Cybercrime is projected to cost a whopping $23.8 Trillion by 2027. This is essentially because there’s no computer network that’s not vulnerable. Fool-proof cybersecurity of personal data in a connected computer is ...Cybercrime is projected to cost a whopping $23.8 Trillion by 2027. This is essentially because there’s no computer network that’s not vulnerable. Fool-proof cybersecurity of personal data in a connected computer is considered practically impossible. The advent of quantum computers (QC) will worsen cybersecurity. QC will be a boon for data-intensive industries by drastically reducing the computing time from years to minutes. But QC will render our current cryptography vulnerable to quantum attacks, breaking nearly all modern cryptographic systems. Before QCs with sufficient qubits arrive, we must be ready with quantum-safe strategies to protect our ICT infrastructures. Post-quantum cryptography (PQC) is being aggressively pursued worldwide as a defence from the potential Q-day threat. NIST (National Institute of Standards and Technology), in a rigorous process, tested 82 PQC schemes, 80 of which failed after the final round in 2022. Recently the remaining two PQCs were also cracked by a Swedish and a French team of cryptographers, placing NIST’s PQC standardization process in serious jeopardy. With all the NIST-evaluated PQCs failing, there’s an urgent need to explore alternate strategies. Although cybersecurity heavily relies on cryptography, recent evidence indicates that it can indeed transcend beyond encryption using Zero Vulnerability Computing (ZVC) technology. ZVC is an encryption-agnostic absolute zero trust (AZT) approach that can potentially render computers quantum resistant by banning all third-party permissions, a root cause of most vulnerabilities. Unachievable in legacy systems, AZT is pursued by an experienced consortium of European partners to build compact, solid-state devices that are robust, resilient, energy-efficient, and with zero attack surface, rendering them resistant to malware and future Q-Day threats.展开更多
With one billion users using 380 exchanges, the security of blockchains and cryptocurrencies remains a major concern as billions are lost to hackers every year. Cryptocurrency hacks negatively impact cryptocurrency ma...With one billion users using 380 exchanges, the security of blockchains and cryptocurrencies remains a major concern as billions are lost to hackers every year. Cryptocurrency hacks negatively impact cryptocurrency markets introducing volatility. Each major scam/hack incident results in a significant price dip for most cryptocurrencies, decelerating the growth of the blockchain economy. Existing blockchain vulnerabilities are further amplified by the impending existential threat from quantum computers. While there’s no reprieve yet from the scam/hack prone blockchain economy, quantum resilience is being aggressively pursued by post quantum cryptography (PQC) researchers, despite 80 of 82 candidate PQCs failing. As PQC has no role in combating inherent vulnerabilities, securing over 1000 existing blockchains against scammers/hackers remains a top priority for this industry. This research proposes a novel Quantum-safe Ledger Technology (QLT) framework that not only secures DLTs/cryptocurrencies and exchanges from current vulnerabilities but protects them from the impending Q-day threats from future quantum computers. As blockchain-agnostic technology, the QLT framework can be easily adapted to secure any blockchain or crypto exchange.展开更多
This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we esta...This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.展开更多
In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient c...In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.展开更多
In this paper, a collection of value-based quantum reinforcement learning algorithms are introduced which use Grover’s algorithm to update the policy, which is stored as a superposition of qubits associated with each...In this paper, a collection of value-based quantum reinforcement learning algorithms are introduced which use Grover’s algorithm to update the policy, which is stored as a superposition of qubits associated with each possible action, and their parameters are explored. These algorithms may be grouped in two classes, one class which uses value functions (V(s)) and new class which uses action value functions (Q(s,a)). The new (Q(s,a))-based quantum algorithms are found to converge faster than V(s)-based algorithms, and in general the quantum algorithms are found to converge in fewer iterations than their classical counterparts, netting larger returns during training. This is due to fact that the (Q(s,a)) algorithms are more precise than those based on V(s), meaning that updates are incorporated into the value function more efficiently. This effect is also enhanced by the observation that the Q(s,a)-based algorithms may be trained with higher learning rates. These algorithms are then extended by adding multiple value functions, which are observed to allow larger learning rates and have improved convergence properties in environments with stochastic rewards, the latter of which is further improved by the probabilistic nature of the quantum algorithms. Finally, the quantum algorithms were found to use less CPU time than their classical counterparts overall, meaning that their benefits may be realized even without a full quantum computer.展开更多
