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Academic literature on the topic 'Grover’s search algorithm'

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Journal articles on the topic "Grover’s search algorithm"

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Qu, Ri, Bingjian Shang, Yanru Bao, Dawei Song, ChunMing Teng, and Zhiwei Zhou. "Multipartite entanglement in Grover’s search algorithm." Natural Computing 14, no. 4 (January 10, 2015): 683–89. http://dx.doi.org/10.1007/s11047-014-9481-2.

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Ye, Bin, Tingzhong Zhang, Liang Qiu, and Xuesong Wang. "Quantum discord and entanglement in grover search algorithm." Open Physics 14, no. 1 (January 1, 2016): 171–76. http://dx.doi.org/10.1515/phys-2016-0020.

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AbstractImperfections and noise in realistic quantum computers may seriously affect the accuracy of quantum algorithms. In this article we explore the impact of static imperfections on quantum entanglement as well as non-entangled quantum correlations in Grover’s search algorithm. Using the metrics of concurrence and geometric quantum discord, we show that both the evolution of entanglement and quantum discord in Grover algorithm can be restrained with the increasing strength of static imperfections. For very weak imperfections, the quantum entanglement and discord exhibit periodic behavior, while the periodicity will most certainly be destroyed with stronger imperfections. Moreover, entanglement sudden death may occur when the strength of static imperfections is greater than a certain threshold.
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Zhu, Yuanye, Zeguo Wang, Bao Yan, and Shijie Wei. "Robust Quantum Search with Uncertain Number of Target States." Entropy 23, no. 12 (December 8, 2021): 1649. http://dx.doi.org/10.3390/e23121649.

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The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked states. In this paper, we study the relation between the success rate and the number of iterations in a quantum search algorithm of given λ=M/N, where M is the number of marked state and N is the number of items in the dataset. We develop a robust quantum search algorithm based on Grover–Long algorithm with some uncertainty in the number of marked states. The proposed algorithm has the same query complexity ON as the Grover’s algorithm, and shows high tolerance of the uncertainty in the ratio M/N. In particular, for a database with an uncertainty in the ratio M±MN, our algorithm will find the target states with a success rate no less than 96%.
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Jang, Kyungbae, Gyeongju Song, Hyeokdong Kwon, Siwoo Uhm, Hyunji Kim, Wai-Kong Lee, and Hwajeong Seo. "Grover on PIPO." Electronics 10, no. 10 (May 17, 2021): 1194. http://dx.doi.org/10.3390/electronics10101194.

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The emergence of quantum computers is threatening the security of cryptography through various quantum algorithms. Among them, the Grover search algorithm is known to be efficient in accelerating brute force attacks on block cipher algorithms. To utilize the Grover’s algorithm for brute force attacks, block ciphers must be implemented in quantum circuits. In this paper, we present optimized quantum circuits of the SPN (Substitution Permutation Network) structured lightweight block cipher, namely the PIPO block cipher. In particular, the compact design of quantum circuits for the 8-bit Sbox is investigated. These optimization techniques are used to implement other cryptographic operations as quantum circuits. Finally, we evaluate quantum resources of Grover search algorithm for the PIPO block cipher in ProejctQ, a quantum simulator provided by IBM.
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Song, Gyeongju, Kyungbae Jang, Hyunji Kim, and Hwajeong Seo. "A Parallel Quantum Circuit Implementations of LSH Hash Function for Use with Grover’s Algorithm." Applied Sciences 12, no. 21 (October 27, 2022): 10891. http://dx.doi.org/10.3390/app122110891.

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Grover’s search algorithm accelerates the key search on the symmetric key cipher and the pre-image attack on the hash function. To conduct Grover’s search algorithm, the target cipher algorithm should be efficiently implemented in a quantum circuit. Currently, small quantum computers are difficult to operate with large quantum circuits due to limited performance. Therefore, if a large quantum computer that can operate Grover’s algorithm appears, it is expected that a cipher attack will be possible. In this paper, we propose a parallel structure quantum circuit for the Korean hash function standard (i.e., LSH). The proposed quantum circuit designed a parallel operation structure for the message expansion (i.e., MsgExp) function and the mix function, which are the internal structures of the LSH hash function. This approach shows an efficient result for quantum circuit implementation in terms of quantum resources by reducing the depth of the quantum circuit by about 96% through the trade-off of appropriate quantum resources compared to previous work. This result can be a reference for the implementation of a parallel quantum circuit in the future and is expected to advance the attack timing of the search algorithm for Grover’s LSH hash function.
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Kravchenko, Dmitry, Nikolajs Nahimovs, and Alexander Rivosh. "Grover’s Search with Faults on Some Marked Elements." International Journal of Foundations of Computer Science 29, no. 04 (June 2018): 647–62. http://dx.doi.org/10.1142/s0129054118410095.

