From Pharmacology to Cryptography and from Geology to Astronomy are some of the scientific fields in which Quantum Computing potentially will take off and fly high. Big Quantum Computing vendors invest a large amount of money in improving the hardware and they claim that soon enough a quantum program will be hundreds of thousands of times faster than a typical one we know nowadays. But still the reliability of such systems is the main obstacle. In this work, the reliability of real quantum devices is tested and techniques of noise and error correction are presented while measurement error mitigation is explored. In addition, a well-known string matching algorithm (Bernstein-Vazirani) was applied to the real quantum computing device in order to measure its accuracy and reliability. Simulated environments were also used in order to evaluate the results. The results obtained, even if these were not 100% accurate, are very promising which proves that even these days a quantum computer working side by side with a typical one is reliable and especially when error mitigation techniques are applied.
From Pharmacology to Cryptography and from Geology to Astronomy are some of the scientific fields in which Quantum Computing potentially will take off and fly high. Big Quantum Computing vendors invest a large amount of money in improving the hardware and they claim that soon enough a quantum program will be hundreds of thousands of times faster than a typical one we know nowadays. But still the reliability of such systems is the main obstacle. In this work, the reliability of real quantum devices is tested and techniques of noise and error correction are presented while measurement error mitigation is explored. In addition, a well-known string matching algorithm (Bernstein-Vazirani) was applied to the real quantum computing device in order to measure its accuracy and reliability. Simulated environments were also used in order to evaluate the results. The results obtained, even if these were not 100% accurate, are very promising which proves that even these days a quantum computer working side by side with a typical one is reliable and especially when error mitigation techniques are applied.
The recent pace of experimental progress in quantum technologies suggests we may soon reach a time when quantum devices can be applied to solve problems of practical interest. Despite this, we are still far from being able to abstract away the effects of noise on quantum computation. The reliable execution of computations on current devices remains a significant challenge. This holds true both for computation with noisy physical qubits and for computation using the limited forms of error correction available on early fault-tolerant quantum devices. In this thesis, I propose methods for improving the reliability of quantum devices, as the field transitions from the regime of noisy intermediate-scale quantum (NISQ) devices to that of early fault-tolerance. These span the topics of quantum error mitigation, quantum error correction and quantum certification. In the first instance, I propose methods for improving the performance of quantum devices affected by limited amounts of noise. Specifically, I present a method for mitigating the effects of time-dependent noise. This adapts a computational certification protocol called accreditation into a method for postselecting on weaker time-dependent noise behaviours. The method is analytically shown to lead to a provable reduction in errors for the case of depolarising noise, and demonstrated in experiments on superconducting hardware. I also present a method for mitigating the effects of photon loss in photonic quantum devices. Through a combination of analytical and numerical analysis, it is shown that there are wide regimes of photon loss for which this method outperforms postselection, the standard method of handling loss in photonic devices. Additionally, evidence is provided that the method enhances the performance of a quantum machine learning model known as a Quantum Circuit Born Machine in the presence of photon loss. Next, I introduce a framework for certifying the correctness of computations run on encoded logical qubits. This is sensitive to considerably more general forms of noise than is usually considered in quantum error correction. It can be applied to efficiently certify the correctness of quantum computations for large system sizes, beyond the capabilities of methods relying on classical simulation. In numerical experiments, the framework was applied to certify the accuracy of instantaneous quantum polynomial (IQP) circuit sampling and Trotterised Hamiltonian simulation. It can be used to efficiently assess whether quantum error mitigation may be usefully applied to a computation, to upper-bound the infidelity of the encoded logical state, and to extend the method of entropy density benchmarking to logical computation. The methods presented in this thesis contribute to the wider effort of building towards reliable quantum computation: both in the sense of reducing the effects of noise on computational output, and in the sense of certifying the correctness of computation beyond the capabilities of classical simulators. Only with reliable quantum computation can the full potential of this technology be realised.
Noisy intermediate-scale quantum (NISQ) devices are valuable platforms for testing the tenets of quantum computing, but these devices are susceptible to errors arising from de-coherence, leakage, cross-talk, and other sources of noise. This raises concerns regarding the stability of results when using NISQ devices since strategies for mitigating errors generally require well-characterized and stationary error models. Here, we quantify the reliability of NISQ devices by assessing the necessary conditions for generating stable results within a given tolerance. We use similarity metrics derived from device characterization data to derive and validate bounds on the stability of a 5-qubit implementation of the Bernstein-Vazirani algorithm. Simulation experiments conducted with noise data from IBM washington, spanning January 2022 to April 2023, revealed that the reliability metric fluctuated between 41% and 92%. This variation significantly surpasses the maximum allowable threshold of 2.2% needed for stable outcomes. Consequently, the device proved unreliable for consistently reproducing the statistical mean in the context of the Bernstein-Vazirani circuit.
Quantum physics is old and mature. Quantum computing and algorithms arose 3 decades ago. Quantum programming on real Quantum Computational Devices (QCD) is something new. Less than the last five years, researchers and scientists could apply quantum programming to QCD since several vendors like IBM, Rigetti, Microsoft or Google could provide access to real machines. In this paper, we experiment and investigate the accuracy of a 5-qubits QCD applying a string search algorithm. Simulating environment used also in order to evaluate the technique and the results obtained were very promising. Even if the accuracy of a real device was around 48% since the possibilities of the other outcomes were extremely low proved the reliability of the real machine. The number of existing qubits was the main obstacle that limits their processing power. In addition, a random number generator was implemented which overcomes all the disadvantages of pseudo-random generators.
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.
Abstract Quantum error control and mitigation techniques help improve how quantum computers handle errors, making algorithms run more efficiently despite noisy hardware. These strategies work at the software level and are built into programs before they run on quantum machines. Unlike quantum error correction, which actively detects and fixes errors during computation, error mitigation does not use real-time corrections but instead reduces the impact of errors after computations. Error mitigation can also help reduce the extra resources needed for full error correction. This chapter explains how these techniques relate to each other, provides an overview of key error mitigation methods and their limitations, and highlights leading academic and technological players in this field. It also covers current trends, such as integrating error-aware programming, benchmarking performance, and ensuring access to quantum hardware for testing. To advance quantum computing, it is recommended that research ecosystems support specialized centers and contribute to key strategic areas in the field.
Quantum computing promises revolutionary advancements across various fields, yet its realization hinges critically on the reliability of its hardware. Unlike classical computing, quantum systems are exceptionally sensitive to environmental noise and prone to errors, leading to significant challenges in maintaining coherence and accurate computation. This research presents a formal model designed to rigorously analyze the reliability of quantum computing hardware. The model incorporates probabilistic representations of quantum gates and qubits, alongside noise models that capture various sources of error, and evaluates the effectiveness of fault-tolerance techniques. The core of the model is a simulation framework allowing for comprehensive evaluation of the impact of these factors on the overall system performance. This approach provides a quantitative basis for designing more robust quantum computing systems and optimizing operational strategies, moving beyond intuitive estimations and towards a scientifically grounded understanding of quantum hardware reliability. The model is presented with detailed formulas and mathematical notations, offering a precise and verifiable framework for analysis.