Abstract Quantum computing uses quantum resources provided by the underlying quantum nature of matter to enhance classical computation. However, the current Noisy Intermediate-Scale Quantum (NISQ) era in quantum computing is characterized by the use of quantum processors comprising from a few tens to, at most, a few hundreds of physical qubits without implementing quantum error correction techniques. This limits the scalability in the implementation of quantum algorithms. Digital-analog quantum computing (DAQC) has been proposed as a more resilient alternative quantum computing paradigm to outperform digital quantum computation within the NISQ era framework. It arises from adding the flexibility provided by fast single-qubit gates to the robustness of analog quantum simulations. Here, we perform a careful comparison between the digital and digital-analog paradigms under the presence of noise sources. The comparison is illustrated by comparing the performance of the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single- and two-qubit noise sources. Indeed, we obtain that when the different noise channels usually present in superconducting quantum processors are considered, the fidelity of these algorithms for the digital-analog paradigm outperforms the one obtained for the digital approach. Additionally, this difference grows when the size of the processor scales up, making DAQC a sensible alternative paradigm in the NISQ era. Finally, we show how to adaptthe DAQC paradigm to quantum error mitigation techniques for canceling different noise sources, including the bang error.

Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and combinatorial optimization. We study five problems. The first three deal with quantum algorithms for computational problems in science and engineering, including quantum simulation of physical systems. In particular, we study quantum algorithms for numerical computation, for the approximation of ground and excited state energies of the Schr\"odinger equation, and for Hamiltonian simulation with applications to physics and chemistry. The remaining two deal with quantum algorithms for approximate optimization. We study the performance of the quantum approximate optimization algorithm (QAOA), and show a generalization of QAOA, the $\textit{quantum}$ $\textit{alternating}$ $\textit{operator}$ $\textit{ansatz}$, particularly suitable for constrained optimization problems and low-resource implementations on near-term quantum devices.

AbstractDigital quantum computers provide a computational framework for solving the Schrödinger equation for a variety of many‐particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed remarkable growth, notwithstanding the limitations of existing quantum hardware, especially as a tool for electronic structure computations in molecules. In this review, we provide a self‐contained introduction to emerging algorithms for the simulation of Hamiltonian dynamics and eigenstates, with emphasis on their applications to the electronic structure in molecular systems. Theoretical foundations and implementation details of the method are discussed, and their strengths, limitations, and recent advances are presented.This article is categorized under: Quantum Computing > Algorithms Electronic Structure Theory > Ab Initio Electronic Structure Methods Quantum Computing > Theory Development

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences.

This research investigates the potential of quantum computing in production planning and addresses the limitations of conventional computing approaches. Traditional methods have been partially effective, but they struggle to solve complex optimization problems, accurately predict demand, and manage supply chains efficiently. The unique computational capabilities of quantum computing offer promising solutions to surmount these obstacles and revolutionize production planning processes. This study seeks to bridge the gap between quantum computing and production planning by analyzing the benefits, limitations, and challenges of its applicability in this field. It proposes customized algorithms and methodologies for leveraging quantum computation to enhance production planning efficiency, cost reduction, and decision-making processes. The research demonstrates the potential of quantum algorithms to minimize total production costs while appeasing demand and resource constraints through a numerical example and mathematical formulation. The results emphasize the advantages of quantum computing in terms of cost reduction, enhanced efficiency, and scalability. Comparisons with conventional methods illuminate the benefits and drawbacks of quantum computing in production planning. This research contributes to the development of novel strategies to improve production planning efficiency, lower costs, and enhance decision-making processes, allowing organizations to leverage quantum computing for optimized production operations

With the development of science and technology, it is difficult for traditional computers to solve cutting-edge problems due to the lack of computing power, and the importance of quantum computers is increasing day by day. This article starts with the simple principle of quantum computing, introduces the most advanced quantum computing instruments and quantum computing algorithms, and points out the application prospects in medicine, chemistry and other fields. This paper explains the basic principles of quantum computing algorithms, their efficiency over traditional algorithms, and focuses on the Shor algorithm and its variations. In terms of applications, the quantum computer Zu Chongzhi and its contribution to the sampling problem of quantum random circuits are introduced. This paper makes a certain analysis of the limitations of quantum computing, and gives the future development goals in a targeted manner. Besides, we summarize popular quantum computing algorithms and applications, and make contributions to the promotion and development of quantum computing. Overall, these results shed light on guiding further exploration of how to improve the computational efficiency of quantum computers.

