Q-Loop: Deterministic Coherence Scaling Without Feedback in NISQ Systems We present the Q-Loop protocol, a deterministic modulation scheme that achieves coherence scaling without measurement-based feedback in noisy intermediate-scale quantum (NISQ) systems. Q-Loop applies a folded, periodic control waveform to collective parity operators, producing destructive interference with dominant decoherence channels. Unlike adaptive protocols such as QEC-C, which require rapid measurement and real-time gain updates, Q-Loop is fully open-loop and relies only on deterministic waveforms implementable with existing arbitrary waveform generators or global control fields. Using filter-function analysis and numerical simulations across superconducting, ion-trap, and photonic models, we show that Q-Loop realizes an exponential scaling of an effective control amplitude beta(n) ~ A * exp(alpha n), with alpha comparable to that obtained in adaptive-feedback schemes, while requiring no ancilla qubits and no real-time classical processing. The protocol reshapes 1/f-type noise into a structured spectrum with suppressed mid-band power and yields substantial fidelity improvements and effective fault-tolerance threshold elevation when used as a preprocessing layer for standard error-correcting codes. This establishes Q-Loop as a simple, hardware-compatible route to deterministic coherence enhancement in current NISQ hardware.
Q-Loop: Deterministic Coherence Scaling Without Feedback in NISQ Systems We present the Q-Loop protocol, a deterministic modulation scheme that achieves coherence scaling without measurement-based feedback in noisy intermediate-scale quantum (NISQ) systems. Q-Loop applies a folded, periodic control waveform to collective parity operators, producing destructive interference with dominant decoherence channels. Unlike adaptive protocols such as QEC-C, which require rapid measurement and real-time gain updates, Q-Loop is fully open-loop and relies only on deterministic waveforms implementable with existing arbitrary waveform generators or global control fields. Using filter-function analysis and numerical simulations across superconducting, ion-trap, and photonic models, we show that Q-Loop realizes an exponential scaling of an effective control amplitude beta(n) ~ A * exp(alpha n), with alpha comparable to that obtained in adaptive-feedback schemes, while requiring no ancilla qubits and no real-time classical processing. The protocol reshapes 1/f-type noise into a structured spectrum with suppressed mid-band power and yields substantial fidelity improvements and effective fault-tolerance threshold elevation when used as a preprocessing layer for standard error-correcting codes. This establishes Q-Loop as a simple, hardware-compatible route to deterministic coherence enhancement in current NISQ hardware.
QEC-C 2: Adaptive-Scaling Quantum Error Correction for NISQ Systems QEC-C 2 is a low-power quantum error correction framework tailored to noisy intermediate-scale quantum (NISQ) devices, in which the strength of error protection adapts dynamically to the observed noise environment. Instead of operating at a fixed code distance and fixed-cycle syndrome extraction rate, QEC-C 2 maintains an online estimate of effective noise strength and modulates the frequency and intensity of checks according to an exponential gain law beta_star(n) = A * exp(alpha n). This adaptive scaling allows near-exponential improvements in logical coherence time while keeping ancilla counts, measurement load, and classical processing within NISQ-compatible limits. Using filter-function analysis and Monte Carlo error-tracking with mixed local, correlated, and collective noise, we show that QEC-C 2 can raise effective fault-tolerance thresholds by factors of order five to six relative to unoptimized repetition-code baselines. The scheme interpolates between dynamical decoupling and full fault-tolerant quantum error correction, providing a practical pathway for stepwise protection on current hardware and a natural benchmark for comparing deterministic open-loop protocols such as Q-Loop.
We study a deterministic modulation protocol, Q-Loop, that replaces multi-axis, measurementdependent control with a single scalar waveform and is implementable as an open-loop schedule on current NISQ hardware. Building on earlier work where Q-Loop was shown to reduce both the dephasing functional χ(τ ) and the minimum control amplitude required to stabilize few-qubit GHZ states under classical 1/f noise, we revisit the protocol with a more conservative analytic treatment and a quantitative comparison to alternative empirical scaling forms for modest system sizes (n = 2–8 qubits). In a pure-dephasing (or effectively commuting) regime we derive the filter-function structure of an idealized Q-Loop waveform and show that it produces a discrete comb of sidebands with tunable low-frequency suppression relative to free evolution and standard Carr–Purcell (CP) sequences. For more general noise channels the scalar filter-function picture is used as a qualitative guide, and quantitative statements are obtained from stochastic-Hamiltonian simulations with classical 1/f γ noise. Using QuTiP-based simulations of Schrödinger dynamics with time-dependent Hamiltonians and classical 1/f γ local and correlated noise, we compute the minimum control amplitude β ∗ (n) needed to maintain a fixed target fidelity as a function of system size n for n = 2–8 qubits. Over this range the ensemble-averaged β ∗ (n) data are empirically well described by β ∗ (n) ≈ Aeαn with α ≃ 0.23–0.25, while quadratic and power-law forms yield systematically higher residuals and poorer goodness-of-fit metrics (including R2 , RMSE, and Bayesian information criterion), with BIC values for the exponential model typically 10–15 units lower than for polynomial alternatives. We emphasize that this exponential behaviour is an empirical description over a finite range, not an asymptotic law. We further map the Q-Loop-induced reduction in decoherence onto a toy physical error rate p and propagate this into a repetition-code capacity model. For a fixed phenomenological mapping, Q-Loop preprocessing yields an apparent 5–6× elevation of toy thresholds relative to an amplitudematched CP baseline, although these numbers are not intended as accurate thresholds for any specific fault-tolerant architecture. Finally, we discuss deployment on superconducting, trapped-ion, and photonic platforms using a Python-based waveform generator with PyVISA AWG integration, and outline how platform-specific noise spectra could be used to tune Q-Loop parameters in situ
Quantum error correction (QEC) faces a significant challenge in realistic noisy intermediate-scale quantum (NISQ) devices: correlated decoherence. Building upon the foundational QEC-C protocol, we introduce QEC-C II, a scalable framework that delivers robust fault tolerance against spatially and temporally correlated noise. By integrating decoherence-free subspace (DFS) principles and correlation-aware adaptive feedback, QEC-C II achieves exponential error suppression in simulation under correlated noise models, with fewer physical qubits than typical topological baselines for the same target error in our benchmarks. The protocol leverages an enhanced scaling law, β(n) = 0.788 e 0.360n , and efficiently suppresses noise with minimal computational overhead. We validate QEC-C II on 28-qubit GHZ states, extend it to 56-qubit subspaces, and conduct 84-qubit stress-test simulations under correlated noise models. The results demonstrate sustained fidelities exceeding 99.99 % in simulations under realistic dephasing, amplitude-damping, burst-error, and correlated decoherence scenarios, with rapid convergence (typically ≤ 2 iterations in our simulations). QEC-C II significantly reduces both resource and control complexity, simplifying hardware integration and improving performance with increasing system size. This work provides a practical pathway toward resource-efficient fault tolerance in quantum processors operating in real-world correlated environments.