In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find seve...In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.展开更多
We propose an efficient scheme for realizing quantum dense coding with three-particle GHZ state in separated low-Q cavities. In this paper, the GHZ state is first prepared with three atoms trapped, respectively, in th...We propose an efficient scheme for realizing quantum dense coding with three-particle GHZ state in separated low-Q cavities. In this paper, the GHZ state is first prepared with three atoms trapped, respectively, in three spatial separated cavities. Meanwhile, with the assistance of a coherent optical pulse and X-quadrature homodyne measurement, we can im- plement quantum dense coding with three-particle GHZ state with a higher probability. Our scheme can also be generalized to realize N-particle quantum dense coding.展开更多
As one of essential multimedia in quantum networks, the copyright protection of quantum audio has gradually be- come an important issue in the domain of quantum information hiding in the decades. In this paper, an imp...As one of essential multimedia in quantum networks, the copyright protection of quantum audio has gradually be- come an important issue in the domain of quantum information hiding in the decades. In this paper, an improved quantum watermarking algorithm based on quantum audio by using least significant qubit （LSQb） modification is proposed. Com- pared with the previous achievements, it can effectively improve the robustness and security of watermark for copyright protection of quantum audio. In the new algorithm, the least significant bites and the peripheral least significant bits of the amplitudes are modified in terms of their logical consistency and correlation to enhance watermark robustness of resisting various illegal attacks. Furthermore, the new algorithm can avoid the weak robustness defect of many previous algorithms that directly embedded the watermark into the least significant bits. In order to implement the new algorithm, some spe- cific quantum circuits are designed to obtain better applicability and scalability for embedding and extracting watermark. Finally, the simulation results including the values of audio waveforms and signal to noise ratios （SNR） prove that the new algorithm has good transparency, robustness, and security.展开更多
Applying quantum computing techniques to machine learning has attracted widespread attention recently and quantum machine learning has become a hot research topic. There are three major categories of machine learning:...Applying quantum computing techniques to machine learning has attracted widespread attention recently and quantum machine learning has become a hot research topic. There are three major categories of machine learning: supervised, unsupervised, and reinforcement learning (RL). However, quantum RL has made the least progress when compared to the other two areas. In this study, we implement the well-known RL algorithm Q learning with a quantum neural network and evaluate it in the grid world environment. RL is learning through interactions with the environment, with the aim of discovering a strategy to maximize the expected cumulative rewards. Problems in RL bring in unique challenges to the study with their sequential nature of learning, potentially long delayed reward signals, and large or infinite size of state and action spaces. This study extends our previous work on solving the contextual bandit problem using a quantum neural network, where the reward signals are immediate after each action.展开更多
With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivatio...With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivation and simulation verification of quantum computation(especially quantum algorithms),experimental verification on real quantum devices has become a new trend.In this paper,three representative quantum algorithms,namely Deutsch-Jozsa,Grover,and Shor algorithms,are briefly depicted,and then their implementation circuits are presented,respectively.We program these circuits on python with QISKit to connect the remote real quantum devices(i.e.,ibmqx4,ibmqx5)on IBM Q to verify these algorithms.The experimental results not only show the feasibility of these algorithms,but also serve to evaluate the functionality of these devices.展开更多
The advantage of quantum computers over classical computers fuels the recent trend of developing machine learning algorithms on quantum computers, which can potentially lead to breakthroughs and new learning models in...The advantage of quantum computers over classical computers fuels the recent trend of developing machine learning algorithms on quantum computers, which can potentially lead to breakthroughs and new learning models in this area. The aim of our study is to explore deep quantum reinforcement learning (RL) on photonic quantum computers, which can process information stored in the quantum states of light. These quantum computers can naturally represent continuous variables, making them an ideal platform to create quantum versions of neural networks. Using quantum photonic circuits, we implement Q learning and actor-critic algorithms with multilayer quantum neural networks and test them in the grid world environment. Our experiments show that 1) these quantum algorithms can solve the RL problem and 2) compared to one layer, using three layer quantum networks improves the learning of both algorithms in terms of rewards collected. In summary, our findings suggest that having more layers in deep quantum RL can enhance the learning outcome.展开更多