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Grover’s algorithm is a quantum query algorithm solving the unstructured search problem of size [Formula: see text] using [Formula: see text] queries. It provides a significant speed-up over any classical algorithm [3]. The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [2, 6]. We study the behavior of Grover’s algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in [Formula: see text] queries. We also analyze the limiting behavior of the algorithm for a large number of steps and show the existence and the structure of a limiting state [Formula: see text].
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Yin, Aihan, Kemeng He, and Ping Fan. "Quantum dialogue protocol based on Grover’s search algorithms." Modern Physics Letters A 34, no. 21 (July 9, 2019): 1950169. http://dx.doi.org/10.1142/s0217732319501694.

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Among many classic heuristic search algorithms, the Grover quantum search algorithm (QSA) can play a role of secondary acceleration. Based on the properties of the two-qubit Grover QSA, a quantum dialogue (QD) protocol is proposed. In addition, our protocol also utilizes the unitary operations and single-particle measurements. The transmitted quantum state (except for the decoy state used for detection) can transmit two-bits of security information simultaneously. Theoretical analysis shows that the proposed protocol has high security.
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Joshi, Saasha, and Deepti Gupta. "Grover’s Algorithm in a 4-Qubit Search Space." Journal of Quantum Computing 3, no. 4 (2021): 137–50. http://dx.doi.org/10.32604/jqc.2021.018114.

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Morikoshi, Fumiaki. "Problem-Solution Symmetry in Grover’s Quantum Search Algorithm." International Journal of Theoretical Physics 50, no. 6 (February 9, 2011): 1858–67. http://dx.doi.org/10.1007/s10773-011-0701-6.

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Biasse, Jean-François, and Benjamin Pring. "A framework for reducing the overhead of the quantum oracle for use with Grover’s algorithm with applications to cryptanalysis of SIKE." Journal of Mathematical Cryptology 15, no. 1 (November 17, 2020): 143–56. http://dx.doi.org/10.1515/jmc-2020-0080.

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AbstractIn this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search problems. This has the effect (for certain problems) of reducing a portion of the polynomial overhead contributed by the implementation cost of quantum oracles and can be used to provide either strict improvements or advantageous trade-offs in circuit-complexity. Our results indicate that it is possible for quantum oracles for certain single-target preimage search problems to reduce the quantum circuit-size from $O\left(2^{n/2}\cdot mC\right)$ (where C originates from the cost of implementing the quantum oracle) to $O(2^{n/2} \cdot m\sqrt{C})$ without the use of quantum ram, whilst also slightly reducing the number of required qubits.This framework captures a previous optimisation of Grover’s algorithm using preprocessing [21] applied to cryptanalysis, providing new asymptotic analysis. We additionally provide insights and asymptotic improvements on recent cryptanalysis [16] of SIKE [14] via Grover’s algorithm, demonstrating that the speedup applies to this attack and impacting upon quantum security estimates [16] incorporated into the SIKE specification [14].
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Dissertations / Theses on the topic "Grover’s search algorithm"

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Sjöborg, Martin, and Hanna Linn. "Simulating a Quantum Computer : Grover's Search Algorithm with Error Correction." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-231739.