Abstract: Measurement-based feedback control is a foundational tool in quantum engineering, quantum thermodynamics, and quantum information processing. While feedback is known to stabilize small quantum systems, its scalability to larger systems remains poorly characterized. In this work, we identify a fundamental measurement–coherence scaling barrier for full-state feedback control in open quantum systems. We show that for generic n-qubit states the measurement resources required for real-time state reconstruction scale exponentially with system size, while the available coherence window remains finite. As a result, beyond a system-size threshold ncrit, the time required to acquire sufficient state information exceeds the decoherence time, preventing closure of the feedback loop. We derive an explicit closed-form expression for ncrit in terms of three hardware parameters—coherence time, single-shot measurement time, and reconstruction accuracy—and show that under realistic device conditions this threshold is typically in the range 2–7 qubits. This provides a quantitative information-theoretic explanation for why full- state tomographic feedback has only been demonstrated at very small scales. Importantly, the barrier is architectural rather than fundamental: syndrome-based control, stabilizer tracking, and measurement-efficient protocols such as classical shadows evade it by exploiting structure and extracting only operationally relevant information. Our results formalize a design principle for scalable quantum control and clarify the operational boundaries of feedback in noisy intermediate-scale quantum (NISQ) devices.
Abstract: The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices remains fundamentally limited by stochastic decoherence, which traditional passive shielding and resource-heavy quantum error correction (QEC) struggle to overcome. Here, we propose a paradigm shift from passive noise mitigation to active internal phase stabilization. By integrating the Lie-algebraic renormalization (LA-ODR) framework with a dynamic model of temporal susceptibility (χ_τ), we derive a nonlinear control law for quantum coherence. We demonstrate that decoherence can be treated as a deterministic dynamical process governed by the feedback equation dχ_τ / dt = −α · Γ_τ · χ_τ + λ · (1 − χ_τ). Our numerical simulations confirm the formation of metastable coherence plateaus, where the effective qubit lifetime is extended significantly beyond the standard Lindbladian limit (e.g., from 100 µs to 1.5 ms in transmon-based models). We further specify a hardware-ready Temporal Phase-Locked Loop (TPLL) architecture, proving that with control latencies below 500 ns, active synchronization of the temporal metric becomes feasible on modern FPGA-based controllers. This framework provides a path toward fault-tolerant quantum computing by enabling fidelity-by-design at the physical layer, potentially providing a substantial reduction in QEC overhead by maintaining high physical fidelity prior to logical encoding. Keywords nonlinear phase stabilization; temporal susceptibility χτ; Lie-observable-dependent renormalization (LA-ODR); fixed-point Lindbladian; quantum decoherence; active feedback control; temporal phase-locked loop (TPLL); NISQ devices; superconducting qubits; cold atom arrays
Quantum computers hold immense promise for solving problems intractable for classical machines, yet their practical realization is hindered by the fragility of quantum states. Quantum Error Correction (QEC) is indispensable for protecting quantum information from environmental noise and operational imperfections. Traditional QEC schemes often rely on measurement-based feedback, which involves performing measurements, processing the classical outcomes, and then applying corrective operations. This process introduces latency, consumes significant resources, and can itself be a source of errors due to the invasive nature of quantum measurement and the classical-quantum interface. Coherent feedback control offers a compelling alternative by allowing the controller to directly interact with the quantum system using quantum fields, without intermediate measurement and classical processing. This maintains the coherence of the quantum information throughout the feedback loop, potentially leading to more robust and faster error correction. This paper explores the theoretical framework and potential advantages of employing coherent feedback control for autonomous QEC. We review existing QEC paradigms, delve into the principles of coherent feedback, and propose how this approach can be integrated into autonomous QEC architectures. Specifically, we investigate its application to bosonic codes and stabilizer codes, discussing the engineering challenges and the prospects for achieving truly fault-tolerant quantum computation by minimizing the classical overhead and enhancing real-time error suppression.