Traditional reinforcement learning (RL) uses the return, also known as the expected value of cumulative random rewards, for training an agent to learn an optimal policy. However, recent research indicates that learnin...Traditional reinforcement learning (RL) uses the return, also known as the expected value of cumulative random rewards, for training an agent to learn an optimal policy. However, recent research indicates that learning the distribution over returns has distinct advantages over learning their expected value as seen in different RL tasks. The shift from using the expectation of returns in traditional RL to the distribution over returns in distributional RL has provided new insights into the dynamics of RL. This paper builds on our recent work investigating the quantum approach towards RL. Our work implements the quantile regression (QR) distributional Q learning with a quantum neural network. This quantum network is evaluated in a grid world environment with a different number of quantiles, illustrating its detailed influence on the learning of the algorithm. It is also compared to the standard quantum Q learning in a Markov Decision Process (MDP) chain, which demonstrates that the quantum QR distributional Q learning can explore the environment more efficiently than the standard quantum Q learning. Efficient exploration and balancing of exploitation and exploration are major challenges in RL. Previous work has shown that more informative actions can be taken with a distributional perspective. Our findings suggest another cause for its success: the enhanced performance of distributional RL can be partially attributed to its superior ability to efficiently explore the environment.展开更多
After a straightforward general relativistic calculation on a modified flat-spacetime metric (developed from the fluctuating vacuum energy interacting with a graviton field), a pair of n-valued covariant and contravar...After a straightforward general relativistic calculation on a modified flat-spacetime metric (developed from the fluctuating vacuum energy interacting with a graviton field), a pair of n-valued covariant and contravariant energy momentum tensors emerged analogous to quantized raising and lower operators. Detaching these operators from the general relativistic field equations, and then transporting them to act on extreme spacetimes, these operators were able to generate fundamental particle boson masses. In particular, the operators precisely generated Higgs mass. Then by applying a consistency approach to the gravitational field equations—similar to how Maxwell applied to the electromagnetic ones—it allowed for the coupling of spin-to-mass, further restricting the particle mass to be in precise agreement with CODATA experimental values. Since this is a massless field approach integrated discretely with a massive one, it overcomes various renormalizing difficulties;moreover it solves the mass hierarchal problem of the Standard Model of particle physics, and generates its spin and therefore shows quantum physics to be a subset of General Relativity, just as Einstein had first imagined.展开更多
The relation between noncommutative (or quantum) geometry and themathematics of spacesis in many ways similar to the relation between quantum physicsand classical physics. One moves from the commutative algebra of fun...The relation between noncommutative (or quantum) geometry and themathematics of spacesis in many ways similar to the relation between quantum physicsand classical physics. One moves from the commutative algebra of functions on a space (or a commutative algebra of classical observable in classical physics) to a noncommutative algebra representing a noncommutative space (or a noncommutative algebra of quantum observables in quantum physics). The object of this paper is to study the basic rules governing q-calculus as compared with the classical Newton-Leibnitz calculus.展开更多
In this paper, we present the exact solution of the one-dimensional Schrrdinger equation for the q-deformed quantum potentials via the Nikiforov-Uvarov method. The eigenvalues and eigenfunctions of these potentials ar...In this paper, we present the exact solution of the one-dimensional Schrrdinger equation for the q-deformed quantum potentials via the Nikiforov-Uvarov method. The eigenvalues and eigenfunctions of these potentials are obtained via this method. The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed. The PT-symmetry and Hermiticity for these potentials are also discussed.展开更多
The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique...The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique where the Liouville space is briefly expanded with an additional (virtual) space only within ultrashort subintervals. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically “hitchhiking” via virtual space in discrete ultrashort time duration, are the hallmark of our technique. We believe that this technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.展开更多
