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Papers on “quantum computing algorithms speedup”

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1. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

   Paolo Giannozzi, Stefano Baroni, Nicola Bonini, et al. · 2009 · Journal of Physics Condensed Matter · 29,300 cites

   QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by

2. Quantum Computing in the NISQ era and beyond

   John Preskill · 2018 · Quantum · 8,676 cites

   Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and,

3. Quantum supremacy using a programmable superconducting processor

   Frank Arute, Kunal Arya, Ryan Babbush, et al. · 2019 · Nature · 7,184 cites

   The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2–7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one i

4. A variational eigenvalue solver on a photonic quantum processor

   Alberto Peruzzo, Jarrod R. McClean, Peter Shadbolt, et al. · 2014 · Nature Communications · 4,733 cites

   Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconf

5. Quantum Machine Learning: Algorithms and Applications in Quantum Computing

   P. Deshmukh, Benjamin Carter · 2025 · International Journal on Advanced Electrical and Computer Engineering · 4,726 cites

   Quantum Machine Learning (QML) is an emerging interdisciplinary field that integrates quantum computing with classical machine learning techniques to enhance computational efficiency and solve complex problems beyond the capabilities of classical systems. This paper explores fundamental QML algorithms, including quantum-enhanced data processing, quantum neural networks, and quantum support vector machines. We discuss how quantum speedup can be achieved through quantum parallelism and entanglement, leading to improvements in optimization and data classification tasks. Additionally, we highlight applications of QML in areas such as drug discovery, financial modeling, and cryptography. While cu

6. Quantum Algorithm for Linear Systems of Equations

   Aram W. Harrow, Avinatan Hassidim, Seth Lloyd · 2009 · Physical Review Letters · 3,376 cites

   Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix $A$ and a vector $\stackrel{\ensuremath{\rightarrow}}{b}$, find a vector $\stackrel{\ensuremath{\rightarrow}}{x}$ such that $A\stackrel{\ensuremath{\rightarrow}}{x}=\stackrel{\ensuremath{\rightarrow}}{b}$. We consider the case where one does not need to know the solution $\stackrel{\ensuremath{\rightarrow}}{x}$ itself, but rather an approximation of the expectation value of some operator associated with $\stackrel{\ensuremath{\rightarrow}}{x}$, e.g., ${\stackrel{\ensuremath{\rightarrow}}{x}}^{\ifmmode\dagger\else\textdagger\fi{}}M\stackrel{\ensurema

7. Variational quantum algorithms

   M. Cerezo, Andrew Arrasmith, Ryan Babbush, et al. · 2021 · Nature Reviews Physics · 3,231 cites

8. Noisy intermediate-scale quantum algorithms

   Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, et al. · 2022 · Reviews of Modern Physics · 1,773 cites

   Noisy quantum computers can in principle perform reliable quantum computations, but truly scalable systems require noise levels lower than are presently achieved. Still, moderate-complexity computations can be performed. This review discusses what is possible in this ``noisy intermediate scale'' quantum (NISQ) era. Topic areas include the simulation of many-body physics and chemistry, combinatorial optimization, and machine learning. It is evident that the NISQ era has produced new paradigms for programming that will be built upon as quantum computers are further perfected.