Abstract Quantum computing is a new and exciting field with the potential to solve some of the world’s most challenging problems. Currently, with the rise of quantum computers, the main challenge is the creation of quantum algorithms (under the limitations of quantum physics) and making them accessible to scientists who are not physicists. This study presents a parametrized quantum circuit and its implementation in estimating the distribution measures for discrete value vectors. Various applications can be derived from this method, including information analysis, exploratory data analysis, and machine learning algorithms. This method is unique in providing access to quantum computation and enabling users to run it without prior knowledge of quantum physics. The proposed method was implemented and tested over a dataset and five discrete value distributions with different parameters. The results showed a high level of agreement between the classical computation and the proposed method using quantum computing. The maximum error obtained for the dataset was 5.996%, while for the discrete distributions, a maximum error of 5% was obtained.
Abstract Quantum computing is a new and exciting field with the potential to solve some of the world’s most challenging problems. Currently, with the rise of quantum computers, the main challenge is the creation of quantum algorithms (under the limitations of quantum physics) and making them accessible to scientists who are not physicists. This study presents a parametrized quantum circuit and its implementation in estimating the distribution measures for discrete value vectors. Various applications can be derived from this method, including information analysis, exploratory data analysis, and machine learning algorithms. This method is unique in providing access to quantum computation and enabling users to run it without prior knowledge of quantum physics. The proposed method was implemented and tested over a dataset and five discrete value distributions with different parameters. The results showed a high level of agreement between the classical computation and the proposed method using quantum computing. The maximum error obtained for the dataset was 5.996%, while for the discrete distributions, a maximum error of 5% was obtained.
Quantum computing is a promising emerging field in computational science, attracting significant international research interest. Data representation is crucial to the success of machine learning models, and covariance analysis to determine relationships between pairs of random variables is an essential step in exploratory data analysis. Here we introduce a novel quantum algorithm for covariance approximation and its circuit implementation for discrete-value vectors. The algorithm leverages vital components of quantum computing, including amplitude encoding, the Grover diffusion algorithm for amplitude amplification and the quantum Fourier transform. As a core innovation, we utilize two quantum states and their properties of superposition product states to estimate the covariance between input vectors. Evaluating the quantum algorithm’s performance over five discrete-value distributions, we found high levels of agreement between the classical and quantum computations, with maximum average errors averaging 0.153. Furthermore, the analysis revealed additional applications of the Grover diffusion operator to solve problems.
A possible approach to tackling computationally demanding issues beyond the capabilities of conventional algorithms is the use of quantum circuits, which provide a fundamental foundation for utilizing the power of quantum computation. This abstract examines how quantum circuits are implemented, emphasizing important topics such as circuit optimization, gate operations, and qubit manipulation. We explore different methods of encoding quantum information into topological qubits, trapped ions, and superconducting circuits, among other physical qubit formats. Furthermore, we go over the function of gate operations in quantum circuits, emphasizing crucial gates like phase, Hadamard, and CNOT gates, which serve as the foundation for quantum algorithms. Additionally, we look at methods for maximizing the efficiency and dependability of quantum processing by designing quantum circuits to minimize gate counts, depth, and error rates. To enhance the capabilities of quantum computing, this abstract presents a novel synthesis of quantum neural networks (QNNs) and quantum parameterized circuits. Through the use of parameterized quantum circuits' inherent flexibility, our approach makes it easier to design and optimize quantum circuits with flexible parameters, providing a flexible foundation for a variety of quantum algorithms. Using this amalgamation, we unleash the capacity of quantum computers to address intricate optimization and machine learning assignments with unparalleled effectiveness and expandability. Our solution bridges the gap between traditional machine learning approaches and quantum computing paradigms by enabling the smooth integration of classical data processing techniques with quantum computation. We use quantum states as data representations in our implementation of quantum neural networks, and we optimize trainable parameters to meet predetermined goals. This new paradigm opens up the investigation of the inherent features of quantum states and provides new perspectives on their processing power compared to their classical counterparts. We show, by thorough testing and analysis, how effective quantum parameterized circuits and QNNs are at solving practical problems in a variety of fields. Our work sets the ground for revolutionary breakthroughs in quantum information processing by pushing the boundaries of quantum computation and machine learning integration, offering hitherto unseen insights and solutions to challenging challenges in science, engineering, and beyond.