A theory of Quantum Gravity based on Primordial Field Theory is applied to a fundamental particle, the neutron. The result is compared to the current quantum description of the neutron bouncing in a gravitational fiel...A theory of Quantum Gravity based on Primordial Field Theory is applied to a fundamental particle, the neutron. The result is compared to the current quantum description of the neutron bouncing in a gravitational field. Our quantum gravity theory yields results in agreement with the Q-bounce experimental data, but ontologically different from quantum mechanics. The differences are summarized and imply that this experiment on a fundamental particle has the potential to radically alter the ontology of field theory.展开更多
文摘Cybercrime is projected to cost a whopping $23.8 Trillion by 2027. This is essentially because there’s no computer network that’s not vulnerable. Fool-proof cybersecurity of personal data in a connected computer is considered practically impossible. The advent of quantum computers (QC) will worsen cybersecurity. QC will be a boon for data-intensive industries by drastically reducing the computing time from years to minutes. But QC will render our current cryptography vulnerable to quantum attacks, breaking nearly all modern cryptographic systems. Before QCs with sufficient qubits arrive, we must be ready with quantum-safe strategies to protect our ICT infrastructures. Post-quantum cryptography (PQC) is being aggressively pursued worldwide as a defence from the potential Q-day threat. NIST (National Institute of Standards and Technology), in a rigorous process, tested 82 PQC schemes, 80 of which failed after the final round in 2022. Recently the remaining two PQCs were also cracked by a Swedish and a French team of cryptographers, placing NIST’s PQC standardization process in serious jeopardy. With all the NIST-evaluated PQCs failing, there’s an urgent need to explore alternate strategies. Although cybersecurity heavily relies on cryptography, recent evidence indicates that it can indeed transcend beyond encryption using Zero Vulnerability Computing (ZVC) technology. ZVC is an encryption-agnostic absolute zero trust (AZT) approach that can potentially render computers quantum resistant by banning all third-party permissions, a root cause of most vulnerabilities. Unachievable in legacy systems, AZT is pursued by an experienced consortium of European partners to build compact, solid-state devices that are robust, resilient, energy-efficient, and with zero attack surface, rendering them resistant to malware and future Q-Day threats.
文摘With one billion users using 380 exchanges, the security of blockchains and cryptocurrencies remains a major concern as billions are lost to hackers every year. Cryptocurrency hacks negatively impact cryptocurrency markets introducing volatility. Each major scam/hack incident results in a significant price dip for most cryptocurrencies, decelerating the growth of the blockchain economy. Existing blockchain vulnerabilities are further amplified by the impending existential threat from quantum computers. While there’s no reprieve yet from the scam/hack prone blockchain economy, quantum resilience is being aggressively pursued by post quantum cryptography (PQC) researchers, despite 80 of 82 candidate PQCs failing. As PQC has no role in combating inherent vulnerabilities, securing over 1000 existing blockchains against scammers/hackers remains a top priority for this industry. This research proposes a novel Quantum-safe Ledger Technology (QLT) framework that not only secures DLTs/cryptocurrencies and exchanges from current vulnerabilities but protects them from the impending Q-day threats from future quantum computers. As blockchain-agnostic technology, the QLT framework can be easily adapted to secure any blockchain or crypto exchange.
文摘This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.
基金Supported by the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2019MS01023)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZZ19209,NJZY20198).
文摘In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.
文摘In this paper, a collection of value-based quantum reinforcement learning algorithms are introduced which use Grover’s algorithm to update the policy, which is stored as a superposition of qubits associated with each possible action, and their parameters are explored. These algorithms may be grouped in two classes, one class which uses value functions (V(s)) and new class which uses action value functions (Q(s,a)). The new (Q(s,a))-based quantum algorithms are found to converge faster than V(s)-based algorithms, and in general the quantum algorithms are found to converge in fewer iterations than their classical counterparts, netting larger returns during training. This is due to fact that the (Q(s,a)) algorithms are more precise than those based on V(s), meaning that updates are incorporated into the value function more efficiently. This effect is also enhanced by the observation that the Q(s,a)-based algorithms may be trained with higher learning rates. These algorithms are then extended by adding multiple value functions, which are observed to allow larger learning rates and have improved convergence properties in environments with stochastic rewards, the latter of which is further improved by the probabilistic nature of the quantum algorithms. Finally, the quantum algorithms were found to use less CPU time than their classical counterparts overall, meaning that their benefits may be realized even without a full quantum computer.
