Design And Implementation Of Variational Quantum Algorithms Under Noisy Conditions

Computing power is the core driving force behind the development of information technology.Quantum computing,as a new computing paradigm,exhibits extremely strong parallel acceleration capabilities in solving specific problems and has the potential to bring disruptive impacts to fields such as big data analysis,artificial intelligence,and cryptography.On current Noisy Intermediate-Scale Quantum computing devices,traditional quantum algorithms,such as the Shor’s algorithm and Grover’s algorithm,struggle in achieving high-fidelity implementations.Variational quantum computing,as a hybrid quantum-classical computing model,employs quantum circuit structures that are easy to implement physically and possesses certain noise resilience,thereby offering promising prospects for near-term applications of quantum computing.This thesis conducts a systematic study around the design and implementation of variational quantum algorithms,with the following main achievements:1.At the algorithm design level,methods for enhancing the performance of variational quantum computing are investigated from the perspectives of data loading/readout and circuit construction.ⅰ.Design and implementation of loading/readout schemes with quantum advantage: Quantum data loading,as a mapping from classical data to quantum states,is a prerequisite step for quantum computing.Although qubits can store more information than classical bits,the collapsibility of quantum measurements and the unclonability of quantum states constrain the amount of information that can be extracted from qubits.This limitation makes it challenging for loading and readout schemes based on qubits to demonstrate advantages compared to classical bit-based schemes.This thesis proposes a new quantum loading/readout scheme based on non-orthogonal measurement operators,which has a larger representation range compared to classical schemes with the same number of bits.Furthermore,a class of node attack problems is designed,which is based on loading and storing high-dimensional network attack scenarios using a small number of bits and maximizing attack gains.The thesis theoretically proves that node attack strategies based on quantum loading/readout schemes are more effective compared to classical optimal solutions.Finally,a variational triangular polarimeter,which can be used for arbitrary ternary Positive Operator Valued Measurements,is designed based on linear optical quantum computing platforms,achieving high-precision implementation of the designed quantum loading/readout scheme.Experiments show that quantum-based node attacks yield gains that are generally 30 times higher than those of classical optimal solutions,verifying the quantum advantage under noisy conditions.This work provides a direction for the development of data loading/readout design and advantage exploration for quantum algorithms.ⅱ.Design of variational quantum circuit training methods: In variational quantum computing,single-qubit gates can adjust parameters flexibly and continuously optimize through iterations during training,while two-qubit gates used to connect qubits are difficult to parameterize and typically remain unchanged.This fixed pattern of the variational quantum circuit structure constrains its optimization space,resulting in a lack of universality in solving problems for variational quantum algorithms.This thesis defines the “presence” and “absence” of quantum gates as binary parameters of two-qubit gates and embeds these binary parameters into continuous parameter space.It derives the gradient calculation formula for two-qubit gate parameters and,borrowing from classical machine learning techniques for Binary Neural Networks,designs a gradientbased variational quantum circuit training method.Numerical simulation results show that compared to fixed-structure variational quantum computing,this method achieves higher solution accuracy with the same number of iterations and reduces the average number of two-qubit gates used by 45% and the average circuit depth by 69%.This work effectively enhances the performance of variational quantum computing and lays the foundation for its large-scale implementation on near-term quantum computing devices.2.At the algorithm implementation level,techniques for error suppression and algorithm acceleration in experimental implementation are studied.ⅰ.Evaluating the resilience of variational quantum algorithms to leakage noise:Ideal qubits typically have only two energy levels,but in practical systems,qubits may be excited to higher energy levels due to level crossing,known as leakage noise.Due to the lack of detection and correction approaches,this noise easily accumulates during circuit operation,posing a serious obstacle to large-scale implementation of quantum computing.Variational quantum computing is generally believed to partially offset the adverse effects of noise due to its characteristic of result feedback adjustment,known as “noise resilience”.However,the noise resilience of variational quantum computing against leakage noise has not been studied.This thesis analyzes the performance of variational quantum computing under leakage noise conditions,proposes an expressibility measure to predict the actual operational performance for general noisy variational quantum computing,and benchmarks the expressibility value of variational quantum computing and its performance on data fitting and classification applications based on typical leakage noise models.The results show that both by predictive expressibility and by actual performance,variational quantum computing struggles to resist the adverse effects of leakage noise,as its errors increase with the increasing of leakage probability and circuit depth.This work points out the limitations of variational quantum computing in noise resilience.ⅱ.Study on noise-resilient quantum state compression readout method: In various quantum computing implementation systems,readout noise is usually an order of magnitude larger than other noises.Moreover,as the system size increases,multi-qubit readout noise will increase exponentially.Traditional error suppression methods struggle to reduce the impact of this noise due to the common correlation between the noise in each qubit.This thesis designs a quantum state compression readout method,which compresses the quantum state into a set of single-qubit states for measurements,and then efficiently restores the information of the original quantum state from single-qubit measurement data.Since only single-qubit measurements are involved,this method directly avoids multi-qubit correlated readout noise,achieving exponential suppression of readout noise.Compared to other error suppression methods,this method avoids largescale readout noise calibration and inversion,and does not rely on simplified assumptions about the readout noise models.Numerical simulation results show that under the noise level of near-term quantum computing platforms,using compression readout achieves higher readout accuracy compared to other error suppression methods with the same number of measurements,and this advantage continues to increase with the increasing system size.This work provides a new solution for large-scale quantum computing implementation.ⅲ.Study on accelerated implementation of a class of variational quantum algorithms based on active learning: Variational quantum algorithms require a large amount of training data to operate.Repeated preparation and labeling of quantum data consume considerable experimental resources,increasing the training cost of variational quantum computing parameters and slowing down its operation speed.This thesis introduces active learning strategies into the training process of variational quantum computing,accelerates algorithm operation by analyzing data features,evaluating model needs,and selecting data subsets that are most useful for training.Furthermore,programmable linear optical experimental techniques are developed to schedule and automatically conduct expectation measurements,gradient calculations,and parameter iterations for variational quantum computing.Finally,for quantum state classification problems,three variational quantum circuits are built,and both the accelerated implementation methods and conventional methods are tested on these models.Experiment results show that the performance of implemented variational quantum classifiers is highly consistent with numerical simulations,achieving the theoretical upper bound of the models’ classification power.In training,active learning reduces the data labeling requirements by 66%and speeds up variational quantum computing by 88% on average.This work advances variational quantum algorithms toward practical applications.