Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,*** this paper,we first present a non-asymptotic quantum ...
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Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,*** this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,*** the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured *** to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.
As semiconductor feature sizes continue to shrink, accurate and efficient simulations of quantum transport become increasingly critical in device design and manufacturing. The nonequilibrium Green's function (NEGF...
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As semiconductor feature sizes continue to shrink, accurate and efficient simulations of quantum transport become increasingly critical in device design and manufacturing. The nonequilibrium Green's function (NEGF) formalism is a widely used method for simulating quantum transport in semiconductor devices, but it is computationally demanding. quantum computing offers a promising solution, in this work, we pioneer the application of the variational quantum linear solver (VQLS) to the NEGF problem, addressing the challenges associated with handling complex numbers inherent in quantum transport equations. We introduce a new cost function tailored to this framework, demonstrating improved performance over existing approaches. Furthermore, we show that VQLS can efficiently parallelize the computation across different energy levels, significantly reducing computational costs. Our results highlight the potential of variational quantum algorithms (VQAs) in enhancing the scalability and efficiency of quantum transport simulations.
Variational quantum algorithms (VQAs) use classical computers as the quantum outer loop optimizer and update the circuit parameters to obtain an approximate ground state. In this article, we present a meta-learning va...
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Variational quantum algorithms (VQAs) use classical computers as the quantum outer loop optimizer and update the circuit parameters to obtain an approximate ground state. In this article, we present a meta-learning variational quantum algorithm (meta-VQA) by recurrent unit, which uses a technique called "meta-learner." Motivated by the hybrid quantum-classical algorithms, we train classical recurrent units to assist quantum computing, learning to find approximate optima in the parameter landscape. Here, aiming to reduce the sampling number more efficiently, we use the quantum stochastic gradient descent method and introduce the adaptive learning rate. Finally, we deploy on the TensorFlow quantum processor within approximate quantum optimization for the Ising model and variational quantum eigensolver for molecular hydrogen (H-2), lithium hydride (LiH), and helium hydride cation (HeH+). Our algorithm can be expanded to larger system sizes and problem instances, which have higher performance on near-term processors.
quantum computing holds the potential to revolutionize various fields by efficiently tackling complex problems. At its core are quantum circuits, sequences of quantum gates manipulating quantum states. The selection o...
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ISBN:
(纸本)9798350368482;9798350368475
quantum computing holds the potential to revolutionize various fields by efficiently tackling complex problems. At its core are quantum circuits, sequences of quantum gates manipulating quantum states. The selection of the right quantum circuit ansatz, which defines initial circuit structures and serves as the basis for optimization techniques, is crucial in quantum algorithm design. This paper presents a categorized catalog of quantum circuit ansatzes aimed at supporting quantum algorithm design and implementation. Each ansatz is described with details such as intent, motivation, applicability, circuit diagram, implementation, example, and see also. Practical examples are provided to illustrate their application in quantum algorithm design. The catalog aims to assist quantum algorithm designers by offering insights into the strengths and limitations of different ansatzes, thereby facilitating decision-making for specific tasks.
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real -world data are represented as vectors, forming a line...
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Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real -world data are represented as vectors, forming a linear subspace for a given data collection. Computing distances between different subspaces is generally a computationally challenging problem with both theoretical and applicable consequences, as, for example, the results can be used to classify data from different categories. Fueled by the fast-growing development of quantum algorithms, we consider such problems in the quantum context and provide a quantum algorithm for estimating two kinds of distance: Grassmann distance and ellipsoid distance. Under appropriate assumptions and conditions, the speedup of our quantum algorithm is exponential with respect to both the dimension of the given data and the number of data points. Some extensions regarding estimating different kinds of distance are then discussed as a corollary of our main quantum algorithmic method.
Classical multidimensional scaling is an important dimensionality reduction method that is characterized by preserving the Euclidean distance between samples in high dimensional space in low dimensional space. However...
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Classical multidimensional scaling is an important dimensionality reduction method that is characterized by preserving the Euclidean distance between samples in high dimensional space in low dimensional space. However the high time complexity limits its application in massive samples and high-dimensional data scenarios. As a promising solution, a quantum algorithm for classical multidimensional scaling is proposed in this work, achieving polynomial speedup in terms of sample size compared to classical algorithms. Our algorithm is built on two quantum subroutines, one involving inner product and matrix multiplication, and the other utilizing quantum singular value estimation.
Recently, a quantum algorithm for a fundamentally important task in data mining, association rules mining (ARM), called qARM for short, has been proposed. Notably, qARM achieves significant speedup over its classical ...
