Quantum oracles are widely adopted in problems, like query oracle in Grover’s algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a given classical function, emerges as a fundamental component in the design and construction of quantum algorithms. Devising methods to optimally implement the bit-flip oracle essentially translates to the efficient synthesis of reversible functions. Prior research has primarily focused on the qubit model, leaving the higher dimensional systems, i.e. qudit model, largely unexplored. By allowing more than two computational bases, qudit model can fully utilize the multi-level nature of the underlying physical mechanism. We propose a method to synthesize even permutations inAdnusing Θ(d) (n− 1)-qudit sub-circuits, which achieve asymptotic optimality in the count of sub-circuits. Moreover, we introduce a technique for synthesizing reversible functions employingO(ndn) two-qudit gates and only a single ancilla. This is asymptotically tight in terms of d and asymptotically almost tight in terms ofn.

Optimizing the depth and number of ancillary qubits in quantum circuits is crucial in quantum computation, given the limitations imposed by current quantum devices. In this article, we introduce an innovative approach for implementing arbitrary symmetric Boolean functions using poly-logarithmic depth quantum circuits with only a logarithmic number of ancillary qubits. Symmetric functions are those whose outputs are dictated solely by the Hamming weight of the inputs. These functions find applications across various domains, including quantum machine learning and arithmetic circuit synthesis. Moreover, by fully leveraging the potential of qutrits, the ancilla count can be further reduced to just one. The key technique involves a novel poly-logarithmic depth quantum circuit designed to compute Hamming weight without the need for ancillary qubits. This quantum circuit for Hamming weight is of independent interest due to its wide-ranging applications, such as in quantum memory, quantum machine learning, and Hamiltonian dynamics simulations.

Quantum arithmetic circuits have attracted extensive attention recently since it plays fundamental roles in many applications of quantum computing. Specifically, quantum circuits for integer multiplication are of great significance to various quantum algorithms, including Shor’s integer factorization and discrete logarithm algorithm. In this article, we design a family of quantum circuits for integer multiplication based on the famous classical integer multiplication algorithm, Schönhage–Strassen algorithm. We have made slight modifications to the algorithm to simplify its quantum circuit implementation. As a result, the quantum circuit we designed has gate depth$O(\log ^{2} n)$. To the best of our knowledge, this is the first poly-logarithmic depth quantum circuit for integer multiplication which keeps the circuit size and the number of ancillary qubits subquadratic. Our design has size$O(n\log n\log \log n)$counted by elementary quantum gates which is the same as the time complexity of the Schönhage–Strassen algorithm, and it consumes$O(n\log n\log \log n)$clean ancillary qubits. In addition, we also utilize a weaker version of Schönhage–Strassen algorithm to give a family of circuits which has depth at the same order$O(\log ^{2} n)$but with significantly smaller constants, while still keeping the size and number of ancillary qubits subquadratic.

One of the fundamental issues in the operation of a mobile communication system is the assignment of channels to cells and to calls. Since the number of channels allocated to a mobile communication system is limited, efficient utilization of these communication channels by using efficient channel assignment strategies is not only desirable but also imperative. This paper presents a novel approach to solving the dynamic channel assignment (DCA) problem by using a form of realtime reinforcement learning known as Q-learning in conjunction with neural network representation. Instead of relying on a known teacher, the system is designed to learn an optimal channel assignment policy by directly interacting with the mobile communication environment. The performance of the Q-learning-based DCA was examined by extensive simulation studies on a 49-cell mobile communication system under various conditions. Comparative studies with the fixed channel assignment (FCA) scheme and one of the best dynamic channel assignment strategies, MAXAVAIL, have revealed that the proposed approach is able to perform better than the FCA in various situations and capable of achieving a performance similar to that achieved by the MAXIAVIAL, but with a significantly reduced computational complexity.

This paper deals with the problem of controlling multivariable nonlinear servomechanisms by means of fuzzy approaches. A specific system under consideration is a passive nonlinear line-of-sight (LOS) stabilization system with strong interactions between two channels. By using the concept of decentralized control, a control structure is developed that is composed of two control loops, each of which is associated with a single-variable fuzzy controller and a decoupling unit. A simplified fuzzy control algorithm is used to implement the fuzzy controller. We propose two novel approaches to designing the decoupling units. The first one is based on the theory of fuzzy reasoning whereas the second scheme relies on the principle of adaptation. Extensive simulation studies on the LOS system have demonstrated the feasibility and effectiveness of the proposed approach.

This paper considers the problem of modeling an unknown system by a rule-based model constructed from measured data. In particular, we address two fundamental issues associated with the rule-based modeling: rule-base construction and rule-base manipulation. A two-step approach consisting of a principal and a refining algorithm has been suggested to extract rules from the available data set. Starting from the notion of product space clustering, we have developed three principal algorithms in which fuzzy concepts and competitive learning are utilized. A particular attention is paid to enabling the algorithms to have self-organizing capability and real-time applicability. Two algorithms have been presented for manipulating the obtained rule-base with novel data, one being a direct application of a fuzzy control algorithm and the other being an optimal algorithm in the sense of least square error with respect to an appropriately chosen cost function. Simulation results on three examples taken from function approximation, time-series prediction, and nonlinear dynamical modeling are given.

This paper describes a general and systematic approach to constructing a multivariable fuzzy model from numerical data through a self-organizing counterpropagation network (SOCPN). Two self-organizing algorithms USOCPN and SSOCPN, being unsupervised and supervised respectively, are introduced. SOCPN can be employed in two ways. In the first place, it can be used as a knowledge extractor by which a set of rules are generated from the available numerical data set. The generated rule-base is then utilized by a fuzzy reasoning model. The second use of the SOCPN is as an online adaptive fuzzy model in which the rule-base in terms of connection weights is updated successively in response to the incoming measured data. The comparative results on three well studied examples suggest that the method has merits of simple structure, fast learning speed, and good modeling accuracy.>

This note describes an approach to integrating fuzzy reasoning systems with radial basis function (RBF) networks and shows how the integrated network can be employed as a multivariable self-organizing and self-learning fuzzy controller. In particular, by drawing some equivalence between a simplified fuzzy control algorithm (SFCA) and a RBF network, we conclude that the RBF network can be interpreted in the context of fuzzy systems and can be naturally fuzzified into a class of more general networks, referred to as FBFN, with a variety of basis functions (not necessarily globally radial) synthesized from each dimension by fuzzy logical operators. On the other hand, as a result of natural generalization from RBF to SFCA, we claim that the fuzzy system like RBF is capable of universal approximation. Next, the FBFN is used as a multivariable rule-based controller but with an assumption that no rule-base exists, leading to a challenging problem of how to construct such a rule-base directly from the control environment. We propose a simple and systematic approach to performing this task by using a fuzzified competitive self-organizing scheme and incorporating an iterative learning control algorithm into the system. We have applied the approach to a problem of multivariable blood pressure control with a FBFN-based controller having six inputs and two outputs, representing a complicated control structure.>