Classical machine learning algorithms seem to be totally incapable of processing tremendous data,while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over...Classical machine learning algorithms seem to be totally incapable of processing tremendous data,while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over classical counterparts.In this paper,we propose two quantum support vector machine algorithms for multi classification.One is the quantum version of the directed acyclic graph support vector machine.The other one is to use the Grover search algorithm before measurement,which amplifies the amplitude of the phase storing of the classification result.For k classification,the former provides quadratic reduction in computational complexity when classifying.The latter accelerates the training speed significantly and more importantly,the classification result can be read out with a probability of at least 50%using only one measurement.We conduct numerical simulations on two algorithms,and their classification success rates are 96%and 88.7%,respectively.展开更多
Our aim is to determine the conditions for quantum computing technology to give rise to the security risks associated with quantum Bitcoin mining.Specifically,we determine the speed and energy efficiency a quantum com...Our aim is to determine the conditions for quantum computing technology to give rise to the security risks associated with quantum Bitcoin mining.Specifically,we determine the speed and energy efficiency a quantum computer needs to offer an advantage over classical mining.We analyze the setting in which the Bitcoin network is entirely classical except for a single quantum miner with a small hash rate compared to the network.We develop a closed-form approximation for the probability that the quantum miner successfully mines a block,with this probability dependent on the number of Grover iterations the quantum miner applies before making a measurement.Next,we show that for a quantum miner that is“peaceful”,this success probability is maximized if the quantum miner applies Grover iterations for 16 min before measuring,which is surprising,as the network mines blocks every 10 min on average.Using this optimal mining procedure,we show that the quantum miner outperforms a classical computer in efficiency(cost per block)if the condition Q<Crb is satisfied,where Q is the cost of a Grover iteration,C is the cost of a classical hash,r is the quantum miner's speed in Grover iterations per second,and b is a factor that attains its maximum if the quantum miner uses our optimal mining procedure.This condition lays the foundation for determining when quantum mining and the known security risks associated with it will arise.展开更多
A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gat...A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gates are constructed and their universality is proved.As an application,a search algorithm is designed for this computer model and is found to be exponentially faster than Grover's search algorithm.展开更多
Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative ...Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success probability.We show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target states.Moreover,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.展开更多
We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs few...We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs fewer iteration steps and uses the carriers of the information more economically. To illustrate how to realize the idea with concrete physical systems, we propose a scheme to carry out a twelve-dimensional partial search of the database partitioned into three blocks with superconducting quantum interference devices （SQUIDs） in cavity QED. Through the appropriate modulation of the amplitudes of the microwave pulses, the scheme can overcome the non-identity of the cavity-SQUID coupling strengths due to the parameter variations resulting from the fabrication processes. Numerical simulation under the influence of the cavity and SQUID decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.展开更多
We explore the possibility of an N-qubit （N 〉 3） Grover search in cavity QED, based on a fast operation of an N-qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytic...We explore the possibility of an N-qubit （N 〉 3） Grover search in cavity QED, based on a fast operation of an N-qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and numerically that our scheme can be achieved efficiently to find a marked state with high fidelity and high success probability. As an example, a ten-qubit Grover search is simulated specifically under the discussion of experimental feasibility and challenge. We argue that our scheme is applicable to the case involving an arbitrary number of qubits. As cavity decay is involved in our quantum trajectory treatment, we can analytically understand the implementation of a Grover search subject to dissipation, which will be very helpful for relevant experiments.展开更多
We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation.Using a set of suitable bases,we construct the reduced density matrix and give th...We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation.Using a set of suitable bases,we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations.For different initial states,we obtain the concurrence and quantum discord compared with the success probability in the algorithm.The results show that the initial states affect the correlations and the limit point of the correlations in the searching process.However,the initial states do not influence the whole cyclical trend.展开更多
Grover’s search algorithm is one of the most significant quantum algorithms,which can obtain quadratic speedup of the extensive search problems.Since Grover's search algorithm cannot be implemented on a real quan...Grover’s search algorithm is one of the most significant quantum algorithms,which can obtain quadratic speedup of the extensive search problems.Since Grover's search algorithm cannot be implemented on a real quantum computer at present,its quantum simulation is regarded as an effective method to study the search performance.When simulating the Grover's algorithm,the storage space required is exponential,which makes it difficult to simulate the high-qubit Grover’s algorithm.To this end,we deeply study the storage problem of probability amplitude,which is the core of the Grover simulation algorithm.We propose a novel memory-efficient method via amplitudes compression,and validate the effectiveness of the method by theoretical analysis and simulation experimentation.The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5%of the storage space than the uncompressed one.Thus under the same hardware conditions,our method can dramatically reduce the required computing nodes,and at the same time,it can simulate at least 3 qubits more than the uncompressed one.Particularly,our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation.展开更多
