEDT Protocol: https://doi.org/10.5281/zenodo.19029431- Bell Decay Clock: https://doi.org/10.5281/zenodo.19367565- Software (Quantum-6502): https://doi.org/10.5281/zenodo.19160835
Abstract Dynamic circuits with mid-circuit measurement (MCM) and classical feed-forward are essential building blocks for quantum error correction and adaptive quantum protocols. However, in superconducting quantum processors the readout process can induce coherent crosstalk on non-measured (spectator) qubits through the readout resonator, residual photons, and other hardware pathways, leading to deterministic phase kicks (effective Z rotations) that accumulate with the number of MCM events. In this work we present a minimal, reproducible two-qubit Ramsey diagnostic to quantify the spectator-induced phase shift as a function of the number of inserted mid-circuit measurements M, and we demonstrate that a simple virtual-Z (frame) compensation proportional to M can mitigate the resulting phase error on real hardware. In a high-SNR dataset archived on Zenodo (T = 40 μs, 4096 shots per circuit), the effective phase difference Δθeff(M) = θMEAS(M) - θDELAY(M) shifts monotonically in the negative direction as M increases, reaching Δθeff (M=8) = -1.944 ± 0.033 rad. While the contrast r decreases mildly with M, it remains relatively high (r ≈ 0.84 at M = 8), consistent with the effect appearing predominantly as a coherent phase rotation. To mitigate the error, we insert a virtual-Z rotation on the target qubit of the form Rz (comp × M) in the MEAS condition and scan the compensation coefficient comp (rad per measurement). In a MAP dataset (ibm_marrakesh, shots = 512, repeats = 1, M ∈ {0,1,2,4,8}, comp ∈ {-0.02,-0.01,0,+0.01,+0.02}), the RMS of the baseline-referenced phase error Δθeff(M) for M>0 is minimized at comp = -0.01, decreasing from 0.1393 rad (baseline) to 0.0601 rad. Finally, we implement a low-cost calibration probe (M = {0,8}) scanning five compensation settings comp ∈ {-0.02,-0.01,0,+0.01,+0.02} (1024 shots per circuit, repeats = 2) and estimate a session-dependent coefficient compopt ≈ -0.013 rad/measurement from a linear fit of Δθeff(M=8) versus comp. A same-session production sweep using comp = -0.01453 rad/measurement (close to compopt) shows a reduced residual phase error, supporting a practical probe → production workflow for dynamic-circuit execution. All analysis scripts and summary data are made publicly available to support independent reproduction of the reported phase metrics and figures.
Dynamic circuits with mid-circuit measurement (MCM) and classical feed-forward are essential building blocks for quantum error correction and adaptive quantum protocols. However, in superconducting quantum processors the readout process can induce coherent crosstalk on non-measured (spectator) qubits through the readout resonator, residual photons, and other hardware pathways, leading to deterministic phase kicks (effective Z rotations) that accumulate with the number of MCM events. In this work we present a minimal, reproducible two-qubit Ramsey diagnostic to quantify the spectator-induced phase shift as a function of the number of inserted mid-circuit measurements M, and we demonstrate that a simple virtual-Z (frame) compensation proportional to M can mitigate the resulting phase error on real hardware. In a high-SNR dataset archived on Zenodo (T = 40 μs, 4096 shots per circuit), the effective phase difference Δθeff(M) = θMEAS(M) - θDELAY(M) shifts monotonically in the negative direction as M increases, reaching Δθeff (M=8) = -1.944 ± 0.033 rad. While the contrast r decreases mildly with M, it remains relatively high (r ≈ 0.84 at M = 8), consistent with the effect appearing predominantly as a coherent phase rotation. To mitigate the error, we insert a virtual-Z rotation on the target qubit of the form Rz (comp × M) in the MEAS condition and scan the compensation coefficient comp (rad per measurement). In a MAP dataset (ibm_marrakesh, shots = 512, repeats = 1, M ∈ {0,1,2,4,8}, comp ∈ {-0.02,-0.01,0,+0.01,+0.02}), the RMS of the baseline-referenced phase error DθCT(M) for M>0 is reduced from 0.1393 rad (baseline) to 0.0601 rad at comp = -0.01, demonstrating effective error reduction with a single-parameter circuit-level correction. Finally, using a pay-as-you-go execution environment we run a low-cost “calibration probe” (M = {0,8}, three comp points, 32 circuits total) and obtain compopt ≈ +0.0088 rad/measurement from a three-point linear fit. This supports a practical two-stage workflow in which a short probe estimates the session-dependent compensation coefficient, followed by same-session production runs with the calibrated virtual-Z correction.
