Mitiq: A software package for error mitigation on noisy quantum computers
Ryan LaRose, Andrea Mari, Sarah Kaiser, Peter J. Karalekas, Andre A. Alves, Piotr Czarnik, Mohamed El Mandouh, Max H. Gordon, Yousef Hindy, Aaron Robertson, Purva Thakre, Misty Wahl, Danny Samuel, Rahul Mistri, Maxime Tremblay, Nick Gardner, Nathaniel T. Stemen, Nathan Shammah, William J. Zeng
We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.
We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.
Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the computation, which experiences a bias in the presence of hardware noise. A systematic way to remove such bias is probabilistic error cancellation (PEC). PEC requires a full characterization of the noise and introduces a sampling overhead that increases exponentially with circuit depth, prohibiting high-depth circuits at realistic noise levels. Probabilistic error reduction (PER) is a related quantum error mitigation method that systematically reduces the sampling overhead at the cost of reintroducing bias. In combination with zero-noise extrapolation, PER can yield expectation values with an accuracy comparable to PEC. Noise reduction through PER is broadly applicable to near-term algorithms, and the automated implementation of PER is thus desirable for facilitating its widespread use. To this end, we present an automated quantum error mitigation software framework that includes noise tomography and application of PER to user-specified circuits. We provide a multi-platform Python package that implements a recently developed Pauli noise tomography (PNT) technique for learning a sparse Pauli noise model and exploits a Pauli noise scaling method to carry out PER. We also provide software tools that leverage a previously developed toolchain, employing PyGSTi for gate set tomography and providing a functionality to use the software Mitiq for PER and zero-noise extrapolation to obtain error-mitigated expectation values on a user-defined circuit.
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.
We apply quantum error mitigation techniques to a variety of benchmark problems and quantum computers to evaluate the performance of quantum error mitigation in practice. To do so, we define an empirically motivated, resource-normalized metric of the improvement of error mitigation which we call the improvement factor, and calculate this metric for each experiment we perform. The experiments we perform consist of zero-noise extrapolation and probabilistic error cancellation applied to two benchmark problems run on IBM, IonQ, and Rigetti quantum computers, as well as noisy quantum computer simulators. Our results show that error mitigation is on average more beneficial than no error mitigation — even when normalized by the additional resources used — but also emphasize that the performance of quantum error mitigation depends on the underlying computer.
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.
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.
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.