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Quantum Antifragility: NISQ Noise Feeds Integrated Information via Zero-Noise Extrapolation

Cruz Sanchez

Published Aug 8, 2026• 0 citations
Publisher

Abstract

We present the first experimental demonstration that quantum noise is informative, not merely destructive — validating Theorem 8 of IIT 5.1 (FEP-MaxCal Bridge). Using a 5-qubit GHZ circuit on an AerSimulator calibrated with real IBM Quantum ibm_fez noise parameters (T1=320µs, T2=150µs, gate2q error=2.83e-3), we show that Zero Noise Extrapolation (ZNE) recovers integrated information (Φ) to a value exceeding the noiseless ideal: Φ_ZNE = 1.1736 > Φ_ideal = 0.9999 (permutation test, p < 0.000001, N=20 runs, 8192 shots each, 10000 bootstrap resamples). ZNE requires controlled noise scaling (identity folding at λ = 1, 2, 3) that is only feasible in simulation; however, the noise model is calibrated from 3766 real IBM Quantum jobs across 6 backends, and prior hardware experiments on ibm_fez (V1: Φ=0.757, V2: Φ=0.832 with ZNE on real hardware) validate the baseline metrics. The experiment follows a four-phase paradigm: (1) Baseline: GHZ-5 ideal yields Φ=0.9999; (2) Attack: NISQ noise degrades Φ to 0.8804 (-12%); (3) Recovery: Hahn Echo alone shows no significant improvement (p=0.853), but ZNE with 3-scale identity folding and linear extrapolation to noise=0 yields Φ=1.1736; (4) Antifragility: the recovered system exceeds the original baseline by +17.4%. Additional findings: Φ scales monotonically with qubit count (2q→7q), distinguishes entanglement topology (GHZ > W-state > Cluster ≈ Separable), is robust across 4 IBM backend noise models (CV=3.35%), and decays exponentially with circuit depth (τ=29.52 layers). Hardware validation on real ibm_fez confirms Φ for entangled vs separable circuits with Cohen's d = 191.3 (p < 0.0001).

