In this paper, we study the string matching problem. We design a quantum string-matching algorithm for noisy intermediate-scale quantum (NISQ) computers, given the current leading quantum processing units (QPUs) having no more than a few hundred qubits [16]. We also compare the performance of classic algorithms and quantum algorithms under various combinations. Our study provides a comprehensive and quantitative guide for users to choose appropriate classic or quantum algorithms for their string matching problems.
In this paper, we study the string matching problem. We design a quantum string-matching algorithm for noisy intermediate-scale quantum (NISQ) computers, given the current leading quantum processing units (QPUs) having no more than a few hundred qubits [16]. We also compare the performance of classic algorithms and quantum algorithms under various combinations. Our study provides a comprehensive and quantitative guide for users to choose appropriate classic or quantum algorithms for their string matching problems.
A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, we provide a thorough summary of NISQ computational paradigms and algorithms. We discuss the key structure of these algorithms, their limitations, and advantages. We additionally provide a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices.
Quantum computing has the potential to solve complex problems that are outside the scope of classical systems, making it a standard shifter. Current devices, which are considered as Noisy Intermediate-Scale Quantum (NISQ) systems, are insufficient in their practical utility due to hardware limitations, error rates, and qubit counts. The dynamic growths wanted to exceed the NISQ era and grow scalable quantum algorithms and architectures that can achieve useful quantum benefit in real-world applications are reviewed in this research. This research gives a comprehensive examination of the complications in scaling quantum systems, adjacent resource efficacy, qubit connectivity, and error correction. In addition to connecting architectural innovations like modular quantum computing, error-resilient circuit design, and distributed quantum systems, the paper provides new hybrid quantum-classical algorithms planned to exploit performance in noisy environments. Results from benchmarking in arenas like machine learning, optimization, and quantum chemistry show how these methods can provide short-term quantum benefit. Lastly, this paper proposes a research roadmap for quantum computing that highlights the requirement of co-designing algorithms, software, and hardware. The goal of this effort is to straighten the progress of quantum systems that can resolve problems in the real world at scale by addressing the inadequacies of NISQ devices and emphasizing scalable solutions.
String matching stands as a cornerstone problem in computer science, finding extensive application in many fields, such as data mining, text retrieval, and bioinformatics, just to cite a few. Its essence lies in identifying all occurrences of a specified pattern, typically denoted by length m, within a text of length n. Despite its seemingly straightforward formulation, the problem has sparked a plethora of solutions, stemming from diverse computational paradigms and approaches. Classical solutions exhibit a worst-case time complexity of Θ(n), contrasting with the capability of quantum computation to achieve a [EQUATION] complexity using Grover search, thereby realizing a quadratic speed-up compared to classical methods. This article presents a first practical implementation of a quantum circuit tailored to address string matching, particularly focusing on binary strings. The exposition delves into the technical intricacies of the implementation, which leverages the Qiskit open-source toolkit developed by IBM. By elucidating various algorithmic nuances overlooked in prior theoretical formulations, our solution serves as a conduit between the realms of text processing and quantum computing, fostering cross-disciplinary dialogue and innovation. While current real-world hardware lacks the capability to execute the proposed circuit, particularly when dealing with lengthy texts, this study presents experimental results from a simulation of the circuit on classical hardware, serving to validate the efficacy of the proposed implementation.
Abstract Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's algorithm was designed without considering the physical resources, such as depth, in the real implementations. Therefore, Grover's algorithm can be improved for NISQ devices. In this paper, we demonstrate how to implement quantum search algorithms better on NISQ devices. We present detailed benchmarks of the five-qubit quantum search algorithm on different quantum processors, including IBMQ, IonQ, and Honeywell quantum devices. We report the highest success probability of the five-qubit search algorithm compared to previous works. Our results show that designing the error-aware quantum search algorithms is possible, which can maximally harness the power of NISQ computers.
<!--HTML-->A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this talk, I provide an overview of NISQ algorithms, their limitations and potential advantages.
In 2019 a quantum computer took 200 seconds for a task for which a state-of-the-art classical supercomputer would need roughly 10,000 years. Quantum supremacy was shown and the development of quantum technology proceeds quickly. However, several aspects limit the implementation and execution of quantum circuits. The vendors of quantum computers provide their own proprietary software development kit (SDK) to execute quantum circuits on their quantum processing units (QPUs). Furthermore, the computers differ regarding various properties like the native gate set and the qubit connectivity. Therefore, quantum circuits cannot be executed on arbitrary QPUs, but there exists a tight coupling between a QPU and a quantum algorithm implementation. To decouple the development of a circuit from the QPU, this thesis proposes a quantum circuit analysis and transpilation framework that integrates quantum SDKs and enables the comparison and analysis of quantum circuits, as well as the export of executable circuits in the respective assembly language of QPUs from different vendors. Currently existing QPUs, also called Noisy Intermediate-Scale Quantum (NISQ) machines, have a very limited number of qubits and are prone to failure. Thus, the integration of different QPUs enhances the possibilities of quantum circuit developers and avoids the SDK lock-in. Additionally, a graphical user interface is developed to support the user in the whole process of importing, visualizing, editing, and simulating a quantum circuit, as well as, choosing a suitable QPU to execute the circuit.