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
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 systematic, measurement-induced irreversibility in quantum circuits on superconducting processors (ibm_kingston and ibm_marrakesh). Using molecular hydrogen (H2, STO-3G basis) as a minimal quantum-chemical model, we prepare ground states at five bond distances R = 0.735–3.0 Å spanning equilibrium to the dissociation limit, and implement time-reversal protocols (U → Mmid-circuit measurements → U†) in both single-qubit and two-qubit entangled configurations. The single-qubit protocol yields a fidelity deficit ΔF that saturates at M = 1 in quantitative agreement with the standard quantum-mechanical projection postulate (ΔF = sin2θ/2, R2 = 0.9997), serving as a control. The two-qubit entangled protocol yields a ΔF that grows linearly with M, with a per-measurement slope a ≈ 0.012 ± 0.002 that is independent of R (CV = 16.2% across 10 data points on two backends). The single- versus two-qubit contrast directly demonstrates that entanglement is a necessary condition for M-dependent accumulation of measurement-induced irreversibility. Independent generic-circuit experiments confirm that the effect is independent of free-evolution time T and reproduces across backends. All tested standard noise mechanisms fail to account simultaneously for these observations; the theoretical implications are discussed. Running title: Measurement-Induced Irreversibility in H2 Circuits Keywords: mid-circuit measurement; measurement-induced irreversibility; H2 dissociation; entanglement; variational quantum eigensolver; superconducting quantum processor
Abstract Complex-Time (CT) theory posits that physical time is not exhausted by a single real parameter t, but includes an internal rotation phase φ such that the time coordinate is τ = t + iφ. In this ontology, φ is not a mere mathematical artifact of complex amplitudes: it is a physical degree of freedom that mediates a rotation between two logically distinct time aspects—future-pending (fp) time that retains unrealized alternatives, and past-fixed (pf) time that corresponds to realized events and stable records. Dynamic quantum circuits with mid-circuit measurement (MCM) are an unusually direct laboratory for CT because they contain repeated, addressable fp→pf conversion events *inside a single circuit*.Here we analyze IBM superconducting quantum-processor data and show that the target-qubit equatorial coherence z ≡ ⟨σx⟩ + i⟨σy⟩ undergoes a deterministic complex rotation whose angle is set primarily by the number M of spectator mid-circuit measurements. In Dataset A (4096 shots; 5 repeats), the complex ratio w(M) ≡ z_MEAS(M)/z_DELAY(M) displays an event-additive phase shift Δθ_eff(M) = arg w(M) that grows from ≈ 0 at M = 0–1 to Δθ_eff(M=8) ≈ 2.279 rad, with an average increment of δ ≈ 0.323 rad per added measurement. In Dataset B (1024 shots), inserting a virtual-Z compensation Rz(comp×M) on the target yields linear response d(Δθ_eff)/d(comp) ≈ M and demonstrates coherent controllability of the rotation.To probe whether the effect is reducible to schedule-level artifacts alone, Dataset C (CT3 Layer3) uses identical classical control-flow (if-structure) while changing only the spectator’s internal phase coherence: mode A forces |+⟩ before each mid-measurement, whereas mode B allows a |+⟩/|−⟩ mixture to accumulate. A small but systematic phase difference Δθ_AB(M) = θ_A(M) − θ_B(M) emerges (≈ 0.06 rad at M = 4–8) alongside a large change in spectator ⟨σx⟩, consistent with an operational coupling between the driven phase rotation and an internal i-phase degree of freedom.We interpret these results as operational evidence that an i-axis phase coordinate is physically actionable: it can be incremented by pf-creating events and steered by coherent frame updates. This provides a concrete, hardware-grounded route for testing CT claims about the physical reality of the imaginary-time phase. Keywords: complex time; τ = t + iφ; i-phase; past-fixed / future-pending; dynamic circuits; mid-circuit measurement; complex-plane diagnostics; virtual-Z compensation.