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Recently, a quantum algorithm for a fundamentally important task in data mining, association rules mining (ARM), called qARM for short, has been proposed. Notably, qARM achieves significant speedup over its classical counterpart for implementing the main task of ARM, i.e., finding frequent itemsets from a transaction database. In this paper, we experimentally implement qARM on both real quantum computers and a quantum computing simulator via the IBM quantum computing platform. In the first place, we design quantum circuits of qARM for a 2 x 2 transaction database (i.e., a transaction database involving two transactions and two items), and run it on four real five-qubit IBM quantum computers as well as on the simulator. For a larger 4 x 4 transaction database which would lead to circuits with more qubits and a higher depth than the currently accessible IBM real quantum devices can handle, we also construct the quantum circuits of qARM and execute them on "aer_simulator" alone. Both experimental results show that all the frequent itemsets from the two transaction databases are successfully derived as desired, demonstrating the correctness and feasibility of qARM. Our work may serve as a benchmarking, and provide prototypes for implementing qARM for larger transaction databases on both noisy intermediate-scale quantum devices and universal fault-tolerant quantum computers.
We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only int...
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We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in its vicinity). This class of Hamiltonians is very general and is believed to capture fundamental interactions of physics. Our algorithm simulates the time evolution of such a Hamiltonian on n qubits for time T up to error epsilon using O (nT polylog(nT/epsilon)) gates with depth O (T polylog(nT/epsilon)). Our algorithm is the first simulation algorithm that achieves gate cost quasilinear in nT and polylogarithmic in 1/epsilon. Our algorithm also readily generalizes to time-dependent Hamiltonians and yields an algorithm with similar gate count for any piecewise slowly varying time-dependent bounded local Hamiltonian. We also prove a matching lower bound on the gate count of such a simulation, showing that any quantum algorithm that can simulate a piecewise constant bounded local Hamiltonian in one dimension to constant error requires (sic) (nT) gates in the worst case. The lower bound holds even if we only require the output state to be correct on local measurements. To the best of our knowledge, this is the first nontrivial lower bound on the gate complexity of the simulation problem. Our algorithm is based on a decomposition of the time-evolution unitary into a product of small unitaries using Lieb-Robinson bounds. In the appendix, we prove a Lieb--Robinson bound tailored to Hamiltonians with small commutators between local terms, giving zero Lieb--Robinson velocity in the limit of commuting Hamiltonians. This improves the performance of our algorithm when the Hamiltonian is close to commuting.
We present a novel quantum algorithm to evaluate the hamming distance between two unknown oracles via measuring the degree of entanglement between two ancillary *** particular,we use the power of the entanglement degr...
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We present a novel quantum algorithm to evaluate the hamming distance between two unknown oracles via measuring the degree of entanglement between two ancillary *** particular,we use the power of the entanglement degree based quantum computing model that preserves at most the locality of interactions within the quantum model *** model uses one of two techniques to retrieve the solution of a quantum computing problem at *** the first technique,the solution of the problem is obtained based on whether there is an entanglement between the two ancillary qubits or *** the second,the solution of the quantum computing problem is obtained as a function in the concurrence value,and the number of states that can be generated from the Boolean *** proposed algorithm receives two oracles,each oracle represents an unknown Boolean function,then it measures the hamming distance between these two *** hamming distance is evaluated based on the second *** is shown that the proposed algorithm provides exponential speedup compared with the classical counterpart for Boolean functions that have large numbers of Boolean *** proposed algorithm is explained via a case ***,employing recently developed experimental techniques,the proposed algorithm has been verified using IBM’s quantum computer simulator.
Anomaly detection of sequences is a hot topic in data mining. Anomaly detection using piecewise aggregate approximation in the amplitude domain (called ADPAAD) is one of the widely used methods in anomaly detection of...
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Anomaly detection of sequences is a hot topic in data mining. Anomaly detection using piecewise aggregate approximation in the amplitude domain (called ADPAAD) is one of the widely used methods in anomaly detection of sequences. The core step in the classical algorithm for performing ADPAAD is to construct an approximate representation of the subsequence, where the elements of each subsequence are divided into several subsections according to the amplitude domain, and then the average of the subsections is computed. It is computationally expensive when processing large-scale sequences. In this paper, a quantum algorithm for ADPAAD is proposed, which can divide the subsequence elements and compute the average in parallel. The quantum algorithm can achieve polynomial speedups on the number of subsequences and the length of subsequences over its classical counterpart.
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