Quantum computing has the potential to solve problems that are currently intractable to classical computers with algorithms like Quantum Phase Estimation (QPE); however, noise significantly hinders the performance of today’s quantum computers. Machine learning has the potential to improve the performance of QPE algorithms, especially in the presence of noise. In this work, QPE circuits were simulated with varying levels of depolarizing noise to generate datasets of QPE output. In each case, the phase being estimated was generated with a phase gate, and each circuit modeled was defined by a randomly selected phase. The model accuracy, prediction speed, overfitting level and variation in accuracy with noise level was determined for 5 machine learning algorithms. These attributes were compared to the traditional method of post-processing and a 6x–36 improvement in model performance was noted, depending on the dataset. No algorithm was a clear winner when considering these 4 criteria, as the lowest-error model (neural network) was also the slowest predictor; the algorithm with the lowest overfitting and fastest prediction time (linear regression) had the highest error level and a high degree of variation of error with noise. The XGBoost ensemble algorithm was judged to be the best tradeoff between these criteria due to its error level, prediction time and low variation of error with noise. For the first time, a machine learning model was validated using a 2-qubit datapoint obtained from an IBMQ quantum computer. The best 2-qubit model predicted within 2% of the actual phase, while the traditional method possessed a 25% error.
Quantum computing has the potential to solve problems that are currently intractable to classical computers with algorithms like Quantum Phase Estimation (QPE); however, noise significantly hinders the performance of today’s quantum computers. Machine learning has the potential to improve the performance of QPE algorithms, especially in the presence of noise. In this work, QPE circuits were simulated with varying levels of depolarizing noise to generate datasets of QPE output. In each case, the phase being estimated was generated with a phase gate, and each circuit modeled was defined by a randomly selected phase. The model accuracy, prediction speed, overfitting level and variation in accuracy with noise level was determined for 5 machine learning algorithms. These attributes were compared to the traditional method of post-processing and a 6x–36 improvement in model performance was noted, depending on the dataset. No algorithm was a clear winner when considering these 4 criteria, as the lowest-error model (neural network) was also the slowest predictor; the algorithm with the lowest overfitting and fastest prediction time (linear regression) had the highest error level and a high degree of variation of error with noise. The XGBoost ensemble algorithm was judged to be the best tradeoff between these criteria due to its error level, prediction time and low variation of error with noise. For the first time, a machine learning model was validated using a 2-qubit datapoint obtained from an IBMQ quantum computer. The best 2-qubit model predicted within 2% of the actual phase, while the traditional method possessed a 25% error.
Quantum phase estimation is one of the most fundamental and useful quantum computing algorithms available to researchers, but traditional methods for estimating the phase of a unitary operator acting on its eigenvalue leave information about the phase contained in all of the output from a quantum computer unused. Mean squared error (MSE) for such a scheme is 0.03 for simulated data with and without noise. Machine learning with classical methods, like linear regression (MSE=0.011 for noisy data and 0.0043 for noise-free data) and random forests (MSE=0.01 for noisy data and 0.006 for noise-free data) increase the accuracy of the estimation drastically without requiring additional qubits like the traditional approach. However, neural networks reduce this number further (MSE=0.0077) in the case of noisy data and with noise-free data (MSE=0.003). Examining the performance of neural networks with different modifications also yields insight into their performance on quantum computing output that could be generalized to output from other algorithms and on quantum computers with different numbers of qubits.
In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical approach that consists of the standard QPE circuit and classical post-processing using curve-fitting, where special attention is given to the latter. We show that our approach achieves high precision with optimal Cramér-Rao lower bound performance and is comparable in error resolution with the Variational Quantum Eigensolver and Maximum Likelihood Amplitude Estimation algorithms. Our method could potentially be further extended to the case of estimating multiple phases.
