quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role...
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quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine learning today. We present quantum algorithms for training and evaluating feedforward neural networks based on the canonical classical feedforward and backpropagation algorithms. Our algorithms rely on an efficient quantum subroutine for approximating inner products between vectors in a robust way, and on implicitly storing intermediate values in quantum random access memory for fast retrieval at later stages. The running times of our algorithms can be quadratically faster in the size of the network than their standard classical counterparts since they depend linearly on the number of neurons in the network, and not on the number of connections between neurons. Furthermore, networks trained by our quantum algorithm may have an intrinsic resilience to overfitting, as the algorithm naturally mimics the effects of classical techniques used to regularize networks. Our algorithms can also be used as the basis for new quantum-inspired classical algorithms with the same dependence on the network dimensions as their quantum counterparts but with quadratic overhead in other parameters that makes them relatively impractical.
In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is th...
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In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.
In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to devise new quantum algorithms. We show how the properties of a weighing matrix ca...
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In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to devise new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is significantly lower than the classical one. It is pointed out that this scheme captures both Bernstein and Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the article we consider Paley's construction of Hadamard matrices, which relies on the properties of quadratic characters over finite fields. We design a query problem that uses the Legendre symbol chi (which indicates if an element of a finite field F-q is a quadratic residue or not). It is shown how for a shifted Legendre function f(s) (i) = chi (i + s), the unknown s is an element of F-q can be obtained exactly with only two quantum calls to f(s). This is in sharp contrast with the observation that any classical, probabilistic procedure requires more than log q + log((1 - epsilon)/2) queries to solve the same problem.
It is known that quantum computer is more powerful than classical *** this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least q...
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It is known that quantum computer is more powerful than classical *** this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least quadratically faster than the classical ones.
A fast quantum algorithm for a search and pattern recognition in a Hilbert space memory structure is proposed. All the memory information is mapped onto a unitary operator acting upon a quantum state which represents ...
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A fast quantum algorithm for a search and pattern recognition in a Hilbert space memory structure is proposed. All the memory information is mapped onto a unitary operator acting upon a quantum state which represents a piece of information to be retrieved. As a result of only one quantum measurement, the address of the required information encoded in a number of the corresponding row of the unitary matrix is determined. By combining direct and dot products, the dimensionality of the memory space can be made exponentially large, using only linear resources. However, since the preprocessing, i.e., mapping the memory information into a Hilbert space can appear to be exponentially expensive, the proposed algorithm will be effective for NASA applications when the preprocessing is implemented on the ground, while the memory search is performed on remote objects.
The ideas of quantum simulation and advances in quantum algorithms to solve quantum chemistry problems have been discussed. Theoretical proposals and experimental investigations both have been studied to gauge the ext...
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The ideas of quantum simulation and advances in quantum algorithms to solve quantum chemistry problems have been discussed. Theoretical proposals and experimental investigations both have been studied to gauge the extent to which quantum computation has been applied to solve quantum chemical problems till date. The distinctive features and limitations of the application of quantum simulation on chemical systems and current approaches to define and improve upon standard quantum algorithms have been studied in detail. The possibility and consequences of designing an efficient quantum computer that can address chemical problems have been assessed. The experimental realization of quantum supremacy defies the conventional belief of chemists, that millions of qubits would be required to solve fundamental chemistry problems. It is predicted that quantum simulation of quantum chemistry problems will radically revolutionize this field.
A promising area of applications for quantum computing is in linear algebra problems. In this work, we introduce two new quantum t-SVD (tensor-SVD) algorithms. The first algorithm is largely based on previous work tha...
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ISBN:
(纸本)9798331541378
A promising area of applications for quantum computing is in linear algebra problems. In this work, we introduce two new quantum t-SVD (tensor-SVD) algorithms. The first algorithm is largely based on previous work that proposed a quantum t-SVD algorithm for context-aware recommendation systems. The new algorithm however seeks to address and fix certain drawbacks in the original, and is fundamentally different in its approach compared to the existing work. The second algorithm proposed uses a hybrid variational approach largely based on a known variational quantum SVD algorithm.
We develop a general framework to construct quantum algorithms that detect if a 3-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a pre-specified constant-sized hypergraph. This framework is ...
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ISBN:
(纸本)9783319087825
We develop a general framework to construct quantum algorithms that detect if a 3-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a pre-specified constant-sized hypergraph. This framework is based on the concept of nested quantum walks recently proposed by Jeffery, Kothari and Magniez (2013) [12], and extends the methodology designed by Lee, Magniez and Santha (2013) [18] for similar problems over graphs. As applications, we obtain a quantum algorithm for finding a 4-clique in a 3-uniform hypergraph on n vertices with query complexity O(n(1.883)), and a quantum algorithm for determining if a ternary operator over a set of size n is associative with query complexity O(n(2.113)). (C) 2015 Elsevier B.V. All rights reserved.
A proposal for a number of interesting quantum algorithms is presented, in the frame of the coupled quantum-wires physical system. Numerical simulations have been carried out to validate the elementary gates. By using...
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A proposal for a number of interesting quantum algorithms is presented, in the frame of the coupled quantum-wires physical system. Numerical simulations have been carried out to validate the elementary gates. By using the universal set of quantum gates for the proposed architecture, the explicit construction of some quantum networks is shown. In particular, the quantum discrete Fourier transform is analyzed, which is the main part of Shor's factorizing algorithm. (C) 2002 Elsevier Science B.V. All rights reserved.
We demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented by our proposed quantum algorithm on the quantum machine propos...
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ISBN:
(纸本)9781424418220
We demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented by our proposed quantum algorithm on the quantum machine proposed by Deutsch. Moreover, we also prove that the logic computation by the bio-molecular operations proposed by Adleman can be implemented by quantum gates (for example, the Hadamard gate, NOT, CNOT, and CCNOT) on the quantum machine. Furthermore, those NP-complete problems solved on a bio-molecular computer are also solvable on a quantum computer. To test our theory, we carry out a three-qubit NMR experiment for solving the simplest satisfiability problem.
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