A review on quantum search algorithms

Giri, Pulak Ranjan; Korepin, V. E.

doi:10.1007/s11128-017-1768-7

Cited by 44 publications

(28 citation statements)

References 21 publications

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“…In fact, the formerly proposed quantum version of random walks, i.e., the quantum walk (QW) [2][3][4][5][6], has been defined by a unitary evolution of the state, without taking into account incoherent effects. This allows the walker's position on a graph to be in a superposition of states, a property that has been exploited to show that QWs are universal for quantum computation [7][8][9] and that they allow to design quantum algorithms with computational advantages over classical algorithms [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Quantum state discrimination on reconfigurable noise-robust quantum networks

Pozza

Caruso

2020

Phys. Rev. Research

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A fundamental problem in quantum information processing is the discrimination among a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by a quantum stochastic walk. In particular, the structure of the graph mimics those of neural networks, with the quantum states to discriminate encoded on input nodes and with the discrimination obtained on the output nodes. We optimize the parameters of the network to obtain the highest probability of correct discrimination. Numerical simulations show that after a transient time the probability of correct decision approaches the theoretical optimal quantum limit. These results are confirmed analytically for small graphs. Finally, we analyze the robustness and reconfigurability of the network for different set of quantum states and show that this architecture can pave the way to experimental realizations of our protocol as well as novel quantum generalizations of deep learning.

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Section: Introductionmentioning

confidence: 99%

Quantum state discrimination on reconfigurable noise-robust quantum networks

Pozza

Caruso

2020

Phys. Rev. Research

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“…According to Eqs. (19) and (22), it is found that the algorithm has advantage of high success probability near its local maximum points, and has disadvantage of low success probability near the corresponding local minimum points. Thus, it is difficult to maintain high success probability over the entire range of λ, by applying k iterations with just a single phase.…”

Section: Generalized Complementary -Multiphase Search Algorithmmentioning

confidence: 99%

“…Appendix A: Proof of all local maximum points of P φ k (λ) on (0, 1) of Eq. (22) According to Eq. (19), the derivative of P φ k (λ) with respect to λ can be written as (1) is no more than 2k +2, which will have up to 2k + 1 real roots for δ ∈ (0, π), now that δ = π is already one of its roots.…”

Section: Acknowledgmentsmentioning

confidence: 99%

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Complementary-multiphase quantum search for all numbers of target items

Li¹,

Bao²,

Huang³

et al. 2018

Phys. Rev. A

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Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of λ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where λ is the fraction of target items in the database. In this paper, we find out that the Grover algorithm can actually apply to the case where one can identify the range that λ belongs to from a given series of disjoint ranges. However, Grover's algorithm still cannot maintain high success probability when there exist multiple target items. For this problem, we proposed a complementary-multiphase quantum search algorithm, in which multiple phases complement each other so that the overall high success probability can be maintained. Compared to the existing algorithms, in the case defined above, for the first time our algorithm achieves the following three goals simultaneously: (1) the success probability can be no less than any given value between 0 and 1, (2) the algorithm is applicable to the entire range of λ, and (3) the number of iterations is almost the same as that of Grover's algorithm. Especially compared to the optimal fixed-point algorithm [Phys. Rev. Lett. 113, 210501 (2014)], our algorithm uses fewer iterations to achieve success probability greater than 82.71%, e.g., when the minimum success probability is required to be 99.25%, the number of iterations can be reduced by 50%.

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“…It is important to note that, due to the nature of quantum states, in a universal quantum computer there is a polynomial time and resource mapping from the classical gate model of these other approaches to a quantum computer. We illustrate this in Figure 8 for Shor's [44] and Grover's [45] algorithms.…”

Section: ) Universal Quantum Computingmentioning

confidence: 99%

Machine Learning: Quantum vs Classical

2020

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Encouraged by growing computing power and algorithmic development, machine learning technologies have became powerful tools for a wide variety of application areas, spanning from agriculture to chemistry and natural language processing. The use of quantum systems to process classical data using machine learning algorithms has given rise to an emerging research area, i.e. quantum machine learning. Despite its origins in the processing of classical data, quantum machine learning also explores the use of quantum phenomena for learning systems, the use of quantum computers for learning on quantum data and how machine learning algorithms and software can be formulated and implemented on quantum computers. Quantum machine learning can have a transformational effect in computer science. It may speed up the processing of information well beyond the existing classical speeds. Recent work has seen the development of quantum algorithms that could serve as foundations for machine learning applications. Despite its great promise, there are still significant hardware and software challenges that need to be resolved before quantum machine learning becomes practical. In this paper, we present an overview of quantum machine learning in the light of classical approaches. Departing from foundational concepts of machine learning and quantum computing, we discusses various technical contributions, strengths and similarities of research works in this domain. We also elaborate upon recent progress of different quantum machine learning approaches, their complexity and applications in various fields such as physics, chemistry and natural language processing.

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A review on quantum search algorithms

Cited by 44 publications

References 21 publications

Quantum state discrimination on reconfigurable noise-robust quantum networks

Quantum state discrimination on reconfigurable noise-robust quantum networks

Complementary-multiphase quantum search for all numbers of target items

Machine Learning: Quantum vs Classical

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