Quantum computing promises unparalleled computational power, but its practical implementation is hampered by quantum noise, which affects the reliability of quantum circuits. This paper addresses the critical challenge of noise classification in NISQ ‘Noisy Intermediate-Scale Quantum’ algorithms, focusing on bit flip, phase flip, and depolarising noise. We introduce a novel balanced quantum noise dataset generated through random quantum circuits, ensuring comprehensive coverage of various noise types and intensities. Additionally, we develop a hybrid quantum-classical machine learning model that achieves over 85% accuracy in classifying bit flip and depolarising noise, and perfect accuracy in detecting phase flip noise under our simulation conditions. Our approach builds on a dual quantum architecture, utilising IBM Qiskit for dataset generation and Pennylane for model training. These simulation results indicate potential improvements for noise-aware modelling and error mitigation; however, we emphasise that translating this performance to physical devices requires further validation due to hardware-specific decoherence and calibration effects.
In this thesis we have implemented three many-body methods in quantum mechanics on quantum computers, namely the Quantum Phase Estimation (QPE) algorithm, the Variational Quantum Eigensolver (VQE) algorithm and the Quantum Adiabatic Time Evolution (QATE) algorithm.We utilized these methods to approximate the ground state energy of the pairing model Hamiltonian.We provided a comparison between the ideal simulation of a quantum computer and a simulation including the noise model from some of IBM's actual quantum devices.For the VQE algortihm, we also run the method on the IBM Q London five-qubit device.As the time complexity (circuit depth) of a quantum algorithm (quantum circuit) is often the bottleneck on current quantum computers, we also introduced a circuit optimization scheme, called Recursive Circuit Optimization, which can be utilized to approximate the action of a quantum circuit by learning the parameters of a parametrized unitary operation and only evaluating small parts of the circuit at a time.We tested out the method by trying to optimize a random circuit, the QATE algorithm and the unitary coupled cluster doubles (UCCD) ansatz.Finally, we implemented a quantum circuit that allows us to encode a real data set into the amplitudes of a quantum state, and we utilized this circuit to implement several realizations of dense and recurrent neural networks on quantum computers.We proposed neural network layers that are consisting of hardware-and parameter-efficient parametrized quantum circuits, and we have made a Python framework to construct and train deep quantum neural networks.We then tested the neural networks by trying to learn a simple non-linear function as well as finding the smallest eigenvalue of the pairing Hamiltonian Full Configuration Interaction (FCI) matrix.We found that all the quantum many-body methods showed promise in providing an upper bound on the ground state energy for the ideal simulation of a quantum computer.When performing the simulation with noise and the execution on the real quantum device however, we found that only the VQE algorithm was able to yield reasonable results due to short circuit depth.Still, the success of the method was found to be dependent on the interaction strength g of the quantum system, as the approximation of the ground state energy started to deviate from the actual value as we increased g.For the recursive circuit optimization of a random circuit, we found that we were able to approximate the state given by the random circuit, and we learned that we should expect some error in the approximation due to finite measurements and the flexibility of the parametrized unitary.When utilizing the recursive optimization scheme to approximate the QATE algorithm, we found that although we were not able to exactly reproduce the action of the operator, we did provide an upper bound to the ground state energy close to the one given by the actual QATE algorithm.In the same time, the circuit depth of the algorithm was drastically decreased.When utilizing the scheme for the VQE algorithm, we got promising results while reducing the circuit depth of the UCCD ansatz.Over to the neural networks, we managed to approximate a non-linear function utilizing a hardware-efficient three layered network, with only three qubits in the intermediate layers.We showed that our proposed neural network are suitable for near-term quantum computers by successfully approximating the lowest eigenvalue of the FCI matrix when running a simulation with the noise model from the IBM Q London five-qubit computer.i I would first like to thank my supervisor, Morten Hjorth-Jensen, for being helpful and motivational throughout my time at the University of Oslo.Your door has always been open when help is needed, which has been a great relief in stressful times.I would also like to thank my friends and family for believing in me and providing emotional support.Your continuous interest in my studies and well-being has meant a lot to me.My next thanks goes to Heidi K. J.I highly appreciate your never-ending support.Finally I would like to thank the computational physics study group.You have been invaluable to me in both a social and educational manner.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.