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Research papers on Quantum computing algorithms

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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 · 29,295 citations

    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

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  2. Quantum Computing in the NISQ era and beyond

    John Preskill · 2018 · Quantum · 8,668 citations

    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,

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  3. Quantum supremacy using a programmable superconducting processor

    Frank Arute, Kunal Arya, Ryan Babbush, et al. · 2019 · Nature · 7,182 citations

    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

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  4. A variational eigenvalue solver on a photonic quantum processor

    Alberto Peruzzo, Jarrod R. McClean, Peter Shadbolt, et al. · 2014 · Nature Communications · 4,732 citations

    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

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  6. Quantum Algorithm for Linear Systems of Equations

    Aram W. Harrow, Avinatan Hassidim, Seth Lloyd · 2009 · Physical Review Letters · 3,375 citations

    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

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  8. Noisy intermediate-scale quantum algorithms

    Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, et al. · 2022 · Reviews of Modern Physics · 1,770 citations

    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.

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  9. Quantum algorithms: an overview

    Ashley Montanaro · 2016 · npj Quantum Information · 1,085 citations

    Abstract Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We include a discussion of recent developments and near-term applications of quantum algorithms.

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  10. Exponential algorithmic speedup by a quantum walk

    Andrew M. Childs, Richard Cleve, E. Deotto, et al. · 2003 · 838 citations

    We construct a black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our black box setting. We then show how this quantum walk solves our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve the problem in subexponential time.

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  11. Demonstration of Blind Quantum Computing

    Stefanie Barz, Elham Kashefi, Anne Broadbent, et al. · 2012 · Science · 478 citations

    Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally se

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  12. Quantum speedup of Monte Carlo methods

    Ashley Montanaro · 2015 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 350 citations

    Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous

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  13. Parallel Algorithms with Optimal Speedup for Bounded Treewidth

    Hans L. Bodlaender, Torben Hagerup · 1998 · SIAM Journal on Computing · 66 citations

    We describe the first parallel algorithm with optimal speedup for constructing minimum-width tree decompositions of graphs of bounded treewidth. On n-vertex input graphs, the algorithm works in O((log n) 2 ) time using O(n) operations on the EREW PRAM. We also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth, including all decision problems expressible in monadic second-order logic. On n-vertex input graphs, the algorithms use O(n) operations together with O(log n log

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  14. Anticoncentration theorems for schemes showing a quantum speedup

    Dominik Hangleiter, Juan Bermejo-Vega, Martin Schwarz, et al. · 2018 · Quantum · 58 citations

    One of the main milestones in quantum information science is to realise quantum devices that exhibit an exponential computational advantage over classical ones without being universal quantum computers, a state of affairs dubbed quantum speedup, or sometimes "quantum computational supremacy". The known schemes heavily rely on mathematical assumptions that are plausible but unproven, prominently results on anticoncentration of random prescriptions. In this work, we aim at closing the gap by proving two anticoncentration theorems and accompanying hardness results, one for circuit-based schemes, the other for quantum quench-type schemes for quantum simulations. Compared to the few other known s

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  15. Enhancing the Performance Prediction of Quantum Computing Algorithms using Gradient Boosting and Ada Boost Regression

    Rajendar Dommeti · 2026 · Journal of Quantum Computing and Advanced Algorithms · 21 citations

    Quantum computing is considered to have tremendous potential to help take the emerging field of "Computational Law" to the next level of growth in terms of the expression and implementation of legal principles. With the promise of quantum technology's increasing influence on the legal industry in mind, this essay utilizes the emerging field of Computational Complexity Theory to explore the types of problems that quantum computing is capable of solving more efficiently than classical computing, which is referred to as Quantum Supremacy. From this foundation, three emerging areas within the legal sector have been identified where quantum computing is likely to show transformative superiority.

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  18. Quantum Speedup Based on Classical Decision Trees

    Salman Beigi, Leila Taghavi · 2020 · Quantum · 15 citations

    Lin and Lin \cite{LL16} have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a function f:{0,1}n→[m] whose input can be accessed via queries to its bits, and a guessing algorithm that predicts answers to the queries, there is a quantum query algorithm for f which makes at most O(GT) quantum queries where T is the depth of the decision tree and G is the maximum number of mistakes of the guessing algorithm. In this paper we give a simple proof of and generalize this result for functions f:[ℓ]n→[m] with non-binary input as well as

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