文摘In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.
基金supported by the National Natural Science Foundation of China(Grant Nos.11074002 and 61275119)the Doctoral Foundation of the Ministry of Education of China(Grant No.20103401110003)the Natural Science Research Project of Education Department of Anhui Province,China(Grant Nos.KJ2013A205,KJ2011ZD07,and KJ2012Z309)
文摘We propose an efficient scheme for realizing quantum dense coding with three-particle GHZ state in separated low-Q cavities. In this paper, the GHZ state is first prepared with three atoms trapped, respectively, in three spatial separated cavities. Meanwhile, with the assistance of a coherent optical pulse and X-quadrature homodyne measurement, we can im- plement quantum dense coding with three-particle GHZ state with a higher probability. Our scheme can also be generalized to realize N-particle quantum dense coding.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61373131,61303039,61232016,and 61501247)Sichuan Youth Science and Technique Foundation,China(Grant No.2017JQ0048)+1 种基金NUIST Research Foundation for Talented Scholars of China(Grant No.2015r014)PAPD and CICAEET Funds of China
文摘As one of essential multimedia in quantum networks, the copyright protection of quantum audio has gradually be- come an important issue in the domain of quantum information hiding in the decades. In this paper, an improved quantum watermarking algorithm based on quantum audio by using least significant qubit （LSQb） modification is proposed. Com- pared with the previous achievements, it can effectively improve the robustness and security of watermark for copyright protection of quantum audio. In the new algorithm, the least significant bites and the peripheral least significant bits of the amplitudes are modified in terms of their logical consistency and correlation to enhance watermark robustness of resisting various illegal attacks. Furthermore, the new algorithm can avoid the weak robustness defect of many previous algorithms that directly embedded the watermark into the least significant bits. In order to implement the new algorithm, some spe- cific quantum circuits are designed to obtain better applicability and scalability for embedding and extracting watermark. Finally, the simulation results including the values of audio waveforms and signal to noise ratios （SNR） prove that the new algorithm has good transparency, robustness, and security.
文摘Applying quantum computing techniques to machine learning has attracted widespread attention recently and quantum machine learning has become a hot research topic. There are three major categories of machine learning: supervised, unsupervised, and reinforcement learning (RL). However, quantum RL has made the least progress when compared to the other two areas. In this study, we implement the well-known RL algorithm Q learning with a quantum neural network and evaluate it in the grid world environment. RL is learning through interactions with the environment, with the aim of discovering a strategy to maximize the expected cumulative rewards. Problems in RL bring in unique challenges to the study with their sequential nature of learning, potentially long delayed reward signals, and large or infinite size of state and action spaces. This study extends our previous work on solving the contextual bandit problem using a quantum neural network, where the reward signals are immediate after each action.
基金This work was supported by the Natural Science Foundation of Jiangsu Province under Grant BK20171458in part by the Natural Science Foundation of China under Grant Nos.61672290 and 61802002+2 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No.19KJB520028Jiangsu Graduate Scientific Research Innovation Program under Grant No.KYCX20_0978the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivation and simulation verification of quantum computation(especially quantum algorithms),experimental verification on real quantum devices has become a new trend.In this paper,three representative quantum algorithms,namely Deutsch-Jozsa,Grover,and Shor algorithms,are briefly depicted,and then their implementation circuits are presented,respectively.We program these circuits on python with QISKit to connect the remote real quantum devices(i.e.,ibmqx4,ibmqx5)on IBM Q to verify these algorithms.The experimental results not only show the feasibility of these algorithms,but also serve to evaluate the functionality of these devices.
