Abstract One of the main important features of the noisy intermediate-scale quantum(NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyze the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover’s algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator’s results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99% of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.
Abstract One of the main important features of the noisy intermediate-scale quantum(NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyze the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover’s algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator’s results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99% of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.
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.
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation will be a necessary tool to extract useful performance out of quantum devices. However, there is a big gap between the noise models often assumed by error mitigation techniques and the actual noise on quantum devices. As a consequence, there arises a gap between the theoretical expectations of the techniques and their everyday performance. Cloud users of quantum devices in particular, who often take the devices as they are, feel this gap the most. How should they parametrize their uncertainty in the usefulness of these techniques and be able to make judgement calls between resources required to implement error mitigation and the accuracy required at the algorithmic level? To answer the first question, we introduce hypothesis testing within the framework of quantum error mitigation and for the second question, we propose an inclusive figure of merit that accounts for both resource requirement and mitigation efficiency of an error mitigation implementation. The figure of merit is useful to weigh the trade-offs between the scalability and accuracy of various error mitigation methods. Finally, using the hypothesis testing and the figure of merit, we experimentally evaluate 16 error mitigation pipelines composed of singular methods such as zero noise extrapolation, randomized compilation, measurement error mitigation, dynamical decoupling, and mitigation with estimation circuits. In total our data involved running 275,640 circuits on two IBM quantum computers.
Context: The main obstacle of quantum computing on its way to scalability is the noisy nature of current hardware. Various types of errors lead to incorrect computational results,and measures such as quantum error mitigation are needed to counteract these errors. Many error mitigation techniques require a thorough understanding of the noise and its impact on computations. Therefore, accurate noise models are indispensable to facilitate meaningful quantum computing in the near future. They also enable realistic simulations of quantum devices. Since these devices are currently limited and quantum computing is expensive, researchers typically rely on simulations for testing their algorithms.Objective: In this thesis, we aim to construct a realistic noise model for quantum computing and optimise its model parameters. The model construction should build on the underlying physical processes, and the number of parameters should scale well with the system size. We also address the evaluation and comparison of different noise models by benchmarks using quantum circuits specific to real-world applications. Finally, we aim to develop useful graphical representations of noise models based on the existing quantum circuit model.Method: We present a benchmarking framework for quantum computing noise models and evaluate it based on benchmarking quality attributes from the literature. Moreover, we construct a quantum computing noise model and develop a training procedure for its parameters. We analyse the parameters of the trained noise model and the impact ofdifferent types of errors on computations. We benchmark the noise model with the above approach and compare it to a noise model provided by IBM’s software development kit Qiskit. Finally, we develop an extension of the quantum circuit model to represent noise channels.Result: The benchmarks performed in this thesis show that our noise model predicts noisy hardware behaviour of IBM’s ibmq_manila quantum device equally well as the Qiskit model, if not better, based on quantum circuits commonly used for variational quantum algorithms. Within the trained noise model, readout error has the most detrimental impact on computations. Our benchmarking approach satisfies relevant quality criteria by choosing suitable quantum circuits and objective functions to compare model predictionsto hardware data. Moreover, the quantum circuit model can be extended meaningfully by noise channels.Conclusion: Our benchmarking approach is suitable for evaluating and comparing quantum computing noise models. In future work, volumetric benchmarks should be performed for various noise models and application contexts. The parameter optimisation based on learning with training circuits yields accurate noise models and shows the importance of mitigating measurement error. Different optimisation algorithms and quantum circuits should be explored, and more types of noise should be incorporated into the noise model.
Current advancements in technology have focused the attention of the quantum computing community toward exploring the potential of near-term devices whose computing power surpasses that of classical computers in practical applications. An unresolved central question revolves around whether the inherent noise in these devices can be overcome or whether any potential quantum advantage would be limited. There is no doubt that crosstalk is one of the main sources of noise in noisy intermediate-scale quantum (NISQ) systems, and it poses a fundamental challenge to hardware designs. Crosstalk between parallel instructions can corrupt quantum states and cause incorrect program execution. In this study, we present a necessary analysis of the crosstalk error effect on NISQ devices. Our approach is extremely straightforward and practical to estimate the crosstalk error of various multi-qubit devices. In particular, we combine the randomized benchmarking (RB) and simultaneous randomized benchmarking (SRB) protocol to estimate the crosstalk error from the correlation controlled-NOT (CNOT) gate. We demonstrate this protocol experimentally on 5-, 7-, \& 16-qubit devices. Our results demonstrate the crosstalk error model of three different IBM quantum devices over the experimental week and compare the error variation against the machine, number of qubits, quantum volume, processor, and topology. We then confirm the improvement in the circuit fidelity on different benchmarks by up to 3.06x via inserting an instruction barrier, as compared with an IBM quantum noisy device which offers near-optimal crosstalk mitigation in practice. Finally, we discuss the current system limitation, its tradeoff on fidelity and depth, noise beyond the NISQ system, and mitigation opportunities to ensure that the quantum operation can perform its quantum magic undisturbed.
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely noiseless outputs from noisy quantum measurements. Our model assumes that circuit depth is sufficient for depolarizing noise, producing corrupted observations that resemble a uniform distribution alongside classical bit-flip errors from readout. Our method consists of two steps: a filtering stage that discards uninformative depolarizing noise and an expectation-maximization (EM) algorithm that computes a maximum likelihood (ML) estimate over the remaining data. We demonstrate the effectiveness of this approach on small-qubit systems using circuit simulations in Qiskit and IBM quantum processing unit (QPU) data, and compare its performance to contemporary statistical QEM techniques. We also show that our method scales to larger qubit counts using synthetically generated data consistent with our noise model. These results suggest that principled statistical methods can offer scalable and interpretable solutions for quantum error mitigation in realistic NISQ settings.
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.