Abstract Dynamic circuits with mid-circuit measurement (MCM) and classical feed-forward are essential building blocks for quantum error correction and adaptive quantum protocols. However, in superconducting quantum processors the readout process can induce coherent crosstalk on non-measured (spectator) qubits through the readout resonator, residual photons, and other hardware pathways, leading to deterministic phase kicks (effective Z rotations) that accumulate with the number of MCM events. In this work we present a minimal, reproducible two-qubit Ramsey diagnostic to quantify the spectator-induced phase shift as a function of the number of inserted mid-circuit measurements M, and we demonstrate that a simple virtual-Z (frame) compensation proportional to M can mitigate the resulting phase error on real hardware. In a high-SNR dataset archived on Zenodo (T = 40 μs, 4096 shots per circuit), the effective phase difference Δθeff(M) = θMEAS(M) - θDELAY(M) shifts monotonically in the negative direction as M increases, reaching Δθeff (M=8) = -1.944 ± 0.033 rad. While the contrast r decreases mildly with M, it remains relatively high (r ≈ 0.84 at M = 8), consistent with the effect appearing predominantly as a coherent phase rotation. To mitigate the error, we insert a virtual-Z rotation on the target qubit of the form Rz (comp × M) in the MEAS condition and scan the compensation coefficient comp (rad per measurement). In a MAP dataset (ibm_marrakesh, shots = 512, repeats = 1, M ∈ {0,1,2,4,8}, comp ∈ {-0.02,-0.01,0,+0.01,+0.02}), the RMS of the baseline-referenced phase error Δθeff(M) for M>0 is minimized at comp = -0.01, decreasing from 0.1393 rad (baseline) to 0.0601 rad. Finally, we implement a low-cost calibration probe (M = {0,8}) scanning five compensation settings comp ∈{-0.02,-0.01,0,+0.01,+0.02} (1024 shots per circuit, repeats = 2) and estimate a session-dependent coefficient compopt ≈ -0.013 rad/measurement from a linear fit of Δθeff(M=8) versus comp. A same-session production sweep using comp = -0.01453 rad/measurement (close to compopt) shows a reduced residual phase error, supporting a practical probe → production workflow for dynamic-circuit execution.
ABSTRACT We report a systematic, measurement-induced irreversibility in superconducting quantum circuits that is not accounted for by any tested conventional noise model. Using IBM Quantum processors (ibm_marrakesh and ibm_kingston), we implement a time-reversal protocol in which mid-circuit measurements are inserted between a unitary U and its inverse U†. The fidelity deficit ΔF = F(dummy) − F(meas) grows linearly with measurement count M, reaching ΔF = 0.235 (22.2σ) and ΔF = 0.164 (24.0σ) at M = 8 on the two processors. Three independent controls rule out conventional noise sources: (1) T-independence of the spectator-qubit phase shift (dA ≈ +0.10 at T = 40 and 80 μs) eliminates crosstalk and leakage; (2) a non-Markovian symmetry test (spread = 1.5σ) eliminates decoherence asymmetry; and (3) cross-backend reproducibility of the linear ΔF(M) scaling eliminates hardware-specific measurement noise. The three observations share a common structural feature: the irreversibility is tied to discrete measurement events rather than free-evolution time, accumulates proportionally to their count, and reproduces across independent hardware. We report these observations as experimental evidence consistent with the interpretation that the imaginary unit i in the Schrödinger equation reflects a physically real internal structure of time, and that quantum measurement drives an irreversible projection of that structure onto the real axis. This interpretation is developed from first principles in Sec. II and connected to an existing theoretical framework [13] in Sec. VI. Keywordsquantum computing, mid-circuit measurement, complex time, irreversibility, IBM Quantum, time-reversal protocol
We report a statistically significant anomaly in quantum coherence measurements from 580 IBM Quantum jobs: Bell state fidelity varies periodically with job execution time modulo a characteristic period τ0 = 46 μs. Jobs executed at 'τ-aligned' phases show 1.81x higher mean fidelity than anti-aligned phases (p < 10^-14, Cohen's d = 1.65). This effect cannot be explained by standard Markovian decoherence. We present a phenomenological Lagrangian incorporating a non-Markovian memory field that predicts F(T) = F0 e^(-Γ T) (1 + ε cos(ω_τ T - θ_lock)), consistent with observations. Bayesian model comparison yields strong evidence (BF = 28) for the oscillatory model over exponential decay.