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Classical simulations of quantum computers give us an insight into various things such as what quantum algorithms can achieve, whether it is possible to verify that they function as postulated, the difficulties that have to be overcome before quantum computers can be realized, as well as how we can handle these difficulties. We build a Python library to simulate a quantum computer that can perform all quantum algorithms by defining an universal gate set, from which all quantum gates – and thereby all circuits – can be constructed. We implement two algorithms that both highlight two important aspects of quantum computing: Grover’s quantum search algorithm, which demonstrates the efficiency of quantum algorithms and their superiority over their classical counterparts by searching an unsorted list quadratically faster; and an error correcting code, the Shor code, which highlights the cost of correcting the possible errors in a quantum computer.We test the rigidity of Grover’s algorithm by introducing errors without correction, and find that the algorithm shows resilience to smaller 1-qubit Pauli errors, but looses its efficiency under larger errors and thus the need for Pauli error correction arise.
Klassiska simuleringar av kvantdatorer ger oss en inblick i vad kvantalgoritmer kan åstadkomma, hur vi kan verifiera att algoritmerna fungerar, vilka problem vi måste lösa innan kvantdator- erna blir en verklighet, samt hur vi kanske kan hantera problemen. Vi bygger ett bibliotek i Python för att simulera en kvantdator som kan utföra alla kvantalgoritmer genom att definiera en grinduniversalmängd, ur vilken alla kvantgrindar – och därmed alla kretsar – kan konstrueras. Vi implementar två algoritmer som båda belyser två viktiga aspekter hos kvantberäkning: Grover’s kvantsökning, som demonstrerar effektiviteten hos kvantalgoritmer över deras klassiska analoger, samt en felhanteringsalgoritm, Shorkoden, som kan jämka Paulifel och är betydelsefull för att förstå vikten hos felkorrigering.Vi prövar motståndskraften hos Grovers algoritm genom att utsätta den för slumpmässiga ro- tationer hos en qubit, och finner att algoritmen är resistent mot mindre Paulifel, men snabbt slutar producera meningsfulla resultat vid större Paulifel.
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Furrow, Bartholomew. "A panoply of quantum algorithms." Thesis, University of British Columbia, 2006. http://hdl.handle.net/2429/75.

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This thesis’ aim is to explore improvements to, and applications of, a fundamental quantum algorithm invented by Grover. Grover’s algorithm is a basic tool that can be applied to a large number of problems in computer science, creating quantum algorithms that are polynomially faster than fastest known and fastest possible classical algorithms that solve the same problems. Our goal in this thesis is to make these techniques readily accessible to those without a strong background in quantum physics: we achieve this by providing a set of tools, each of which makes use of Grover’s algorithm or similar techniques, that can be used as subroutines in many quantum algorithms. The tools we provide are carefully constructed: they are easy to use, and they are asymptotically faster than the best tools previously available. The tools that we supersede include algorithms by Boyer, Brassard, Hoyer and Tapp, Buhrman, Cleve, de Witt and Zalka and Durr and Hoyer. After creating our tools, we create several new quantum algorithms, each of which is faster than the fastest known classical algorithm that accomplishes the same aim, and some of which are faster than the fastest possible classical algorithm. These algorithms come from graph theory, computational geometry and dynamic programming. We discuss a breadth-first search that is faster than (edges) (the classical limit) in a dense graph, maximum-points-on-a-line in (N3/2 lgN) (faster than the fastest classical algorithm known), as well as several other algorithms that are similarly illustrative of solutions in some class of problem. Through these new algorithms we illustrate the use of our tools, working to encourage their use and the study of quantum algorithms in general.
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Lutze, David. "Solving Chromatic Number with Quantum Search and Quantum Counting." DigitalCommons@CalPoly, 2021. https://digitalcommons.calpoly.edu/theses/2342.

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This thesis presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2n/2n2(log2n)2). This is an improvement over the best known algorithm, with a run time of 2nnO(1) [1]. This algorithm uses the Quantum Search algorithm (often called Grover's Algorithm), and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, which suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can be framed as NP-Hard problems, so any speed-up in the solution of these problems is highly sought after. A bulk of this thesis consists of a review of the underlying principles of quantum mechanics and quantum computing, building to the Quantum Search and Quantum Counting algorithms. The review is written with the assumption that the reader has no prior knowledge on quantum computing. This culminates with a presentation of algorithms for generating the quantum circuits required to solve K-Coloring and Chromatic Number.
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Katabira, Joseph. "Groverův algoritmus v kvantovém počítání a jeho aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445458.

