With sub-threshold quantum error correction on quantum hardware still out of reach, quantum error mitigation methods are currently deemed an attractive option for implementing certain applications on near-term noisy quantum devices. One such application is quantum routing - the ability to map an incoming quantum signal into a superposition of paths. In this work, we use a 7-qubit IBM quantum device to experimentally deploy two promising quantum error mitigation methods, Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC), in the context of quantum routing. Importantly, beyond investigating the improved performance of quantum routing via ZNE and PEC separately, we also investigate the routing performance provided by the concatenation of these two error-mitigation methods. Our experimental results demonstrate that such concatenation leads a very significant performance improvement relative to implementation with no error mitigation. Indeed, an almost perfect performance in terms of fidelity of the output entangled paths is found. These new results reveal that with concatenated quantum error-mitigation embedded, useful quantum routing becomes feasible on current devices without the need for quantum error correction - opening up a potential implementation pathway to other applications that utilize a superposition of communication links.
With sub-threshold quantum error correction on quantum hardware still out of reach, quantum error mitigation methods are currently deemed an attractive option for implementing certain applications on near-term noisy quantum devices. One such application is quantum routing - the ability to map an incoming quantum signal into a superposition of paths. In this work, we use a 7-qubit IBM quantum device to experimentally deploy two promising quantum error mitigation methods, Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC), in the context of quantum routing. Importantly, beyond investigating the improved performance of quantum routing via ZNE and PEC separately, we also investigate the routing performance provided by the concatenation of these two error-mitigation methods. Our experimental results demonstrate that such concatenation leads a very significant performance improvement relative to implementation with no error mitigation. Indeed, an almost perfect performance in terms of fidelity of the output entangled paths is found. These new results reveal that with concatenated quantum error-mitigation embedded, useful quantum routing becomes feasible on current devices without the need for quantum error correction - opening up a potential implementation pathway to other applications that utilize a superposition of communication links.
Quantum routers direct a quantum signal from one input path to a quantum superposition of multiple output paths and are considered important elements of future quantum networks. To extend the scalability of quantum networks, multi-layer quantum routers, which allow for further superposition of paths, were proposed. Due to the numerous limitations of current quantum devices, quantum error mitigation methods become potential solutions for realizing practical quantum routers in the near term. Zero-Noise Extrapolation (ZNE) and Clifford Data Regression (CDR) are two promising quantum error mitigation methods. Based on the characteristics of these two methods, we propose a new method, named extrapolated CDR (eCDR). We benchmark the performance of multi-layer quantum routers implemented on current superconducting quantum devices instantiated with the ZNE, CDR, and eCDR methods. Our experimental results show that the new eCDR method improves the fidelity result of the two-layer quantum router. Our work highlights how new mitigation methods built from different components of pre-existing methods, and designed with a core application in mind, can lead to significant performance enhancements.
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.
As an alternative to quantum error correction, quantum error mitigation methods, including Zero-Noise Extrapolation (ZNE), have been proposed to alleviate run-time errors in current noisy quantum devices. In this work, we propose a modified version of ZNE that provides for a significant performance enhancement on current noisy devices. Our modified ZNE method extrapolates to zero-noise data by evaluating groups of noisy data obtained from noise-scaled circuits and selecting extrapolation functions for each group with the assistance of estimated noisy simulation results. To quantify enhancement in a real-world quantum application, we embed our modified ZNE in Quantum Random Access Memory (QRAM) - a memory system important for future quantum networks and computers. Our new ZNE-enhanced QRAM designs are experimentally implemented on a 27-qubit noisy superconducting quantum device, the results of which demonstrate QRAM fidelity can be improved significantly relative to traditional ZNE usage. Our results demonstrate the critical role the extrapolation function plays in ZNE - judicious choice of that function on a per-measurement basis can make the difference between a quantum application being functional or non-functional.
We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device's noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.
Quantum noise poses a significant challenge for current near-term quantum computing. Quantum error mitigation (QEM) has therefore emerged as a key strategy, offering a practical and effective solution to reduce error impacts and enhance the performance of near-term variational quantum circuits (VQC). Given the lack of a comprehensive survey on this important topic in the literature, this article provides a dedicated overview of QEM, including both during and after the training of VQC. Specifically, during VQC training, we explore and discuss key QEM techniques such as optimal control and dynamical decoupling. For the post-processing stage of VQC, we will examine and discuss mitigation techniques such as zero-noise extrapolation (ZNE) and probabilistic error cancellation (PEC). For each of these QEM techniques, we will investigate the fundamentals, mitigation concepts, and recent advances. Subsequently, we also explore research toolboxes, including Mitiq and Qiskit Aer, as well as provide a case study that demonstrates contextual multi-armed bandit-guided ZNE. Finally, we discuss ongoing problems and future research initiatives, including ML-assisted mitigation and integration with error correction. This survey article aims to synthesize the state-of-the-art in QEM, offer organized insights across approaches, and propose potential paths towards error-resilient quantum computing.
Quantum error mitigation (QEM) bridges the gap between today's noisy NISQ hardware and fault-tolerant quantum computing by reducing the effect of hardware errors on expectation value estimates without the qubit overhead of full quantum error correction. This paper proposes the Quantum Error Mitigation Design (QEMD) framework, a systematic evaluation of six QEM techniques across four circuit families on IBM Quantum Eagle and IonQ Forte: Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), Clifford Data Regression (CDR), Symmetry Verification (SV), Dynamical Decoupling (DD), and a novel Adaptive Ensemble Mitigation (AEM) combining ZNE and CDR with context-aware technique selection. QEMD finds: ZNE 3-point Richardson provides the best cost-performance trade-off for QAOA and VQE circuits (4.8x overhead, 28.4pp error reduction); PEC provides the highest accuracy but at 48x shot overhead -- practical only for n <= 12; DD reduces coherence-limited errors by 18.4% on IonQ Forte at zero shot overhead; AEM outperforms all individual techniques by 6.4pp at 8.4x overhead. QEMD provides a decision guide mapping circuit type, qubit count, and shot budget to optimal QEM technique selection.