DOI
10.5281/zenodo.21844935

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We present the first experimental demonstration that quantum noise is informative, not merely destructive — validating Theorem 8 of IIT 5.1 (FEP-MaxCal Bridge). Using a 5-qubit GHZ circuit on an AerSimulator calibrated with real IBM Quantum ibm_fez noise parameters (T1=320µs, T2=150µs, gate2q error=2.83e-3), we show that Zero Noise Extrapolation (ZNE) recovers integrated information (Φ) to a value exceeding the noiseless ideal: Φ_ZNE = 1.1736 > Φ_ideal = 0.9999 (permutation test, p < 0.000001, N=20 runs, 8192 shots each, 10000 bootstrap resamples). ZNE requires controlled noise scaling (identity folding at λ = 1, 2, 3) that is only feasible in simulation; however, the noise model is calibrated from 3766 real IBM Quantum jobs across 6 backends, and prior hardware experiments on ibm_fez (V1: Φ=0.757, V2: Φ=0.832 with ZNE on real hardware) validate the baseline metrics. The experiment follows a four-phase paradigm: (1) Baseline: GHZ-5 ideal yields Φ=0.9999; (2) Attack: NISQ noise degrades Φ to 0.8804 (-12%); (3) Recovery: Hahn Echo alone shows no significant improvement (p=0.853), but ZNE with 3-scale identity folding and linear extrapolation to noise=0 yields Φ=1.1736; (4) Antifragility: the recovered system exceeds the original baseline by +17.4%. Additional findings: Φ scales monotonically with qubit count (2q→7q), distinguishes entanglement topology (GHZ > W-state > Cluster ≈ Separable), is robust across 4 IBM backend noise models (CV=3.35%), and decays exponentially with circuit depth (τ=29.52 layers). Hardware validation on real ibm_fez confirms Φ for entangled vs separable circuits with Cohen's d = 191.3 (p < 0.0001).
Increasing the utility of currently available Noisy Intermediate-Scale Quantum (NISQ) devices requires developing efficient methods to mitigate hardware errors. In this work we propose a novel Cyclic Layout Permutations-based Zero-Noise Extrapolation (CLP-ZNE) protocol for such a task. The method leverages the inherent non-uniformity of gate errors in NISQ hardware to extrapolate the expectation value, averaged over cyclic circuit layout permutations, to the level of zero noise. In contrast to the previous layout permutation based approaches, for an nnn-qubit circuit CLP-ZNE requires execution of only O(n)O(n)O(n) and at most O(n2)O(n^2)O(n2) different circuit layouts for circuits of one-dimensional and arbitrary connectivity, respectively. When benchmarked against noise channels modeling the IBM Torino quantum computer, the method reduces a typical error in expectation values of n=12n=12n=12 qubit circuits by an order of magnitude, outperforming standard unitary folding ZNE. By demonstrating the ability to mitigate noise of real hardware specifications, including both depolarizing and T1/T2T_1/T_2T1​/T2​ relaxation processes, these results give evidence for the applicability of CLP-ZNE to present-day NISQ processors.
Abstract The practical application of Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally limited by gate-level noise, which corrupts computational results. This research addresses this challenge through the development and validation of a modular software framework for Quantum Error Mitigation (QEM). We implement and compare two leading QEM strategies: Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC). The framework is built using the Qiskit library and is validated using a realistic, hardware-calibrated noisy simulator that mimics the error characteristics of a real IBM Quantum device. Our methodology focuses on a robust implementation of ZNE via unitary folding and a proof-of-concept demonstration of the PEC algorithm. The framework's effectiveness is demonstrated on a simulated noisy backend where, for a 3-qubit Greenberger-Horne-Zeilinger (GHZ) state, the baseline state fidelity was increased from 93.5% to 97.3% via ZNE, corresponding to a 59% reduction in the state's infidelity. This work provides a practical demonstration of how software-based error mitigation can enhance the reliability of quantum computations on current noisy hardware.
Near term quantum processors operate in a noise dominated regime, motivating error mitigation techniques that recover accurate expectation values without full fault tolerance. Zero Noise Extrapolation (ZNE) is a widely used but biased error mitigation method that lacks rigorous error bounds. Its effective application requires nontrivial technical choices, most notably the selection of noise scaling factors and extrapolation models, making ZNE sensitive to user expertise and often necessitating costly trial and error procedures. Here, we introduce Folding Free Zero Noise Extrapolation (FF-ZNE), a method that removes the need for noise factor selection by achieving effective noise amplification without circuit folding. FF-ZNE exploits isomorphic hardware layouts with distinct native noise profiles, such that executing a fixed circuit across these layouts induces controllable variations in the effective noise strength. Under a depolarizing noise model, we analytically show that the resulting extrapolation admits a fixed linear form, eliminating extrapolator choice and enabling a seamless, user independent mitigation procedure. We further propose two algorithms that identify sets of isomorphic hardware layouts on which a given circuit yields sufficiently distinct expectation values to enable reliable zero noise extrapolation. Experiments on a 133 qubit IBM Quantum device demonstrate that FF-ZNE yields mitigated expectation values with average deviations of ~6% and 4.5% for up to 50 qubit EfficientSU2 (sparse) and Hamiltonian simulation (dense) circuits, respectively. The method is thus scalable and applicable to a broad range of circuits. By eliminating noise factor and extrapolator selection, FF-ZNE transforms zero noise extrapolation from a technique requiring expert tuning into a practical, scalable, and broadly accessible error mitigation method for current quantum hardware.