Abstract We introduce a complex-time framework in which the imaginary unit i is interpreted not as a formal algebraic device but as the generator of a physically meaningful temporal transformation. In this formulation, time is represented as a complex quantity T = pf + i·fp with |T| = 1, where pf (past-fixed) denotes the real component representing actualized, recorded history, and fp (future-pending) denotes the imaginary component representing undetermined possibilities. The constraint |T| = 1 expresses conservation of total temporal magnitude: as possibilities are determined (fp decreases), actualized history accumulates (pf increases). Temporal evolution is described by continuous rotation in the complex-time plane, governed by dT/dθ = iT, while a non-Hermitian extension dT/dθ = iT − γT (γ > 0) describes dissipative processes and the emergence of the arrow of time. Within this framework, quantum measurement is identified with a discrete, irreversible real-axis projection—the conversion of fp into pf—that constitutes a single step of time’s advance from the imaginary to the real axis. This identification yields three concrete predictions for quantum circuits: (i) measurement-induced effects depend on measurement count M rather than free-evolution time T (T-independence); (ii) irreversibility accumulates linearly with M in time-reversal protocols; and (iii) the elementary duration δ of one real-axis projection is implementation-dependent. The framework provides a unified structural basis for the continuity of motion, quantum uncertainty, and macroscopic irreversibility, suggesting that these phenomena arise from a single generative process: the continuous, irreversible conversion of future-pending structure into past-fixed record. Keywords: complex time; past-fixed / future-pending decomposition; quantum measurement; irreversibility; arrow of time; uncertainty principle
Complex-Time (CT) theory posits that physical time is not exhausted by a single real parameter t, but includes an internal rotation phase φ such that the time coordinate is τ = t + iφ. In this ontology, φ is not a mere mathematical artifact of complex amplitudes: it is a physical degree of freedom that mediates a rotation between two logically distinct time aspects—future-pending (fp) time that retains unrealized alternatives, and past-fixed (pf) time that corresponds to realized events and stable records. Dynamic quantum circuits with mid-circuit measurement (MCM) are an unusually direct laboratory for CT because they contain repeated, addressable fp→pf conversion events *inside a single circuit*.Here we analyze IBM superconducting quantum-processor data and show that the target-qubit equatorial coherence z ≡ ⟨σx⟩ + i⟨σy⟩ undergoes a deterministic complex rotation whose angle is set primarily by the number M of spectator mid-circuit measurements. In Dataset A (4096 shots; 5 repeats), the complex ratio w(M) ≡ z_MEAS(M)/z_DELAY(M) displays an event-additive phase shift Δθ_eff(M) = arg w(M) that grows from ≈ 0 at M = 0–1 to Δθ_eff(M=8) ≈ 2.279 rad, with an average increment of δ ≈ 0.323 rad per added measurement. In Dataset B (1024 shots), inserting a virtual-Z compensation Rz(comp×M) on the target yields linear response d(Δθ_eff)/d(comp) ≈ M and demonstrates coherent controllability of the rotation.To probe whether the effect is reducible to schedule-level artifacts alone, Dataset C (CT3 Layer3) uses identical classical control-flow (if-structure) while changing only the spectator’s internal phase coherence: mode A forces |+⟩ before each mid-measurement, whereas mode B allows a |+⟩/|−⟩ mixture to accumulate. A small but systematic phase difference Δθ_AB(M) = θ_A(M) − θ_B(M) emerges (≈ 0.06 rad at M = 4–8) alongside a large change in spectator ⟨σx⟩, consistent with an operational coupling between the driven phase rotation and an internal i-phase degree of freedom.We interpret these results as operational evidence that an i-axis phase coordinate is physically actionable: it can be incremented by pf-creating events and steered by coherent frame updates. This provides a concrete, hardware-grounded route for testing CT claims about the physical reality of the imaginary-time phase. Keywords: complex time; τ = t + iφ; i-phase; past-fixed / future-pending; dynamic circuits; mid-circuit measurement; complex-plane diagnostics; virtual-Z compensation.
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.
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.