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Kvantová výpočetní technika je rychle rostoucí obor informatiky, který přenáší principy kvantových jevu do našeho každodenního života. Díky své kvantové podstatě získávají kvantové počítače převahu nad klasickými počítači. V této práci jsme se zaměřili na vysvětlení základů kvantového počítání a jeho implementaci na kvantovém počítači. Zejména se zaměřujeme na popis fungování, konstrukci a implementaci Groverova algoritmu jako jednoho ze základních kvantových algoritmů. Demonstrovali jsme sílu tohoto kvantového algoritmu při prohledávání databáze a porovnávali ho s klasickými nekvantovými algoritmy pomocí implementace prostřednictvím simulačního prostředí QISKit. Pro simulaci jsme použili QASM Simulator a State vector Simulator Aer backends a ukázali, že získané výsledky korelují s dříve diskutovanými teoretickými poznatky. Toto ukazuje, že Groverův algoritmus umožňuje kvadratické zrychlení oproti klasickému nekvantovému vyhledávacímu algoritmu, Použitelnost algoritmu stejně jako ostatních kvantových algoritmů je ale stále omezena několika faktory, mezi které patří vysoké úrovně dekoherence a chyby hradla.
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Priyadarsini, Anjali V. "Efficient Quantum Algorithms for Linear Algebra Problems." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/5386.

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Many simulation problems can be expressed as time evolution under specific interactions, from some simple initial state to a final state whose properties are to be investigated. In this context, the Hamiltonian evolution problem has been extensively studied. Quantum simulations can sum multiple evolutionary paths contributing to a quantum process in superposition at one go, while classical simulations need to evaluate these paths one by one. Real physical systems are governed by local Hamiltonians, i.e. where each component interacts only with a limited number of its neighbours independent of the overall size of the system, which helps in parallelisation of their simulations. The procedure is not simple, however. Although, in the 2n-dimensional Hilbert space of n qubits, we can superpose 2n components evolving in parallel, we can measure only n binary observables at the end. So the exponential gain of superposition is limited by the restriction to extract only a small number of results at the end. This dichotomy means that quantum algorithms will be advantageous only when the final observables are local in some manner; no general prescription is available, and one has to look at the problems on a case by case basis. Early quantum evolution algorithms exploited locality of Hamiltonians for efficient use of time and space resources during evolution [3, 4]. More recently, the error complexity of the evolution has been reduced from power-law to logarithmic in the inverse error, using large step discrete time algorithms [5–7]. After the Hamiltonian evolution, investigation of final state properties requires expectation values of various observables to be measured. The problem of how to do this efficiently has not been adequately addressed so far. Since quantum measurements are probabilistic, determination of the expectation values needs multiple repetitions of the same algorithm. Thereafter, importance sampling or phase estimation based results yield errors that decrease as power-law in the number of repetitions [8, 9], e.g. Niter × *2 as per the central limit theorem, and that is not efficient. What we want is a strategy that decreases the errors exponentially with the number of repetitions, e.g. finding zeroes of a function by bisection is efficient with Niter × log , and finding them by Newton’s method is super-efficient with Niter × log log . While that may not be possible for generic observables, it can be achieved for k-local observables that appear in evaluations of k-point Green’s functions for many-body systems. We explicitly show how to do that. The novel concept we introduce is a digital state representation of quantum states, which maps non-unitary linear algebra operations to unitary operators. High precision calculations need 3 1.1. Scope of the Thesis a digital representation instead of an analog one. Our digital representation for both the quantum states and the operators maintains the expectation values of all physical observables. It combines classical reversible logic with equally weighted linear superposition, and is essentially free of the unitarity constraint for quantum states. This digital implementation can help in construction of efficient quantum algorithms for many linear algebra problems.
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葉清河. "Quantum optical circuit design for grover's algorithm for multiobject search." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/86569735126250421817.

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Tulsi, Tathagat Avatar. "Generalizations Of The Quantum Search Algorithm." Thesis, 2009. https://etd.iisc.ac.in/handle/2005/951.