Zero-noise extrapolation (ZNE) mitigates errors in near-term quantum devices by extrapolating measurements obtained at amplified noise levels to estimate noise-free expectation values. In practice, commonly used extrapolation models are fitted without enforcing physical constraints, which can yield predictions outside the valid range of quantum observables. In this work, we introduce physically bounded variants of polynomial, exponential, and polynomial--exponential extrapolation models by explicitly parameterizing the zero-noise estimate and constraining it during optimization. We evaluate the approach using a large synthetic benchmark comprising 180,000 circuits and approximately 3.6 million ZNE experiments generated under realistic device noise models derived from IBM quantum backends. We also perform preliminary validation on real quantum hardware using GHZ and W-state circuits. Across the synthetic benchmark, bounded extrapolation substantially reduces unphysical predictions and improves the stability of exponential- and polynomial--exponential-family models, whereas polynomial models show little difference between bounded and unbounded variants. Hardware experiments show similar qualitative behaviour: bounded models generally avoid pathological extrapolations and often provide a more reliable balance between accuracy and usable coverage. At the same time, the results highlight practical limitations of current devices, including stronger-than-expected noise effects and variability not fully captured by simulation models. These results suggest that enforcing physical constraints during extrapolation improves the reliability of ZNE and that this approach can be incorporated into existing workflows with minimal modification.
Reliable benchmarking of Quantum Error Mitigation (QEM) requires distinguishing genuine improvements from artefacts of the post-processing arithmetic. In this paper, we expose a failure mode in Richardson Zero-Noise Extrapolation (ZNE), a widely used technique routinely (and often implicitly) relied upon in benchmarks and experiments. When noise amplification operates beyond usable signals - a regime that is quickly reached on current hardware for non-trivial circuits - we show that the extrapolation no longer reflects the underlying physics, but collapses into a fixed rescaling of a single noisy measurement, producing a bogus apparent improvement that is independent of noise amplification. This poses a rarely considered threat to the validity of many empirical evaluations in quantum computing. Measurements on real hardware (IQM Euro-Q-Exa) confirm this collapse with ordinary folding alone: as circuit depth erodes the signal, the reported estimate decouples from the truth and overshoots the ideal by up to 21%. We further introduce a matched-cost "garbage-folding" negative control that carries no usable signal yet reports a larger apparent improvement than genuine folding - showing that the magnitude of an improvement is not evidence of its correctness - alongside a zero-cost check flagging the artefact from data a benchmark already holds. We distil both into a short reporting checklist for ZNE benchmarks.
Variational quantum circuits (VQCs) are central to near-term quantum computing, yet their practical deployment is severely hindered by noise. While existing error mitigation methods, such as zero-noise extrapolation (ZNE), typically assume static noise, real noisy intermediate-scale quantum (NISQ) systems exhibit dynamic, time-varying noise that remains largely unaddressed. To overcome this critical gap, our work introduces a novel adaptive noise mitigation framework for VQCs that integrates ZNE with contextual multi-armed bandits (CMAB), enabling dynamic, context-aware selection of circuit-folding levels based on ansatz parameters (e.g., depth, parameter count) and the evolving noise environment. Unlike fixed-fold or heuristic ZNE, our approach uses online adaptation to improve the accuracy of ZNE and reduce redundant quantum circuit executions. Our extensive simulations and experiments on real quantum hardware reveal the following important properties: (i) deeper VQCs accumulate noise, degrading accuracy and increasing the number of quantum circuit executions; (ii) ZNE restores estimator fidelity when the folding level is chosen appropriately; and (iii) CMAB-guided folding cuts quantum circuit execution round trips by up to 40\%, bytes exchanged by up to 35\%, and end-to-end cost by up to 30\% under a 10~Mbps budget, with up to 6.9\% higher estimator fidelity (CIFAR-10, depth 3, noise band η=0.05η=0.05η=0.05), versus fixed-fold and grid-search ZNE. These results demonstrate substantial performance gains over existing noise mitigation methods, underscoring the effectiveness of our design in supporting robust noise mitigation for VQCs. The source code is also publicly released to support reproducibility.