Noisy Intermediate-Scale Quantum (NISQ) devices suffer from calibration drift—slow, coherent phase errors accumulating between active corrections. We present EEDT (Entanglement-Enhanced Dynamical Tracking), a measurement-gated quantum error correction protocol utilizing noisy measurements to dictate intervention timing. Initial Lindblad simulations yielded a counterintuitive 339% deviation from theoretical bounds, which we identify as the Golden Eye collapse in low-noise regimes (σ_ro < 3%). This motivates a bifurcated theoretical model incorporating Golden Eye Occupancy (high-σ) and noise-floor saturation (low-σ) regimes, achieving 78% prediction accuracy improvement over prior models, with the critical threshold σ_c ≈ 2% analytically derived. New in v8: We report the first statistically significant real-hardware demonstration on three IBM Heron devices (ibm_fez, ibm_torino, ibm_marrakesh). After systematic qubit selection (ε_01 = 1.18%) and direct ZZ Ramsey measurement (ν_ZZ = 0.13 kHz), the stroboscopic CDQEM protocol achieves a correction gain of +0.112 at N_meas = 8 with 2.7σ significance on ibm_marrakesh, confirming the MCM post-selection effect predicted by the stroboscopic convergence theorem. All code, data, and IBM Quantum job IDs are publicly available.
Noisy Intermediate-Scale Quantum (NISQ) devices suffer from calibration drift—slow, coherent phase errors accumulating between active corrections. We present EEDT (Entanglement-Enhanced Dynamical Tracking), a measurement-gated quantum error correction protocol utilizing noisy measurements to dictate intervention timing. Initial Lindblad simulations yielded a counterintuitive 339% deviation from theoretical bounds, which we identify as the Golden Eye collapse in low-noise regimes (σ_ro < 3%). This motivates a bifurcated theoretical model incorporating Golden Eye Occupancy (high-σ) and noise-floor saturation (low-σ) regimes, achieving 78% prediction accuracy improvement over prior models, with the critical threshold σ_c ≈ 2% analytically derived. New in v8: We report the first statistically significant real-hardware demonstration on three IBM Heron devices (ibm_fez, ibm_torino, ibm_marrakesh). After systematic qubit selection (ε_01 = 1.18%) and direct ZZ Ramsey measurement (ν_ZZ = 0.13 kHz), the stroboscopic CDQEM protocol achieves a correction gain of +0.112 at N_meas = 8 with 2.7σ significance on ibm_marrakesh, confirming the MCM post-selection effect predicted by the stroboscopic convergence theorem. All code, data, and IBM Quantum job IDs are publicly available.
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.
Reliably executing quantum algorithms on noisy intermediate-scale quantum (NISQ) devices is challenging, as they are severely constrained and prone to errors. Efficient quantum circuit compilation techniques are therefore crucial for overcoming their limitations and dealing with their high error rates. These techniques consider the quantum hardware restrictions, such as the limited qubit connectivity, and perform some transformations to the original circuit that can be executed on a given quantum processor. Certain compilation methods use error information based on calibration data to further improve the success probability or the fidelity of the circuit to be run. However, it is uncertain to what extent incorporating calibration information in the compilation process can enhance the circuit performance. For instance, considering the most recent error data provided by vendors after calibrating the processor might not be functional enough as quantum systems are subject to drift, making the latest calibration data obsolete within minutes. In this paper, we explore how different usage of calibration data impacts the circuit fidelity, by using several compilation techniques and quantum processors (IBM Perth and Brisbane). To this aim, we implemented a framework that incorporates some of the state-of-the-art noise-aware and non-noise-aware compilation techniques and allows the user to perform fair comparisons under similar processor conditions. Our experiments yield valuable insights into the effects of noise-aware methodologies and the employment of calibration data. The main finding is that pre-processing historical calibration data can improve fidelity when real-time calibration data is not available due to factors such as cloud service latency and waiting queues between compilation and execution on the quantum backend.
