Quantum Secret Sharing (QSS) employs the principles of quantum entanglement to securely distribute confidential information among multiple participants, such that the original secret can only be recovered through collaboration among an authorized subset of users. While QSS offers information-theoretic security independent of computational assumptions, its practical deployment on Noisy Intermediate-Scale Quantum (NISQ) hardware remains challenging. The presence of device imperfections, including gate errors, decoherence, and measurement inaccuracies, adversely affects quantum state fidelity and reduces the reliability of secret reconstruction during protocol execution. This paper presents a noise-resilient multiparty QSS framework integrating a (2,3)- threshold Shamir Secret Sharing scheme over Galois Field GF (8) with nine-qubit Greenberger–Horne–Zeilinger (GHZ) entanglement circuits, fully implemented on the IBM ibm_kingston 156-qubit Heron r2 quantum processor. A three-phase experimental methodology is adopted: noiseless simulation via Qiskit Aer, authentic hardware execution with 1024 measurement shots, and a combined Local Readout Error Mitigation (LRE) and Zero Noise Extrapolation (ZNE) pipeline. Across 24 participants in eight secret-sharing sessions, hardware noise introduced a 6.0% accuracy degradation relative to the ideal baseline, which the LRE+ZNE pipeline substantially recovered. The (2,3)-threshold security invariant was preserved throughout all phases, with singleplayer reconstruction rates held at exactly 0.000, well below the 12.5% random-guess baseline. Security is further reinforced through CRYSTALS-Kyber512 (NIST FIPS 203) post-quantum authentication, SHA-256 share commitments, SHA3-256 fairness verification, and bulletin board consensus, with verified resistance against seven attack categories. Results confirm that reliable hardware-validated QSS on current NISQ devices is achievable through systematic multi-technique error mitigation.
Quantum Secret Sharing (QSS) employs the principles of quantum entanglement to securely distribute confidential information among multiple participants, such that the original secret can only be recovered through collaboration among an authorized subset of users. While QSS offers information-theoretic security independent of computational assumptions, its practical deployment on Noisy Intermediate-Scale Quantum (NISQ) hardware remains challenging. The presence of device imperfections, including gate errors, decoherence, and measurement inaccuracies, adversely affects quantum state fidelity and reduces the reliability of secret reconstruction during protocol execution. This paper presents a noise-resilient multiparty QSS framework integrating a (2,3)- threshold Shamir Secret Sharing scheme over Galois Field GF (8) with nine-qubit Greenberger–Horne–Zeilinger (GHZ) entanglement circuits, fully implemented on the IBM ibm_kingston 156-qubit Heron r2 quantum processor. A three-phase experimental methodology is adopted: noiseless simulation via Qiskit Aer, authentic hardware execution with 1024 measurement shots, and a combined Local Readout Error Mitigation (LRE) and Zero Noise Extrapolation (ZNE) pipeline. Across 24 participants in eight secret-sharing sessions, hardware noise introduced a 6.0% accuracy degradation relative to the ideal baseline, which the LRE+ZNE pipeline substantially recovered. The (2,3)-threshold security invariant was preserved throughout all phases, with singleplayer reconstruction rates held at exactly 0.000, well below the 12.5% random-guess baseline. Security is further reinforced through CRYSTALS-Kyber512 (NIST FIPS 203) post-quantum authentication, SHA-256 share commitments, SHA3-256 fairness verification, and bulletin board consensus, with verified resistance against seven attack categories. Results confirm that reliable hardware-validated QSS on current NISQ devices is achievable through systematic multi-technique error mitigation.
Quantum secret sharing (QSS) is a cryptographic protocol that leverages quantum mechanics to distribute a secret among multiple parties. With respect to the classical counterpart, in QSS, the secret is encoded into quantum states and shared by a dealer such that only an authorized subsets of participants, i.e., the players, can reconstruct it. Several state-of-the-art studies aim to transpose classical secret sharing into the quantum realm, while maintaining their reliance on traditional network topologies (e.g., star, ring, and fully connected), and require that all thenplayers calculate the secret. These studies exploit the Greenberger–Horne–Zeilinger state, which is a type of maximally entangled quantum state involving three or more qubits. However, none of these works account for redundancy, enhanced security/privacy features, or authentication mechanisms able to fingerprint players. To address these gaps, in this article, we introduce a new concept of QSS, which leans on a generic distributed quantum network, based on a threshold scheme, where all the players collaborate also to the routing of quantum information among them. The dealer, by exploiting a custom flexible weighting system, takes advantage of a newly defined quantum Dijkstra algorithm to select the most suitable subset oftplayers, out of the entire set onnplayers, to involve in the computation. To fingerprint and authenticate users, CRYSTAL-Kyber primitives are adopted, while also protecting each player’s privacy by hiding their identities. We show the effectiveness and performance of the proposed protocol by testing it against the main classical and quantum attacks, thereby improving the state-of-the-art security measures.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.
In quantum computing, noisy intermediate-scale quantum (NISQ) devices offer unprecedented computational capabilities but are vulnerable to errors, notably measurement inaccuracies that impact computation accuracy. This study explores the efficacy of error mitigation techniques in improving quantum circuit performance on NISQ devices. Techniques such as dynamic decoupling (DD), twirled readout error extraction (T-REx) and zero-noise extrapolation (ZNE) are examined through extensive experimentation on an ideal simulator, IBM Kyoto, and IBM Osaka quantum computers. Results reveal significant performance discrepancies across scenarios, with error mitigation techniques notably enhancing both estimator result and variance values, aligning more closely with ideal simulator outcomes. The comparison results with ideal simulator (having expected result value 0.8284) shows that T-Rex has improved results on IBM Kyoto and enhanced average expected result value from 0.09 to 0.35. Similarly, DD has improved average expected result values from 0.2492 to 0.3788 on IBM Osaka. These findings underscore the critical role of error mitigation in bolstering quantum computation reliability. The results suggest that selection of mitigation technique depends upon quantum circuit and its depth, type of hardware and operations to be performed.
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.
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).
The Quantum Approximate Optimization Algorithm (QAOA) is widely regarded as a promising near-term quantum algorithm for addressing hard combinatorial optimization problems on Noisy Intermediate-Scale Quantum (NISQ) devices; however, its real-world effectiveness is severely constrained by hardware noise, including gate infidelities, decoherence, and measurement errors. This work explores an error mitigation–driven approach to enhance the performance and robustness of QAOA without altering its algorithmic structure or requiring fault-tolerant quantum resources. Measurement error mitigation and zero-noise extrapolation are incorporated into the execution and post-processing stages of QAOA circuits and evaluated using the Minimum Vertex Cover problem as a representative benchmark. Performance is assessed through approximation ratios, solution stability, and noise sensitivity across multiple circuit depths. The results indicate that error mitigation not only improves approximation accuracy but also stabilizes output distributions and delays performance degradation at increased circuit depths. Additionally, the mitigated executions demonstrate better consistency across repeated runs, highlighting improved resilience to stochastic noise. These findings emphasize that lightweight and hardware-efficient error mitigation techniques can significantly extend the practical usability of QAOA on current NISQ hardware, providing a scalable and realistic pathway for executing quantum optimization algorithms more reliably in near-term quantum computing environments.