This paper provides an introduction to a quantum search algorithm,known as Grover’s Algorithm,for unsorted search purposes.The algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit SDK ...This paper provides an introduction to a quantum search algorithm,known as Grover’s Algorithm,for unsorted search purposes.The algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit SDK by IBM.While providing detailed proof,the computational complexity of the algorithm is generalized to n qubits.The implementation results obtained from the IBM QASM Simulator and IBMQ Santiago quantum backend are analyzed and compared.Finally,the paper discusses the challenges faced in implementation and real-life applications of the algorithm hitherto.Overall,the implementation and analysis depict the advantages of this quantum search algorithm over its classical counterparts.展开更多
We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for applying the speed limit of the imaginary-time Schrödinger equation derived by Okuyama and Ohzeki and t...We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for applying the speed limit of the imaginary-time Schrödinger equation derived by Okuyama and Ohzeki and the new class of energy-time uncertainty relation proposed by Kieu. It is found that the computational time of the imaginary-time quantum annealing of this Grover search can be exponentially small, while the counterpart of the quantum evolution driven by the real-time Schrödinger equation could only provide square root speedup, compared with classic search. The present results are consistent with the cases of the time-dependent quantum evolution of the natural Grover problem in previous works. We once again emphasize that the logarithm and square root algorithmic performances are generic in imaginary-time quantum annealing and quantum evolution driven by real-time Schrödinger equation, respectively. Also, we provide evidences to search deep reasons why the imaginary-time quantum annealing can lead to exponential speedup and the real-time quantum annealing can make square root speedup.展开更多
A detailed analysis has showed that the quantum secret sharing protocol based on the Grover algorithm (Phys Rev A, 2003, 68: 022306) is insecure. A dishonest receiver may obtain the full information without being dete...A detailed analysis has showed that the quantum secret sharing protocol based on the Grover algorithm (Phys Rev A, 2003, 68: 022306) is insecure. A dishonest receiver may obtain the full information without being detected. A quantum secret-sharing protocol is presents here, which mends the security loophole of the original secret-sharing protocol, and doubles the information capacity.展开更多
基金supported by the Shandong Provincial Natural Science Foundation for Quantum Science(No.ZR2021LLZ002)the Fundamental Research Funds for the Central Universities(No.22CX03005A).
文摘Classical machine learning algorithms seem to be totally incapable of processing tremendous data,while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over classical counterparts.In this paper,we propose two quantum support vector machine algorithms for multi classification.One is the quantum version of the directed acyclic graph support vector machine.The other one is to use the Grover search algorithm before measurement,which amplifies the amplitude of the phase storing of the classification result.For k classification,the former provides quadratic reduction in computational complexity when classifying.The latter accelerates the training speed significantly and more importantly,the classification result can be read out with a probability of at least 50%using only one measurement.We conduct numerical simulations on two algorithms,and their classification success rates are 96%and 88.7%,respectively.
文摘Our aim is to determine the conditions for quantum computing technology to give rise to the security risks associated with quantum Bitcoin mining.Specifically,we determine the speed and energy efficiency a quantum computer needs to offer an advantage over classical mining.We analyze the setting in which the Bitcoin network is entirely classical except for a single quantum miner with a small hash rate compared to the network.We develop a closed-form approximation for the probability that the quantum miner successfully mines a block,with this probability dependent on the number of Grover iterations the quantum miner applies before making a measurement.Next,we show that for a quantum miner that is“peaceful”,this success probability is maximized if the quantum miner applies Grover iterations for 16 min before measuring,which is surprising,as the network mines blocks every 10 min on average.Using this optimal mining procedure,we show that the quantum miner outperforms a classical computer in efficiency(cost per block)if the condition Q<Crb is satisfied,where Q is the cost of a Grover iteration,C is the cost of a classical hash,r is the quantum miner's speed in Grover iterations per second,and b is a factor that attains its maximum if the quantum miner uses our optimal mining procedure.This condition lays the foundation for determining when quantum mining and the known security risks associated with it will arise.
基金supported by the National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)the National Natural Science Foundation of China(Grant No.11921005)Shanghai Municipal Science and Technology Major Project(Grant No.2019SHZDZX01)。
文摘A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gates are constructed and their universality is proved.As an application,a search algorithm is designed for this computer model and is found to be exponentially faster than Grover's search algorithm.
基金supported by the National Natural Science Foundation of China(Grant Nos.12161056,12075159,12171044)Beijing Natural Science Foundation(Grant No.Z190005)the Academician Innovation Platform of Hainan Province。
文摘Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success probability.We show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target states.Moreover,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.
