The field of quantum computing has experienced a rapid expansion in recent years, with ongoing exploration of new technologies, a decrease in error rates, and a growth in the number of qubits available in quantum processors. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction and Mitigation are rapidly advancing areas of research in the quantum computing landscape, with a goal of reducing errors. IBM has recently emphasized that Quantum Error Mitigation is the key to unlocking the full potential of quantum computing. A recent work, namely HAMMER, demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they assumed that errors occur solely in local clusters, whereas we observe that at higher average Hamming distances this structure falls away. Our study demonstrates that the correlated structure is not just limited to local patterns, but it also encompasses certain non-local clustering patterns that can be accurately characterized through a Poisson distribution model. This model takes into account the input circuit, the current state of the device, including calibration statistics, and the qubit topology. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Our Q-Beep approach delivers state-of-the-art results, thanks to its problem-aware modeling of the error distribution's underlying structure and the implementation of an Bayesian network state-graph. This has resulted in an increase of up to 234.6% in circuit execution accuracy on BV circuits and an average improvement of 71.0% in the quality of QAOA solutions when tested on 16 IBMQ quantum processors.
The field of quantum computing has experienced a rapid expansion in recent years, with ongoing exploration of new technologies, a decrease in error rates, and a growth in the number of qubits available in quantum processors. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction and Mitigation are rapidly advancing areas of research in the quantum computing landscape, with a goal of reducing errors. IBM has recently emphasized that Quantum Error Mitigation is the key to unlocking the full potential of quantum computing. A recent work, namely HAMMER, demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they assumed that errors occur solely in local clusters, whereas we observe that at higher average Hamming distances this structure falls away. Our study demonstrates that the correlated structure is not just limited to local patterns, but it also encompasses certain non-local clustering patterns that can be accurately characterized through a Poisson distribution model. This model takes into account the input circuit, the current state of the device, including calibration statistics, and the qubit topology. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Our Q-Beep approach delivers state-of-the-art results, thanks to its problem-aware modeling of the error distribution's underlying structure and the implementation of an Bayesian network state-graph. This has resulted in an increase of up to 234.6% in circuit execution accuracy on BV circuits and an average improvement of 71.0% in the quality of QAOA solutions when tested on 16 IBMQ quantum processors.
Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processors' qubit capacity growing. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction (in-situ error mitigation) and Quantum Error Mitigation (post-induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors. IBM recently published an article stating that Quantum Error Mitigation is the path to quantum computing usefulness. A recent work, namely HAMMER, demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they assumed that errors occur solely in local clusters, whereas we observe that at higher average Hamming distances this structure falls away. In this work, we show that such a correlated structure is not only local but extends certain non-local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i.e., calibration statistics) and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the proposed iterative method, our Q-Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein-Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, a fidelity improvement of up to 17.8% is attained. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to adopt and provide more reliable circuit induction results. Q-Beep is maintained at github.com/pnnl/qbeep
Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this paper, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by1.26x,1.29x,1.47x, and 2.65 x, respectively.
In recent years, there have been significant advancements in various aspects of quantum computing. However, despite this substantial progress, the availability of fault-tolerant quantum computers is still out of reach and may remain so for decades. Therefore, a key challenge is to leverage current NISQ devices to achieve a quantum advantage effectively. In this context, the Quantum Approximate Optimization Algorithm (QAOA) was proposed to potentially demonstrate computational advantages in combinatorial optimization problems using NISQ computers. Meanwhile, quantum error mitigation (QEM) techniques have been developed to address errors, with their effectiveness validated in practical problems involving more than 100 qubits. Therefore, in this paper, we optimize QAOA circuits and apply various error mitigation methods, such as dynamic decoupling and Pauli-twirling, to scale problem sizes on IBM quantum processors. Additionally, we discuss optimal implementation strategies for scalable QAOA. We test our implementations on Max-Cut problems and compare our results with previous works.
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.
Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data regression (CDR), rely on noise scaling or global regression, and their performance is constrained by the exponential growth of the system degrees of freedom. We construct a graph-enhanced mitigation (GEM) framework, which incorporates physical information into the model representation. In this work, quantum circuits are encoded as attributed graphs. Hardware-level physical information is mapped to node and edge features: local noise parameters such as calibration parameters T1, T2, and readout errors are encoded at nodes, while coupling-related information such as two-qubit gate errors is encoded as edge features. Graph neural networks are used to model how errors propagate along the physical coupling structure and build up into non-local correlations. This allows the model to capture local interactions and part of the resulting non-local correlations across qubits. A dual-branch affine correction is applied to maintain consistency with physical constraints. Experiments on 10-qubit and 16-qubit random circuits executed on superconducting quantum processors show that GEM provides a level of accuracy comparable to CDR at small scales, while yielding lower mean absolute error and improved stability in zero-shot transfer to larger systems. Results of the traditional QEM strategy indicate that global regression methods remain effective in low-dimensional settings but become less reliable as system degrees of freedom grow. In contrast, GEM makes use of local physical structures to show better scalability and generalization, while preserving the overall error propagation patterns. This work provides a practical scalable approach to QEM for NISQ devices.
In quantum computing, error mitigation is a method to improve the results of an error-prone quantum processor by post-processing them on a classical computer. In this work, we improve the General Error Mitigation (GEM) method for scalability. GEM relies on the use of a matrix to represent the device error, which requires the execution of 2n+1 calibration circuits on the quantum hardware, where n is the number of qubits. With our improved method, the number of calibration runs is independent of the number of qubits and depends only on the number of non-zero states in the output distribution. We run 1853 randomly generated circuits with widths between 2-7 qubits and depths between 10-140 gates on IBMQ superconducting devices. The experiments show that the mitigation works comparably well to GEM, while requiring a fraction of the calibration runs. Finally, an experiment to mitigate errors in a 100 qubit circuit demonstrates the scalable features of our method.