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Quantum computation has attracted a great deal of attention from the scientific community in recent years. By using the quantum mechanical phenomena of superposition and entanglement, a quantum computer can solve certain problems much faster than classical computers. Several quantum algorithms have been developed to demonstrate this quantum speedup. Two important examples are Shor’s algorithm for the factorization problem, and Grover’s algorithm for the search problem. Significant efforts are on to build a large scale quantum computer for implementing these quantum algorithms. This thesis deals with Grover’s search algorithm, and presents its several generalizations that perform better in specific contexts. While writing the thesis, we have assumed the familiarity of readers with the basics of quantum mechanics and computer science. For a general introduction to the subject of quantum computation, see [1]. In Chapter 1, we formally define the search problem as well as present Grover’s search algorithm [2]. This algorithm, or more generally the quantum amplitude amplification algorithm [3, 4], drives a quantum system from a prepared initial state (s) to a desired target state (t). It uses O(α-1 = | (t−|s)| -1) iterations of the operator g = IsIt on |s), where { IsIt} are selective phase inversions selective phase inversions of the corresponding states. That is a quadratic speedup over the simple scheme of O(α−2) preparations of |s) and subsequent projective measurements. Several generalizations of Grover’s algorithm exist. In Chapter 2, we study further generalizations of Grover’s algorithm. We analyse the iteration of the search operator S = DsI t on |s) where Ds is a more general transformation than Is, and I t is a selective phase rotation of |t) by angle . We find sufficient conditions for S to produce a successful quantum search algorithm. In Chapter 3, we demonstrate that our general framework encapsulates several previous generalizations of Grover’s algorithm. For example, the phase-matching condition for the search operator requires the angles and and to be almost equal for a successful quantum search. In Kato’s algorithm, the search operator is where Ks consists of only single-qubit gates, which are easier to implement physically than multi-qubit gates. The spatial search algorithms consider the search operator where is a spatially local operator and provides implementation advantages over Is. The analysis of Chapter 2 provides a simpler understanding of all these special cases. In Chapter 4, we present schemes to improve our general quantum search algorithm, by controlling the operators through an ancilla qubit. For the case of two dimensional spatial search problem, these schemes yield an algorithm with time complexity . Earlier algorithms solved this problem in time steps, and it was an open question to design a faster algorithm. The schemes can also be used to find, for a given unitary operator, an eigenstate corresponding to a specified eigenvalue. In Chapter 5, we extend the analysis of Chapter 2 to general adiabatic quantum search. It starts with the ground state |s) of an initial Hamiltonian Hs and evolves adiabatically to the target state |t) that is the ground state of the final Hamiltonian The evolution uses a time dependent Hamiltonian HT that varies linearly with time . We show that the minimum excitation gap of HT is proportional to α. Also, the ground state of HT changes significantly only within a very narrow interval of width around the transition point, where the excitation gap has its minimum. This feature can be used to reach the target state (t) using adiabatic evolution for time In Chapter 6, we present a robust quantum search algorithm that iterates the operator on |s) to successfully reach |t), whereas Grover’s algorithm fails if as per the phase-matching condition. The robust algorithm also works when is generalized to multiple target states. Moreover, the algorithm provides a new search Hamiltonian that is robust against certain systematic perturbations. In Chapter 7, we look beyond the widely studied scenario of iterative quantum search algorithms, and present a recursive quantum search algorithm that succeeds with transformations {Vs,Vt} sufficiently close to {Is,It.} Grover’s algorithm generally fails if while the recursive algorithm is nearly optimal as long as , improving the error tolerance of the transformations. The algorithms of Chapters 6-7 have applications in quantum error-correction, when systematic errors affect the transformations The algorithms are robust as long as the errors are small, reproducible and reversible. This type of errors arise often from imperfections in apparatus setup, and so the algorithms increase the flexibility in physical implementation of quantum search. In Chapter 8, we present a fixed-point quantum search algorithm. Its state evolution monotonically converges towards |t), unlike Grover’s algorithm where the evolution passes through |t) under iterations of the operator . In q steps, our algorithm monotonically reduces the failure probability, i.e. the probability of not getting |t), from . That is asymptotically optimal for monotonic convergence. Though the fixed-point algorithm is of not much use for , it is useful when and each oracle query is highly expensive. In Chapter 9, we conclude the thesis and present an overall outlook.
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Tulsi, Tathagat Avatar. "Generalizations Of The Quantum Search Algorithm." Thesis, 2009. http://hdl.handle.net/2005/951.