基金Project supported by the National Natural Science Foundation of China(Grant No.10774192)
文摘We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs fewer iteration steps and uses the carriers of the information more economically. To illustrate how to realize the idea with concrete physical systems, we propose a scheme to carry out a twelve-dimensional partial search of the database partitioned into three blocks with superconducting quantum interference devices （SQUIDs） in cavity QED. Through the appropriate modulation of the amplitudes of the microwave pulses, the scheme can overcome the non-identity of the cavity-SQUID coupling strengths due to the parameter variations resulting from the fabrication processes. Numerical simulation under the influence of the cavity and SQUID decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.
基金Project supported by National Natural Science Foundation of China (Grant Nos 10474118, 60490280 and 10774161)partly by the National Fundamental Research Program of China (Grants Nos 2005CB724502 and 2006CB921203)
文摘We explore the possibility of an N-qubit （N 〉 3） Grover search in cavity QED, based on a fast operation of an N-qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and numerically that our scheme can be achieved efficiently to find a marked state with high fidelity and high success probability. As an example, a ten-qubit Grover search is simulated specifically under the discussion of experimental feasibility and challenge. We argue that our scheme is applicable to the case involving an arbitrary number of qubits. As cavity decay is involved in our quantum trajectory treatment, we can analytically understand the implementation of a Grover search subject to dissipation, which will be very helpful for relevant experiments.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)Shandong Province Higher Educational Science and Technology Program,China(Grant No.J18KZ012).
文摘We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation.Using a set of suitable bases,we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations.For different initial states,we obtain the concurrence and quantum discord compared with the success probability in the algorithm.The results show that the initial states affect the correlations and the limit point of the correlations in the searching process.However,the initial states do not influence the whole cyclical trend.
基金This work was supported by Funding of National Natural Science Foundation of China(Grant No.61571226,Grant No.61701229).
文摘Grover’s search algorithm is one of the most significant quantum algorithms,which can obtain quadratic speedup of the extensive search problems.Since Grover's search algorithm cannot be implemented on a real quantum computer at present,its quantum simulation is regarded as an effective method to study the search performance.When simulating the Grover's algorithm,the storage space required is exponential,which makes it difficult to simulate the high-qubit Grover’s algorithm.To this end,we deeply study the storage problem of probability amplitude,which is the core of the Grover simulation algorithm.We propose a novel memory-efficient method via amplitudes compression,and validate the effectiveness of the method by theoretical analysis and simulation experimentation.The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5%of the storage space than the uncompressed one.Thus under the same hardware conditions,our method can dramatically reduce the required computing nodes,and at the same time,it can simulate at least 3 qubits more than the uncompressed one.Particularly,our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation.
文摘This paper provides an introduction to a quantum search algorithm,known as Grover’s Algorithm,for unsorted search purposes.The algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit SDK by IBM.While providing detailed proof,the computational complexity of the algorithm is generalized to n qubits.The implementation results obtained from the IBM QASM Simulator and IBMQ Santiago quantum backend are analyzed and compared.Finally,the paper discusses the challenges faced in implementation and real-life applications of the algorithm hitherto.Overall,the implementation and analysis depict the advantages of this quantum search algorithm over its classical counterparts.
基金Project supported by the China Postdoctoral Science Foundation (Grant No. 2017M620322)the Priority Fund for the Postdoctoral Scientific and Technological Program of Hubei Province in 2017, the Seed Foundation of Huazhong University of Science and Technology (Grant No. 2017KFYXJJ070)the Science and Technology Program of Shenzhen of China (Grant No. JCYJ 20180306124612893).
文摘We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for applying the speed limit of the imaginary-time Schrödinger equation derived by Okuyama and Ohzeki and the new class of energy-time uncertainty relation proposed by Kieu. It is found that the computational time of the imaginary-time quantum annealing of this Grover search can be exponentially small, while the counterpart of the quantum evolution driven by the real-time Schrödinger equation could only provide square root speedup, compared with classic search. The present results are consistent with the cases of the time-dependent quantum evolution of the natural Grover problem in previous works. We once again emphasize that the logarithm and square root algorithmic performances are generic in imaginary-time quantum annealing and quantum evolution driven by real-time Schrödinger equation, respectively. Also, we provide evidences to search deep reasons why the imaginary-time quantum annealing can lead to exponential speedup and the real-time quantum annealing can make square root speedup.
基金supported by the National Natural Science Foundation of China (GrantNos. 10775076 and 60635040)the National Basic Research Program of China (Grant No. 2006CB921106)the SRFPD Program of Education Ministry of China
文摘A detailed analysis has showed that the quantum secret sharing protocol based on the Grover algorithm (Phys Rev A, 2003, 68: 022306) is insecure. A dishonest receiver may obtain the full information without being detected. A quantum secret-sharing protocol is presents here, which mends the security loophole of the original secret-sharing protocol, and doubles the information capacity.
基金Supported by National Natural Science Foundation of China under Grant Nos.60073039 60273080 (国家自然科学基金)+1 种基金 the Science and Technology Development Program of Jilin Provience of China under Grant No.20020306 (吉林省科技发展计划) the Foundation
