Larisa Latypova, F. Murzakhanov, G. Mamin, M. Sadovnikova, H. J. von Bardeleben, Marat Gafurov
The distinct spin, optical, and coherence characteristics of solid-state spin defects in semiconductors have positioned them as potential qubits for quantum technologies. Both bulk and two-dimensional materials, with varying structural properties, can serve as crystalline hosts for color centers. In this study, we conduct a comparative analysis of the spin–optical, electron–nuclear, and relaxation properties of nitrogen-bound vacancy defects using electron paramagnetic resonance (EPR) and electron–nuclear double resonance (ENDOR) techniques. We examine key parameters of the spin Hamiltonian for the nitrogen vacancy (NV−) center in 4H-SiC: D = 1.3 GHz, Azz = 1.1 MHz, and CQ = 2.53 MHz, as well as for the boron vacancy (VB−) in hBN: D = 3.6 GHz, Azz = 85 MHz, and CQ = 2.11 MHz, and their dependence on the material matrix. The spin–spin relaxation times T2 (NV− center: 50 µs and VB−: 15 µs) are influenced by the local nuclear environment and spin diffusion while Rabi oscillation damping times depend on crystal size and the spatial distribution of microwave excitation. The ENDOR absorption width varies significantly among color centers due to differences in crystal structures. These findings underscore the importance of selecting an appropriate material platform for developing quantum registers based on high-spin color centers in quantum information systems.
{"title":"Nitrogen-Related High-Spin Vacancy Defects in Bulk (SiC) and 2D (hBN) Crystals: Comparative Magnetic Resonance (EPR and ENDOR) Study","authors":"Larisa Latypova, F. Murzakhanov, G. Mamin, M. Sadovnikova, H. J. von Bardeleben, Marat Gafurov","doi":"10.3390/quantum6020019","DOIUrl":"https://doi.org/10.3390/quantum6020019","url":null,"abstract":"The distinct spin, optical, and coherence characteristics of solid-state spin defects in semiconductors have positioned them as potential qubits for quantum technologies. Both bulk and two-dimensional materials, with varying structural properties, can serve as crystalline hosts for color centers. In this study, we conduct a comparative analysis of the spin–optical, electron–nuclear, and relaxation properties of nitrogen-bound vacancy defects using electron paramagnetic resonance (EPR) and electron–nuclear double resonance (ENDOR) techniques. We examine key parameters of the spin Hamiltonian for the nitrogen vacancy (NV−) center in 4H-SiC: D = 1.3 GHz, Azz = 1.1 MHz, and CQ = 2.53 MHz, as well as for the boron vacancy (VB−) in hBN: D = 3.6 GHz, Azz = 85 MHz, and CQ = 2.11 MHz, and their dependence on the material matrix. The spin–spin relaxation times T2 (NV− center: 50 µs and VB−: 15 µs) are influenced by the local nuclear environment and spin diffusion while Rabi oscillation damping times depend on crystal size and the spatial distribution of microwave excitation. The ENDOR absorption width varies significantly among color centers due to differences in crystal structures. These findings underscore the importance of selecting an appropriate material platform for developing quantum registers based on high-spin color centers in quantum information systems.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"21 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141340654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Clement Atachegbe Onate, Ituen B. Okon, Edwin Samson Eyube, Ekwevugbe Omugbe, Kizito O. Emeje, Michael C. Onyeaju, Olumide O. Ajani, Jacob A. Akinpelu
The solutions to the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potential have been studied separately in the past. Despite different reports on the Kratzer potential, the fundamental theoretical quantities such as Fisher information have not been reported. In this study, we obtain the solution to the radial Schrödinger equation for the combination of the pseudoharmonic and Kratzer potentials in the presence of a constant-dependent potential, utilizing the concepts and formalism of the supersymmetric and shape invariance approach. The position expectation value and momentum expectation value are calculated employing the Hellmann–Feynman Theory. These expectation values are then used to calculate the Fisher information for both position and momentum spaces in both the absence and presence of the constant-dependent potential. The results obtained revealed that the presence of the constant-dependent potential leads to an increase in the energy eigenvalue, as well as in the position and momentum expectation values. Additionally, the constant-dependent potential increases the Fisher information for both position and momentum spaces. Furthermore, the product of the position expectation value and the momentum expectation value, along with the product of the Fisher information, satisfies both Fisher’s inequality and Cramer–Rao’s inequality.
{"title":"Fisher Information for a System Composed of a Combination of Similar Potential Models","authors":"Clement Atachegbe Onate, Ituen B. Okon, Edwin Samson Eyube, Ekwevugbe Omugbe, Kizito O. Emeje, Michael C. Onyeaju, Olumide O. Ajani, Jacob A. Akinpelu","doi":"10.3390/quantum6020015","DOIUrl":"https://doi.org/10.3390/quantum6020015","url":null,"abstract":"The solutions to the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potential have been studied separately in the past. Despite different reports on the Kratzer potential, the fundamental theoretical quantities such as Fisher information have not been reported. In this study, we obtain the solution to the radial Schrödinger equation for the combination of the pseudoharmonic and Kratzer potentials in the presence of a constant-dependent potential, utilizing the concepts and formalism of the supersymmetric and shape invariance approach. The position expectation value and momentum expectation value are calculated employing the Hellmann–Feynman Theory. These expectation values are then used to calculate the Fisher information for both position and momentum spaces in both the absence and presence of the constant-dependent potential. The results obtained revealed that the presence of the constant-dependent potential leads to an increase in the energy eigenvalue, as well as in the position and momentum expectation values. Additionally, the constant-dependent potential increases the Fisher information for both position and momentum spaces. Furthermore, the product of the position expectation value and the momentum expectation value, along with the product of the Fisher information, satisfies both Fisher’s inequality and Cramer–Rao’s inequality.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140984467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Starting from the dynamics of a bouncing ball in classical and quantum regime, we have suggested in a previous paper to add an arbitrary function of time to the standard expression of the probability current in quantum mechanics. In this paper, we suggest a way to determine this function: imposing a suitable normalization condition. The application of our proposal to the case of the harmonic oscillator is discussed.