We are interested in fundamental limits to computation imposed by physical constraints. In particular, the physical laws of motion constrain the speed at which a computer can transition between well-defined states. Here, we discuss speed limits in the context of quantum computing. We review some relevant parts of the theory of Finsler metrics on Lie groups and homogeneous spaces such as the special unitary groups and complex projective spaces. We show how these constructions can be applied to analysing the limit to the speed of quantum information processing operations in constrained quantum systems with finite dimensional Hilbert spaces of states. We demonstrate the approach applied to a spin chain system.

The emergence of noisy intermediate-scale quantum (NISQ) computers has important consequences for cryptographic algorithms. It is theoretically well-established that key algorithms used in cybersecurity are vulnerable to quantum computers due to the fact that theoretical security guarantees, designed based on algorithmic complexity for classical computers, are not sufficient for quantum circuits. Many different quantum algorithms have been developed, which have potentially broad applications on future computing systems. However, this potential depends on the continued maturation of quantum hardware, which remains an area of active research and development. Theoretical limits provide an upper bound on the performance for algorithms. In practice, threats to encryption can only be accurately be assessed in the context of the rapidly evolving hardware and software landscape. Software co-design refers to the concurrent design of software and hardware as a way to understand the limitations of current capabilities and develop effective strategies to advance the state of the art. Since the capabilities for classical computation currently exceed quantum capabilities, quantum emulation techniques can play an important role in the co-design process. In this paper, we describe how the {\em cuQuantum} environment can support quantum algorithm co-design activities using widely-available commodity hardware. We describe how emulation techniques can be used to assess the impact of noise on algorithms of interest, and identify limitations associated with current hardware. We present our analysis in the context of areas of priority for cybersecurity and cryptography in particular since these algorithms are extraordinarily consequential for securing information in the digital world.

Quantum computers are capable of ultra fast computation in the fields where classical computers fail. Even though quantum computers are nowhere near commercialization, many researchers have developed quantum algorithms in fields such as modern encryption and molecular simulation, which, in theory, are exponentially faster than their classical counterparts. In this case, this paper will discuss the advantages of quantum computers over classical computers in those fields by examining and analyzing the various quantum algorithms. To be specific, the develop routine as well as detail examples will be exhibited to illustrate the differences and preferences. In addition, this study will also fully aware of the challenges that quantum computing researchers are facing. On this basis, possible limitations of quantum computers are also presented. The aim is to promote interest in quantum computing by introducing their supremacy in modern encryption and biological science. These results shed light on guiding further exploration of quantum computing algorithms.

Since the mid-1990s theoretical quadratic exponential and polynomial Quantum Computing (QC) speedup algorithms have been discussed. Recently the advent of relativistic information processing (RIP) introducing a relativistic qubit (r-qubit) with additional degrees of freedom beyond the current Hilbert space Bloch 2-sphere qubit formalism extended theory has appeared. In this work a penultimate form of QC speedup – Instantaneous Quantum Computing Algorithms (IQCA) is proposed. Discussion exists on passing beyond the quantum limits of locality and unitarity heretofore restricting the evolution of quantum systems to the standard Copenhagen Interpretation. In that respect as introduced in prior work an ontological-phase topological QC avails itself of extended modeling. As well-known by EPR experiments instantaneous connectivity exists inherently in the nonlocal arena. As our starting point we utilize Bohm’s super-implicate order where inside a wave packet a super-quantum potential introduces nonlocal connectivity. Additionally EPR experiments entangle simultaneously emitted photon pairs by parametric down-conversion. Operating an IQCA requires a parametric up-conversion cycle an M-Theoretic Unified Field Mechanical (MUFM) set of topological transformations beyond the current Galilean Lorentz-Poincairé transforms of the standard model (SM). Yang-Mills Kaluza-Klein (YM-KK) correspondence is shown to provide a path beyond the semi-quantum limit to realize the local-nonlocal duality required to implement IQCA.