Verifying system specifications is a crucial requirement in science and technology, as it improves accuracy and efficiency in systems engineering. However, traditional computers are time-consuming and cannot efficient...
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Verifying system specifications is a crucial requirement in science and technology, as it improves accuracy and efficiency in systems engineering. However, traditional computers are time-consuming and cannot efficiently check the consistency of system specifications for classical and quantum systems due to exponential complexity costs. Currently, there is no quantum approach available for verifying consistency in quantum systems. This article introduces a novel quantum algorithm that utilizes the virtual degree of entanglement to efficiently check the consistency of unknown system specifications represented by m oracles. The proposed algorithm has a time complexity of O(m epsilon(-2)), which is independent of the input size n and depends only on a predetermined error margin epsilon, providing exponential speedup compared to the classical approach with a time complexity of O(m2(n)). Moreover, the proposed algorithm can handle weighted superposition input states, which are impossible for classical computers to handle. Thus, the algorithm has the potential to check the consistency of both quantum and classical system specifications. The proposed algorithm is realized experimentally using IBM's Aer simulator with an input size of n = 12. The experimental results closely aligned with the theoretical predictions, demonstrating the algorithm's efficiency in checking the consistency of system specifications. Specifically, the proposed algorithm achieved a quantum supremacy ratio of 300% to 3100% compared to the classical algorithm, highlighting its significant advantage in terms of time complexity. Additionally, the simulation results confirmed the efficiency of the proposed algorithm in checking the consistency of the quantum system's specifications.
Non-convex optimization is an essential problem in the field of machine learning. Optimization methods for non-convex problems can be roughly di- vided into first-order methods and second-order methods, depending on t...
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Non-convex optimization is an essential problem in the field of machine learning. Optimization methods for non-convex problems can be roughly di- vided into first-order methods and second-order methods, depending on the or- der of the derivative to the objective function they used. Generally, to find the local minima, the second-order methods are applied to find the effective direc- tion to escape the saddle point. Specifically, finding the Negative Curvature is considered as the subroutine to analyze the characteristic of the saddle point. However, the calculation of the Negative Curvature is expensive, which prevents the practical usage of second-order algorithms. In this thesis, we present an efficient quantum algorithm aiming to find the negative curvature direction for escaping the saddle point, which is a critical subroutine for many second-order non-convex optimization algorithms. We prove that our algorithm could produce the target state corresponding to the negative curvature direction with query complexity ˜ O(polylog(d)ϵ −1 ), where d is the dimension of the optimization function. The quantum negative curva- ture finding algorithm is exponentially faster than any known classical method, which takes time at least O(dϵ −1/2 ). Moreover, we propose an efficient quan- tum algorithm to achieve the classical read-out of the target state. Our classical read-out algorithm runs exponentially faster on the degree of d than existing counterparts.
A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than ...
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A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.
An algorithm is exact if it always produces the correct answer on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. Nim ga...
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An algorithm is exact if it always produces the correct answer on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. Nim game is a well-known combinatorial game which has a complete mathematical theory, and many kinds of Nim games have been studied in the literature. One famous kind of Nim games are subtraction games played with one heap of tokens, with players taking turns removing from the heap a number of tokens belonging to a specified subtraction set. The last player to move wins. In this paper, we propose a restricted subtraction game with the subtraction set determined by a specified matrix, and present an exact quantum algorithm to solve it. We show that the query complexity of our quantum algorithm is O(n(3/2)), while the classical exact query complexity is Theta(n(2)).
Ant colony optimisation (ACO) is a commonly used meta-heuristic to solve complex combinatorial optimisation problems like the travelling salesman problem (TSP), vehicle routing problem (VRP) etc. However, classical AC...