Parameterized quantum circuits (PQCs), as one of the most promising schemes to realize quantum machine learning algorithms on near-term quantum computers, have been designed to solve machine earning tasks with quantum advantages. In this paper, we explain why PQCs with different structures can achieve generative tasks in the discrete case from the perspective of probability estimation. Although different kinds of PQCs are proposed for generative tasks, the current methods often encounter the following three hurdles: (1) the mode contraction problem; (2) unexpected data are often generated with a high proportion; (3) target data cannot be sampled directly. For the purpose of tackling the above hurdles, we devise Bayesian quantum circuit (BQC) through introducing ancillary qubits to represent prior distributions. BQC advances both generative and semi-supervised quantum circuit learning tasks, where its effectiveness is validated by numerical simulations using the Rigetti Forest platform.
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing workflow, most data processing remains in the classical domain except for running the quantum circuit in the quantum processor. This leaves massive opportunities for classical automation and optimization toward future utilization of quantum computing. We kickstart the first step in this direction by introducing Q-gen, a high-level, parameterized quantum circuit generator incorporating 15 realistic quantum algorithms. Each customized generation function comes with algorithmspecific parameters beyond the number of qubits, providing a large generation volume with high circuit variability. To demonstrate the functionality of Q-gen, we organize the algorithms into 5 hierarchical systems and generate a quantum circuit dataset accompanied by their measurement histograms and state vectors. This dataset enables researchers to statistically analyze the structure, complexity, and performance of large-scale quantum circuits, or quickly train novel machine learning models without worrying about the exponentially growing simulation time. Q-gen is an open-source and multipurpose project that serves as the entrance for users with a classical computer science background to dive into the world of quantum computing.
This monograph is motivated by a number of recent developments that appear to define a possible new role for researchers with an engineering profile. First, there are now several software libraries – such as IBM’s Qiskit, Google’s Cirq, and Xanadu’s PennyLane – that make programming quantum algorithms more accessible, while also providing cloud-based access to actual quantum computers. Second, a new framework is emerging for programming quantum algorithms to be run on current quantum hardware: quantum machine learning. In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parametrized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.
Quantum computing is a new and advanced topic that refers to calculations based on the principles of quantum mechanics. It makes certain kinds of problems be solved easier compared to classical computers. This advantage of quantum computing can be used to implement many existing problems in different fields incredibly effectively. One important field that quantum computing has shown great results in machine learning. Until now, many different quantum algorithms have been presented to perform different machine learning approaches. In some special cases, the execution time of these quantum algorithms will be reduced exponentially compared to the classical ones. But at the same time, with increasing data volume and computation time, taking care of systems to prevent unwanted interactions with the environment can be a daunting task and since these algorithms work on machine learning problems, which usually includes big data, their implementation is very costly in terms of quantum resources. Here, in this paper, we have proposed an approach to reduce the cost of quantum circuits and to optimize quantum machine learning circuits in particular. To reduce the number of resources used, in this paper an approach including different optimization algorithms is considered. Our approach is used to optimize quantum machine learning algorithms for big data. In this case, the optimized circuits run quantum machine learning algorithms in less time than the original ones and by preserving the original functionality. Our approach improves the number of quantum gates by 10.7% and 14.9% in different circuits respectively. This is the amount of reduction for one iteration of a given sub-circuit U in the main circuit. For cases where this sub-circuit is repeated more times in the main circuit, the optimization rate is increased. Therefore, by applying the proposed method to circuits with big data, both cost and performance are improved.