Abstract Hardware Error Outputs of Quantum Computing Not Reliable because of Hardware Calibration Drift, Measurement Noise, Gate Errors on NISQ Systems. Even though MEMs, ZNEs, and CDRs slightly increase output accuracy, they operate under the assumption of static noise, therefore they do not account for changing output of the NISQ devices in real-time. The limitations of MEMs, ZNEs, and CDRs can be overcome by using the Hybrid Adaptive Error Mitigation (HAEM) method proposed in this article that has the capability to combine baseline measurement-error mitigation with Real-time Calibration Circuits and Lightweight-Machine-learning algorithms for adaptive error-correcting and increasing the overall output integrity of quantum devices affected by fluctuations in noise. The application of the HAEM method will utilize Qiskit Runtime to develop, implement, and validate the Hybrid Adaptive Error Mitigation method through testing using controlled noisy simulated environments based on the characteristics of current advanced NISQ quantum computers. The results of the tests demonstrate the HAEM architecture provides a higher level of accuracy and fidelity than static and non-mitigated executions ("mitigated execution vs. HAEM execution"), providing an increase of up to thirty-four percent in fidelity under high-noise conditions with minimal computational overhead. The results demonstrate that the use of adaptive and data-driven mitigation techniques, like those used in the Hybrid Adaptive Error Mitigation method, are an efficient way to increase the accuracy of quantum computations.
Accurate assessment and management of errors is indispensable for extracting useful results from noisy intermediate-scale quantum devices. In this work, we propose the qubit error probability (QEP), a device specific metric that combines relaxation, dephasing, gate, and measurement contributions into a single per qubit figure of merit computable before execution. Leveraging QEP as the control variable, we revisit zero noise extrapolation (ZNE) by adding pairs of controlled native two-qubit gates on all connected qubit pairs to generate circuits with successively larger mean QEP; the zero error limit is then approximated by a linear regression of the measured observable against those values. Benchmarking on IBM Quantum Heron processors, we apply QEP guided ZNE to first order Trotterized simulations of the two dimensional transverse field Ising model, chosen as a representative interacting many body system, involving up to 68 qubits and 15 Trotter steps. In regimes where the raw circuits exhibit a finite mean QEP, the method suppresses observable errors beyond those attainable with circuit depth scaled ZNE, while requiring only three noise scaled evaluations and no additional classical post processing. These results demonstrate that QEP serves as a transparent and efficient error metric and that its integration into ZNE provides a practical route to reliability gains on current superconducting hardware, without the resource costs associated with full quantum error correction.
Noisy Intermediate-Scale Quantum (NISQ) devices represent current quantum computing technology with 50-1000 qubits operating without comprehensive fault-tolerant error correction. The fundamental challenge lies in balancing error correction necessity against prohibitive resource overhead. Conventional quantum error correction codes require 10:1 to 1000:1 qubit ratios and syndrome extraction circuits exceeding 50 gates, consuming entire NISQ capacities. This work presents a comprehensive low-overhead quantum error correction framework specifically designed for NISQ constraints. Our approach combines three elements: optimised stabiliser codes which get qubit ratios of 3:1 to 10:1, adaptive syndrome extraction which works with circuits with less than 20 gates and machine learning-enhanced decoding which is specific to the noise profiles of the hardware. Experimental validation on IBM Quantum (127- qubit Eagle), IonQ trapped-ion systems, and Google Sycamore simulation demonstrates successful quantum state protection achieving 2.7× error suppression with 60% overhead reduction versus conventional surface codes. The proposed code achieves logical error rates of 0.0065 using only 10 physical qubits compared to 25 qubits for equivalent surface codes. Machine learning decoder attains 94.3% accuracy with 12-microsecond inference latency, enabling real-time error correction. Break-even performance achieved at 0.8% physical error rates establishes practical pathways for near-term quantum advantage in variational algorithms and quantum simulation applications.
Noisy Intermediate-Scale Quantum (NISQ) devices represent current quantum computing technology with 50-1000 qubits operating without comprehensive fault-tolerant error correction. The fundamental challenge lies in balancing error correction necessity against prohibitive resource overhead. Conventional quantum error correction codes require 10:1 to 1000:1 qubit ratios and syndrome extraction circuits exceeding 50 gates, consuming entire NISQ capacities. This work presents a comprehensive low-overhead quantum error correction framework specifically designed for NISQ constraints. Our approach combines three elements: optimised stabiliser codes which get qubit ratios of 3:1 to 10:1, adaptive syndrome extraction which works with circuits with less than 20 gates and machine learning-enhanced decoding which is specific to the noise profiles of the hardware. Experimental validation on IBM Quantum (127- qubit Eagle), IonQ trapped-ion systems, and Google Sycamore simulation demonstrates successful quantum state protection achieving 2.7× error suppression with 60% overhead reduction versus conventional surface codes. The proposed code achieves logical error rates of 0.0065 using only 10 physical qubits compared to 25 qubits for equivalent surface codes. Machine learning decoder attains 94.3% accuracy with 12-microsecond inference latency, enabling real-time error correction. Break-even performance achieved at 0.8% physical error rates establishes practical pathways for near-term quantum advantage in variational algorithms and quantum simulation applications.