27 research outputs found
Quantum belief function
The belief function in Dempster Shafer evidence theory can express more
information than the traditional Bayesian distribution. It is widely used in
approximate reasoning, decision-making and information fusion. However, its
power exponential explosion characteristics leads to the extremely high
computational complexity when handling large amounts of elements in classic
computers. In order to solve the problem, we encode the basic belief assignment
(BBA) into quantum states, which makes each qubit correspond to control an
element. Besides the high efficiency, this quantum expression is very conducive
to measure the similarity between two BBAs, and the measuring quantum algorithm
we come up with has exponential acceleration theoretically compared to the
corresponding classical algorithm. In addition, we simulate our quantum version
of BBA on Qiskit platform, which ensures the rationality of our algorithm
experimentally. We believe our results will shed some light on utilizing the
characteristic of quantum computation to handle belief function more
conveniently
QAOA with fewer qubits: a coupling framework to solve larger-scale Max-Cut problem
Maximum cut (Max-Cut) problem is one of the most important combinatorial
optimization problems because of its various applications in real life, and
recently Quantum Approximate Optimization Algorithm (QAOA) has been widely
employed to solve it. However, as the size of the problem increases, the number
of qubits required will become larger. With the aim of saving qubits, we
propose a coupling framework for designing QAOA circuits to solve larger-scale
Max-Cut problem. This framework relies on a classical algorithm that
approximately solves a certain variant of Max-Cut, and we derive an
approximation guarantee theoretically, assuming the approximation ratio of the
classical algorithm and QAOA. Furthermore we design a heuristic approach that
fits in our framework and perform sufficient numerical experiments, where we
solve Max-Cut on various -vertex Erd\H{o}s-R\'enyi graphs. Our framework
only consumes qubits and achieves approximation ratio on average,
which outperforms the previous methods showing (quantum algorithm
using the same number of qubits) and (classical algorithm). The
experimental results indicate our well-designed quantum-classical coupling
framework gives satisfactory approximation ratio while reduces the qubit cost,
which sheds light on more potential computing power of NISQ devices
Optimization of CNOT circuits on topological superconducting processors
We focus on optimization of the depth/size of CNOT circuits under topological
connectivity constraints. We prove that any -qubit CNOT circuit can be
paralleled to depth with ancillas for -dimensional grid
structure. For the high dimensional grid topological structure in which every
quibit connects to other qubits, we achieves the asymptotically
optimal depth with only ancillas. We also consider the
synthesis without ancillas. We propose an algorithm uses at most CNOT
gates for arbitrary connected graph, considerably better than previous works.
Experiments also confirmed the performance of our algorithm. We also designed
an algorithm for dense graph, which is asymptotically optimal for regular
graph. All these results can be applied to stabilizer circuits
A Neutrosophic Approach Based on TOPSIS Method to Image Segmentation
Neutrosophic set (NS) is a formal framework proposed recently. NS can not only describe the incomplete information in the decision-making system but also depict the uncertainty and inconsistency, so it has applied successfully in several fields such as risk assessment, fuzzy decision and image segmentation. In this paper, a new neutrosophic approach based on TOPSIS method, which can make full use of NS information, is proposed to separate the graphics. Firstly, the image is transformed into the NS domain. Then, two operations, a modified alpha-mean and the beta-enhancement operations are used to enhance image edges and to reduce uncertainty. At last, the segmentation is achieved by the TOPSIS method and the modified fuzzy c-means (FCM). Simulated images and real images are illustrated that the proposed method is more effective and accurate in image segmentation
Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
Quantum computing is a game-changing technology for global academia, research
centers and industries including computational science, mathematics, finance,
pharmaceutical, materials science, chemistry and cryptography. Although it has
seen a major boost in the last decade, we are still a long way from reaching
the maturity of a full-fledged quantum computer. That said, we will be in the
Noisy-Intermediate Scale Quantum (NISQ) era for a long time, working on dozens
or even thousands of qubits quantum computing systems. An outstanding
challenge, then, is to come up with an application that can reliably carry out
a nontrivial task of interest on the near-term quantum devices with
non-negligible quantum noise. To address this challenge, several near-term
quantum computing techniques, including variational quantum algorithms, error
mitigation, quantum circuit compilation and benchmarking protocols, have been
proposed to characterize and mitigate errors, and to implement algorithms with
a certain resistance to noise, so as to enhance the capabilities of near-term
quantum devices and explore the boundaries of their ability to realize useful
applications. Besides, the development of near-term quantum devices is
inseparable from the efficient classical simulation, which plays a vital role
in quantum algorithm design and verification, error-tolerant verification and
other applications. This review will provide a thorough introduction of these
near-term quantum computing techniques, report on their progress, and finally
discuss the future prospect of these techniques, which we hope will motivate
researchers to undertake additional studies in this field.Comment: Please feel free to email He-Liang Huang with any comments,
questions, suggestions or concern