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Quantum computation has attracted a great deal of attention from the scientific community in recent years. By using the quantum mechanical phenomena of superposition and entanglement, a quantum computer can solve certain problems much faster than classical computers. Several quantum algorithms have been developed to demonstrate this quantum speedup. Two important examples are Shor’s algorithm for the factorization problem, and Grover’s algorithm for the search problem. Significant efforts are on to build a large scale quantum computer for implementing these quantum algorithms. This thesis deals with Grover’s search algorithm, and presents its several generalizations that perform better in specific contexts. While writing the thesis, we have assumed the familiarity of readers with the basics of quantum mechanics and computer science. For a general introduction to the subject of quantum computation, see [1]. In Chapter 1, we formally define the search problem as well as present Grover’s search algorithm [2]. This algorithm, or more generally the quantum amplitude amplification algorithm [3, 4], drives a quantum system from a prepared initial state (s) to a desired target state (t). It uses O(α-1 = | (t−|s)| -1) iterations of the operator g = IsIt on |s), where { IsIt} are selective phase inversions selective phase inversions of the corresponding states. That is a quadratic speedup over the simple scheme of O(α−2) preparations of |s) and subsequent projective measurements. Several generalizations of Grover’s algorithm exist. In Chapter 2, we study further generalizations of Grover’s algorithm. We analyse the iteration of the search operator S = DsI t on |s) where Ds is a more general transformation than Is, and I t is a selective phase rotation of |t) by angle . We find sufficient conditions for S to produce a successful quantum search algorithm. In Chapter 3, we demonstrate that our general framework encapsulates several previous generalizations of Grover’s algorithm. For example, the phase-matching condition for the search operator requires the angles and and to be almost equal for a successful quantum search. In Kato’s algorithm, the search operator is where Ks consists of only single-qubit gates, which are easier to implement physically than multi-qubit gates. The spatial search algorithms consider the search operator where is a spatially local operator and provides implementation advantages over Is. The analysis of Chapter 2 provides a simpler understanding of all these special cases. In Chapter 4, we present schemes to improve our general quantum search algorithm, by controlling the operators through an ancilla qubit. For the case of two dimensional spatial search problem, these schemes yield an algorithm with time complexity . Earlier algorithms solved this problem in time steps, and it was an open question to design a faster algorithm. The schemes can also be used to find, for a given unitary operator, an eigenstate corresponding to a specified eigenvalue. In Chapter 5, we extend the analysis of Chapter 2 to general adiabatic quantum search. It starts with the ground state |s) of an initial Hamiltonian Hs and evolves adiabatically to the target state |t) that is the ground state of the final Hamiltonian The evolution uses a time dependent Hamiltonian HT that varies linearly with time . We show that the minimum excitation gap of HT is proportional to α. Also, the ground state of HT changes significantly only within a very narrow interval of width around the transition point, where the excitation gap has its minimum. This feature can be used to reach the target state (t) using adiabatic evolution for time In Chapter 6, we present a robust quantum search algorithm that iterates the operator on |s) to successfully reach |t), whereas Grover’s algorithm fails if as per the phase-matching condition. The robust algorithm also works when is generalized to multiple target states. Moreover, the algorithm provides a new search Hamiltonian that is robust against certain systematic perturbations. In Chapter 7, we look beyond the widely studied scenario of iterative quantum search algorithms, and present a recursive quantum search algorithm that succeeds with transformations {Vs,Vt} sufficiently close to {Is,It.} Grover’s algorithm generally fails if while the recursive algorithm is nearly optimal as long as , improving the error tolerance of the transformations. The algorithms of Chapters 6-7 have applications in quantum error-correction, when systematic errors affect the transformations The algorithms are robust as long as the errors are small, reproducible and reversible. This type of errors arise often from imperfections in apparatus setup, and so the algorithms increase the flexibility in physical implementation of quantum search. In Chapter 8, we present a fixed-point quantum search algorithm. Its state evolution monotonically converges towards |t), unlike Grover’s algorithm where the evolution passes through |t) under iterations of the operator . In q steps, our algorithm monotonically reduces the failure probability, i.e. the probability of not getting |t), from . That is asymptotically optimal for monotonic convergence. Though the fixed-point algorithm is of not much use for , it is useful when and each oracle query is highly expensive. In Chapter 9, we conclude the thesis and present an overall outlook.
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王文楷. "Tight bounds on grover-based quantum search algorithms." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/22884432750805203157.