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Ant colony optimisation (ACO) is a commonly used meta-heuristic to solve complex combinatorial optimisation problems like the travelling salesman problem (TSP), vehicle routing problem (VRP) etc. However, classical ACO algorithms provide better optimal solutions but do not reduce computation time overhead to a significant extent. algorithmic speed-up can be achieved by using parallelism offered by quantum computing. Existing quantum algorithms to solve ACO are either quantum-inspired classical algorithms or hybrid quantum-classical algorithms. Since all these algorithms need the intervention of classical computing, leveraging the true potential of quantum computing on real quantum hardware remains a challenge. This study's main contribution is to propose a fully quantum algorithm to solve ACO, enhancing the quantum information processing toolbox in the fault-tolerant quantum computing (FTQC) era. We have solved the single source single destination (SSSD) shortest-path problem using our proposed adaptive quantum circuit for representing the dynamic pheromone-updating strategy in real IBMQ devices. Our quantum ACO technique can be further used as a quantum ORACLE to solve complex optimisation problems in a fully quantum setup with significant speed up upon the availability of more qubits.
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the line...
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Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum mechanics has limited analogous progress for the nonlinear case. Despite this obstacle, we develop a quantum algorithm for dissipative quadratic n-dimensional ordinary differential equations. Assuming R < 1, where R is a parameter characterizing the ratio of the non-linearity and forcing to the linear dissipation, this algorithm has complexity T-2 q poly(log T, log n, log 1/epsilon)/epsilon, where T is the evolution time, E is the allowed error, and q measures decay of the solution. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in T. While exponential decay precludes efficiency, driven equations can avoid this issue despite the presence of dissipation. Our algorithm uses the method of Carleman linearization, for which we give a convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for R >= root 2 Finally, we discuss potential applications, showing that the R < 1 condition can be satisfied in realistic epidemiological models and giving numerical evidence that the method may describe a model of fluid dynamics even for larger values of R.
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach...
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Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm which is a combination of the ordinary quantum algorithm with a chaotic dynamical system. We consider the satisfiability problem as an example of NP-complete problems and argue that the problem, in principle, can be solved in polynomial time by using our new quantum algorithm.
There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. ...
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There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we define the continuous hidden shift problem on R-n with a continuous oracle function as an extension of the hidden shift problem, and also define the epsilon-random linear disequations which is a generalization of the random linear disequations. By employing the newly defined concepts, we show that there exists a quantum computational algorithm which solves this problem in time polynomial in n.
To solve the subset sum problem, a well-known nondeterministic polynomial-time complete problem that is widely used in encryption and resource scheduling, we propose a feasible quantum algorithm that utilizes fewer qu...
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To solve the subset sum problem, a well-known nondeterministic polynomial-time complete problem that is widely used in encryption and resource scheduling, we propose a feasible quantum algorithm that utilizes fewer qubits to encode and achieves quadratic speedup. Specifically, this algorithm combines an amplitude amplification algorithm with quantum phase estimation, and requires n + t + 1 qubits and O(2(0.5+o(1))n) operations to obtain the solution, where n is the number of elements, and t is the number of qubits used to store the eigenvalues. To verify the performance of the algorithm, we simulate the algorithm with the online quantum simulator of IBM named ibmq simulator using Qiskit and then run it on two IBM quantum computers called ibmq santiago and ibmq bogota. The experimental results indicate that compared with the brute force algorithm, the proposed algorithm results in quadratic acceleration for the problem of a set S with four elements and two subsets whose sum equals target w. Using the iterator twice, we obtain success probabilities of 0.940 ± 0.004, 0.751 ± 0.040, and 0.665 ± 0.060 on the simulator, ibmq santiago, and ibmq bogota, respectively, and the fidelity between the theoretical and experimental quantum states is calculated to be 0.944 ± 0.002, 0.753 ± 0.017, and 0.657 ± 0.028, respectively. If the error rates of the experimental quantum logic gates can be reduced, the success probabilities of the proposed algorithm on real quantum devices can be further improved.
Adaptive active noise control based on least mean square (LMS) algorithm is a linear adaptive filter so that it cannot obtain desired noise reduction. quantum algorithm is combined with noise control to form quantum a...
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ISBN:
(纸本)9783037853559
Adaptive active noise control based on least mean square (LMS) algorithm is a linear adaptive filter so that it cannot obtain desired noise reduction. quantum algorithm is combined with noise control to form quantum adaptive controller. quantum adaptive algorithm is discussed completely and noise control system is simulated in order to analyze the effects of noise control.
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