Explore the vast range of titles available.

The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem. However, Shor’s algorithm involves complex modular exponentiation computation, which leads to the construction of complicated quantum circuits. Moreover, the precision of continued fraction computations in Shor’s algorithm is influenced by the number of qubits, making it difficult to implement the algorithm on Noisy Intermediate-Scale Quantum (NISQ) computers. To address these issues, this paper proposes variational quantum computation integer factorization (VQCIF) algorithm based on variational quantum algorithm (VQA). Inspired by classical computing, this algorithm utilizes the parallelism of quantum computing to calculate the product of parameterized quantum states. Subsequently, the quantum multi-control gate is used to map the product satisfying p q = N onto an auxiliary qubit. Then the variational quantum circuit is adjusted by the optimizer, and it is possible to obtain a prime factor of the integer N with a high probability. While maintaining generality, VQCIF has a simple quantum circuit structure and requires only 2 n + 1 qubits. Furthermore, the time complexity is exponentially accelerated. VQCIF algorithm is implemented using the Qiskit framework, and tests are conducted on factorization instances to demonstrate its feasibility.

We present the enhanced feature quantum autoencoder, or EF-QAE, a variational quantum algorithm capable of compressing quantum states of different models with higher fidelity. The key idea of the algorithm is to define a parameterized quantum circuit that depends upon adjustable parameters and a feature vector that characterizes such a model. We assess the validity of the method in simulations by compressing ground states of the Ising model and classical handwritten digits. The results show that EF-QAE improves the performance compared to the standard quantum autoencoder using the same amount of quantum resources, but at the expense of additional classical optimization. Therefore, EF-QAE makes the task of compressing quantum information better suited to be implemented in near-term quantum devices.

Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly initialized parameterized quantum circuits (PQCs) in the region of vanishing gradients. We show that using the NES gradient estimator the exponential decrease in variance can be alleviated. We implement two specific approaches, the exponential and separable NES, for parameter optimization of PQCs and compare them against standard gradient descent. We apply them to two different problems of ground state energy estimation using variational quantum eigensolver and state preparation with circuits of varying depth and length. We also introduce batch optimization for circuits with larger depth to extend the use of ES to a larger number of parameters. We achieve accuracy comparable to state-of-the-art optimization techniques in all the above cases with a lower number of circuit evaluations. Our empirical results indicate that one can use NES as a hybrid tool in tandem with other gradient-based methods for optimization of deep quantum circuits in regions with vanishing gradients.

For a large number of tasks, quantum computing demonstrates the potential for exponential acceleration over classical computing. In the NISQ era, variable-component subcircuits enable applications of quantum computing. To reduce the inherent noise and qubit size limitations of quantum computers, existing research has improved the accuracy and efficiency of Variational Quantum Algorithm (VQA). In this paper, we explore the various ansatz improvement methods for VQAs at the gate level and pulse level, and classify, evaluate and summarize them.

Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations only requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate its effectiveness, efficiency, and advantages with the two-dimensional Heisenberg model and the Fermi–Hubbard chain. Numerical experiments show that MBHVA can have similar performance as circuit-based ansatz, and is expected to reduce operation counts during execution compared to quantum circuits, bringing the advantage of running time. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in the noisy intermediate-scale quantum era, especially in the presence of large multi-qubit rotation operations.

Variational quantum algorithms (VQAs) are widely applied in the noisy intermediate-scale quantum era and are expected to demonstrate quantum advantage. However, training VQAs faces difficulties, one of which is the so-called barren plateaus (BPs) phenomenon, where gradients of cost functions vanish exponentially with the number of qubits. In this paper, inspired by transfer learning, where knowledge of pre-solved tasks could be further used in a different but related work with training efficiency improved, we report a parameter initialization method to mitigate BP. In the method, a small-sized task is solved with a VQA. Then the ansatz and its optimum parameters are transferred to tasks with larger sizes. Numerical simulations show that this method could mitigate BP and improve training efficiency. A brief discussion on how this method can work well is also provided. This work provides a reference for mitigating BP, and therefore, VQAs could be applied to more practical problems.

In this study, the PennyLane quantum device simulator was used to investigate quantum and hybrid, quantum/classical physics-informed neural networks (PINNs) for solutions to both transient and steady-state, 1D and 2D partial differential equations. The comparative expressibility of the purely quantum, hybrid and classical neural networks is discussed, and hybrid configurations are explored. The results show that (1) for some applications, quantum PINNs can obtain comparable accuracy with less neural network parameters than classical PINNs, and (2) adding quantum nodes in classical PINNs can increase model accuracy with less total network parameters for noiseless models.

Machine learning has achieved dramatic success in a broad spectrum of applications. Its interplay with quantum physics may lead to unprecedented perspectives for both fundamental research and commercial applications, giving rise to an emergent research frontier of quantum machine learning. Along this line, quantum classifiers, which are quantum devices that aim to solve classification problems in machine learning, have attracted tremendous attention recently. In this review, we give a relatively comprehensive overview for the studies of quantum classifiers, with a focus on recent advances. First, we will review a number of quantum classification algorithms, including quantum support vector machines, quantum kernel methods, quantum decision tree classifiers, quantum nearest neighbor algorithms, and quantum annealing based classifiers. Then, we move on to introduce the variational quantum classifiers, which are essentially variational quantum circuits for classifications. We will review different architectures for constructing variational quantum classifiers and introduce the barren plateau problem, where the training of quantum classifiers might be hindered by the exponentially vanishing gradient. In addition, the vulnerability aspect of quantum classifiers in the setting of adversarial learning and the recent experimental progress on different quantum classifiers will also be discussed.

Variational quantum algorithms are among the most prominent methods in quantum computing, with applications in quantum machine learning, quantum simulation, and related fields. However, as the number of qubits grows, these algorithms often encounter the barren-plateau phenomenon, which severely limits their scalability. In this work, we introduce a novel parameter-initialization strategy based on Gaussian mixture models. We rigorously prove that for a hardware-efficient ansatz initialized in the |0⟩⊗N state, our scheme avoids barren plateaus regardless of circuit depth, qubit count, or choice of cost function. Specifically, the lower bound on the initial gradient norm provided by our method remains independent of the number of qubits Building on this foundation, we validate our theoretical results through numerical experiments, including variational ground-state searches for Hamiltonians, to demonstrate the practical effectiveness of our approach. Our findings highlight the critical role of Gaussian mixture model-based initialization in enhancing the trainability of quantum circuits and offer valuable guidance for future theoretical and experimental advances in quantum machine learning.

We design a variational quantum algorithm (VQA) to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated with the concept of the minimal potential energy, we not only present in-depth discussion on the cost-efficient & noise-robust design of quantum circuits that are essential for evaluation of the objective function, but, more remarkably, employ the proposed algorithm to calculate bias-dependent spatial distributions of electric fields in semiconductor systems that are described with a two-dimensional domain and up to 10-qubit circuits. Extending the application scope to multi-dimensional problems with mixed boundary conditions for the first time, fairly solid computational results of this work clearly demonstrate the potential of VQAs to tackle Poisson equations derived from physically meaningful problems.