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Bassa, Humairah. "Implementing Grover's search algorithm using the one-way quantum computing model and photonic orbital angular momentum." Thesis, 2011. http://hdl.handle.net/10413/9704.

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Standard quantum computation proceeds via the unitary evolution of physical qubits (two-level systems) that carry the information. A remarkably different model is one-way quantum computing where a quantum algorithm is implemented by a set of irreversible measurements on a large array of entangled qubits,, known as the cluster state. The order and sequence of these measurements allow for different algorithms to be implemented. With a large enough cluster state and a method in which to perform single-qubit measurements the desired computation can be realised. We propose a potential implementation of one-way quantum computing using qubits encoded in the orbital angular momentum degree of freedom of single photons. Photons are good carriers of quantum information because of their weak interaction with the environment and the orbital angular momentum of single photons offers access to an infinite-dimensional Hilbert space for encoding information. Spontaneous parametric down-conversion is combined with a series of optical elements to generate a four-photon orbital angular momentum entangled cluster state and single-qubit measurements are carried out by means of digital holography. The proposed set-up, which is based on an experiment that utilised polarised photons, can be used to realise Grover’s search algorithm which performs a search through an unstructured database of four elements. Our application is restricted to a two-dimensional subspace of a multi-dimensional system, but this research facilitates the use of orbital angular momentum qubits for quantum information processing and points towards the usage of photonic qudits (multi-level systems). We also review the application of Dirac notation to paraxial light beams on a classical and quantum level. This formalism is generally employed in quantum mechanics but the analogy with paraxial optics allows us to represent the classical states of light by means of Dirac kets. An analysis of the analogy between the classical and quantum states of light using this formalism, is presented.
Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.
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Book chapters on the topic "Grover’s search algorithm"

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Hirvensalo, Mika. "Grover’s Search Algorithm." In Quantum Computing, 83–100. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-09636-9_6.

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Hirvensalo, Mika. "Grover’s Search Algorithm." In Quantum Computing, 73–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04461-2_5.

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de Lima Marquezino, Franklin, Renato Portugal, and Carlile Lavor. "Grover’s Algorithm for Unstructured Search." In SpringerBriefs in Computer Science, 35–55. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-19066-8_3.

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Portugal, Renato. "Grover’s Algorithm and Its Generalization." In Quantum Walks and Search Algorithms, 39–63. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6336-8_4.

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Okamoto, Kyoichi, and Osamu Watanabe. "Deterministic Application of Grover’s Quantum Search Algorithm." In Lecture Notes in Computer Science, 493–501. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44679-6_55.

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Goswami, Debabrata. "Quantum Distributed Computing Applied to Grover’s Search Algorithm." In Computing with New Resources, 192–99. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-13350-8_14.

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Liber, Arkadiusz, and Laurentiu Nita. "The Research of Grover’s Quantum Search Algorithm with Use of Quantum Circuits QX2 and QX4." In Advances in Intelligent Systems and Computing, 146–55. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99981-4_14.

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de Jesus, Brian Kenneth A., Jeffrey A. Aborot, and Henry N. Adorna. "Solving the Exact Pattern Matching Problem Constrained to Single Occurrence of Pattern P in String S Using Grover’s Quantum Search Algorithm." In Proceedings in Information and Communications Technology, 124–42. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54436-4_10.

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Chareton, Christophe, Sébastien Bardin, François Bobot, Valentin Perrelle, and Benoît Valiron. "An Automated Deductive Verification Framework for Circuit-building Quantum Programs." In Programming Languages and Systems, 148–77. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72019-3_6.