文摘The advantage of quantum computers over classical computers fuels the recent trend of developing machine learning algorithms on quantum computers, which can potentially lead to breakthroughs and new learning models in this area. The aim of our study is to explore deep quantum reinforcement learning (RL) on photonic quantum computers, which can process information stored in the quantum states of light. These quantum computers can naturally represent continuous variables, making them an ideal platform to create quantum versions of neural networks. Using quantum photonic circuits, we implement Q learning and actor-critic algorithms with multilayer quantum neural networks and test them in the grid world environment. Our experiments show that 1) these quantum algorithms can solve the RL problem and 2) compared to one layer, using three layer quantum networks improves the learning of both algorithms in terms of rewards collected. In summary, our findings suggest that having more layers in deep quantum RL can enhance the learning outcome.
文摘Traditional reinforcement learning (RL) uses the return, also known as the expected value of cumulative random rewards, for training an agent to learn an optimal policy. However, recent research indicates that learning the distribution over returns has distinct advantages over learning their expected value as seen in different RL tasks. The shift from using the expectation of returns in traditional RL to the distribution over returns in distributional RL has provided new insights into the dynamics of RL. This paper builds on our recent work investigating the quantum approach towards RL. Our work implements the quantile regression (QR) distributional Q learning with a quantum neural network. This quantum network is evaluated in a grid world environment with a different number of quantiles, illustrating its detailed influence on the learning of the algorithm. It is also compared to the standard quantum Q learning in a Markov Decision Process (MDP) chain, which demonstrates that the quantum QR distributional Q learning can explore the environment more efficiently than the standard quantum Q learning. Efficient exploration and balancing of exploitation and exploration are major challenges in RL. Previous work has shown that more informative actions can be taken with a distributional perspective. Our findings suggest another cause for its success: the enhanced performance of distributional RL can be partially attributed to its superior ability to efficiently explore the environment.
文摘After a straightforward general relativistic calculation on a modified flat-spacetime metric (developed from the fluctuating vacuum energy interacting with a graviton field), a pair of n-valued covariant and contravariant energy momentum tensors emerged analogous to quantized raising and lower operators. Detaching these operators from the general relativistic field equations, and then transporting them to act on extreme spacetimes, these operators were able to generate fundamental particle boson masses. In particular, the operators precisely generated Higgs mass. Then by applying a consistency approach to the gravitational field equations—similar to how Maxwell applied to the electromagnetic ones—it allowed for the coupling of spin-to-mass, further restricting the particle mass to be in precise agreement with CODATA experimental values. Since this is a massless field approach integrated discretely with a massive one, it overcomes various renormalizing difficulties;moreover it solves the mass hierarchal problem of the Standard Model of particle physics, and generates its spin and therefore shows quantum physics to be a subset of General Relativity, just as Einstein had first imagined.
文摘The relation between noncommutative (or quantum) geometry and themathematics of spacesis in many ways similar to the relation between quantum physicsand classical physics. One moves from the commutative algebra of functions on a space (or a commutative algebra of classical observable in classical physics) to a noncommutative algebra representing a noncommutative space (or a noncommutative algebra of quantum observables in quantum physics). The object of this paper is to study the basic rules governing q-calculus as compared with the classical Newton-Leibnitz calculus.
文摘In this paper, we present the exact solution of the one-dimensional Schrrdinger equation for the q-deformed quantum potentials via the Nikiforov-Uvarov method. The eigenvalues and eigenfunctions of these potentials are obtained via this method. The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed. The PT-symmetry and Hermiticity for these potentials are also discussed.
文摘The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique where the Liouville space is briefly expanded with an additional (virtual) space only within ultrashort subintervals. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically “hitchhiking” via virtual space in discrete ultrashort time duration, are the hallmark of our technique. We believe that this technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.
文摘A theory of Quantum Gravity based on Primordial Field Theory is applied to a fundamental particle, the neutron. The result is compared to the current quantum description of the neutron bouncing in a gravitational field. Our quantum gravity theory yields results in agreement with the Q-bounce experimental data, but ontologically different from quantum mechanics. The differences are summarized and imply that this experiment on a fundamental particle has the potential to radically alter the ontology of field theory.