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AbstractWhile recent progress in quantum hardware open the door for significant speedup in certain key areas, quantum algorithms are still hard to implement right, and the validation of such quantum programs is a challenge. In this paper we propose Qbricks, a formal verification environment for circuit-building quantum programs, featuring both parametric specifications and a high degree of proof automation. We propose a logical framework based on first-order logic, and develop the main tool we rely upon for achieving the automation of proofs of quantum specification: PPS, a parametric extension of the recently developed path sum semantics. To back-up our claims, we implement and verify parametric versions of several famous and non-trivial quantum algorithms, including the quantum parts of Shor’s integer factoring, quantum phase estimation (QPE) and Grover’s search.
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Biron, David, Ofer Biham, Eli Biham, Markus Grassl, and Daniel A. Lidar. "Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution." In Quantum Computing and Quantum Communications, 140–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-49208-9_10.

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Conference papers on the topic "Grover’s search algorithm"

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Wang, Yan. "Global Optimization With Quantum Walk Enhanced Grover Search." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34634.

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One of the significant breakthroughs in quantum computation is Grover’s algorithm for unsorted database search. Recently, the applications of Grover’s algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed. By taking advantage of quantum tunneling effect, local barriers are overcome and better threshold values can be found at the early stage of search process. The new algorithm based on the formalism is demonstrated with benchmark examples of global optimization. The results between the new algorithm and the Grover search method are also compared.
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Wang, Runqian. "Comparing Grover’s Quantum Search Algorithm with Classical Algorithm on Solving Satisfiability Problem." In 2021 IEEE Integrated STEM Education Conference (ISEC). IEEE, 2021. http://dx.doi.org/10.1109/isec52395.2021.9764017.

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Bag, Kingsuk, Manish Goswami, and Kavindra Kandpal. "FPGA Based Resource Efficient Simulation and Emulation Of Grover’s Search Algorithm." In 2022 IEEE 19th India Council International Conference (INDICON). IEEE, 2022. http://dx.doi.org/10.1109/indicon56171.2022.10040039.

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Groppe, Sven, and Jinghua Groppe. "Optimizing Transaction Schedules on Universal Quantum Computers via Code Generation for Grover’s Search Algorithm." In IDEAS 2021: 25th International Database Engineering & Applications Symposium. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3472163.3472164.

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Aborot, Jeffrey A. "An Oracle Design for Grover’s Quantum Search Algorithm for Solving the Exact String Matching Problem." In Seventh Workshop on Computation: Theory and Practice, WCTP 2017. WORLD SCIENTIFIC, 2018. http://dx.doi.org/10.1142/9789813279674_0003.

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Prodan, Adrian, Vasile-Ion Manta, and Alexandru-Gabriel Tudorache. "The performance impact of the graph topology in Ibm’s Quantum devices on Grover’s search algorithm." In 2021 25th International Conference on System Theory, Control and Computing (ICSTCC). IEEE, 2021. http://dx.doi.org/10.1109/icstcc52150.2021.9607230.

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Fogel, Gerardo G., Benjamín Barán, and Marcos Villagra. "Comparison of two types of Quantum Oracles based on Grover’s Adaptative Search Algorithm for Multiobjective Optimization Problems." In 2017 Federated Conference on Computer Science and Information Systems. IEEE, 2017. http://dx.doi.org/10.15439/2017f259.

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Saraiva, Lorenzo, Edward Hermann Haeusler, and Vaston Costa. "Quantum Algorithm for Multiplicative Linear Logic." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação, 2023. http://dx.doi.org/10.5753/wbl.2023.229335.

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This paper describes a quantum algorithm for proof search in sequent calculus of a subset of Linear Logic using the Grover Search Algorithm. We briefly overview the Grover Search Algorithm and Linear Logic, show the detailed steps of the algorithm and then present the results obtained on quantum simulators.
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Zuliani, Paolo. "A Formal Derivation of Grover's Quantum Search Algorithm." In First Joint IEEE/IFIP Symposium on Theoretical Aspects of Software Engineering (TASE '07). IEEE, 2007. http://dx.doi.org/10.1109/tase.2007.3.

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Alsing, Paul M., and Nathan McDonald. "Grover's search algorithm with an entangled database state." In SPIE Defense, Security, and Sensing, edited by Eric Donkor, Andrew R. Pirich, and Howard E. Brandt. SPIE, 2011. http://dx.doi.org/10.1117/12.883092.

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