{"title":"A Normalization Condition for the Probability Current in Some Remarkable Cases","authors":"A. Feoli, E. Benedetto, A. L. Iannella","doi":"10.3390/quantum6020012","DOIUrl":"https://doi.org/10.3390/quantum6020012","url":null,"abstract":"Starting from the dynamics of a bouncing ball in classical and quantum regime, we have suggested in a previous paper to add an arbitrary function of time to the standard expression of the probability current in quantum mechanics. In this paper, we suggest a way to determine this function: imposing a suitable normalization condition. The application of our proposal to the case of the harmonic oscillator is discussed.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"14 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140666369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This is a preface to a Special Issue of Quantum Reports devoted to the results of the workshop “The Many-Worlds Interpretation of Quantum Mechanics: Current Status and Relation to Other Interpretations” [...]
{"title":"The Many-Worlds Interpretation of Quantum Mechanics: Current Status and Relation to Other Interpretations","authors":"L. Vaidman","doi":"10.3390/quantum6020011","DOIUrl":"https://doi.org/10.3390/quantum6020011","url":null,"abstract":"This is a preface to a Special Issue of Quantum Reports devoted to the results of the workshop “The Many-Worlds Interpretation of Quantum Mechanics: Current Status and Relation to Other Interpretations” [...]","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140688896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Sainz, Ernesto Camacho, Andrés García, Andrei B. Klimov
We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.
我们观察到，具有奇数局部维度的 n 部分系统的离散维格纳函数（DWF）在断层扫描上是通用的，这反映在任何稳定器的 DWF 的三角函数形式上。然而，在 n-qubit 情况下，由于映射核的非因子化，这一特性并不成立，因为映射核的明确形式取决于离散相空间的特定分区。然而，事实证明，某些特定稳定器的 DWF（不包括在用于构建维格纳映射的集合中）具有三角函数的形式。这意味着，在给定稳定器状态下对四比特系统的保利测量进行经典模拟的可能性与实验装置密切相关。
{"title":"Tomographic Universality of the Discrete Wigner Function","authors":"I. Sainz, Ernesto Camacho, Andrés García, Andrei B. Klimov","doi":"10.3390/quantum6010005","DOIUrl":"https://doi.org/10.3390/quantum6010005","url":null,"abstract":"We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Energy efficiency considerations in terms of reduced power dissipation are a significant issue in the design of digital circuits for very large-scale integration (VLSI) systems. Quantum-dot cellular automata (QCA) is an emerging ultralow power dissipation approach, distinct from traditional, complementary metal-oxide semiconductor (CMOS) technology, for building digital computing circuits. Developing fully reversible QCA circuits has the potential to significantly reduce energy dissipation. Multiplexers are fundamental elements in the construction of useful digital circuits. In this paper, a novel, multilayer, fully reversible QCA 8:1 multiplexer circuit with ultralow energy dissipation is introduced. The power dissipation of the proposed multiplexer is simulated using the QCADesigner-E version 2.2 tool, describing the microscopic physical mechanisms underlying the QCA operation. The results show that the proposed reversible QCA 8:1 multiplexer consumes 89% less energy than the most energy-efficient 8:1 multiplexer circuit previously presented in the literature.
{"title":"An Ultra-Energy-Efficient Reversible Quantum-Dot Cellular Automata 8:1 Multiplexer Circuit","authors":"Mohammed Alharbi, Gerard Edwards, Richard Stocker","doi":"10.3390/quantum6010004","DOIUrl":"https://doi.org/10.3390/quantum6010004","url":null,"abstract":"Energy efficiency considerations in terms of reduced power dissipation are a significant issue in the design of digital circuits for very large-scale integration (VLSI) systems. Quantum-dot cellular automata (QCA) is an emerging ultralow power dissipation approach, distinct from traditional, complementary metal-oxide semiconductor (CMOS) technology, for building digital computing circuits. Developing fully reversible QCA circuits has the potential to significantly reduce energy dissipation. Multiplexers are fundamental elements in the construction of useful digital circuits. In this paper, a novel, multilayer, fully reversible QCA 8:1 multiplexer circuit with ultralow energy dissipation is introduced. The power dissipation of the proposed multiplexer is simulated using the QCADesigner-E version 2.2 tool, describing the microscopic physical mechanisms underlying the QCA operation. The results show that the proposed reversible QCA 8:1 multiplexer consumes 89% less energy than the most energy-efficient 8:1 multiplexer circuit previously presented in the literature.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139620339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Today, we are already using several-component devices and systems based on the technologies developed during the first quantum revolution. Examples include microchips for servers, laptops and smartphones, medical imaging devices, LED, lasers, etc. Now, a second quantum revolution is progressing fast, exploiting technological advances for the ability to engineer and manipulate other quantum phenomena such as superposition, entanglement and measurement. As a matter of fact, there is an impressive increase in research and development activities, innovation, public and private investments in a new wave of quantum services and applications. In this scenario, quantum information and communication technologies (QICTs) can be defined as a set of technological components, devices, systems and methods for elaborating, storing and transmitting/sharing quantum information. This paper addresses the challenges and opportunities enabling the rise of QICTs. In order to provide a concrete example, the paper describes an overview of the European project EQUO (European Quantum ecOsystems) dealing with ongoing innovation activities in the QICT avenue; in fact, EQUO aims at developing and demonstrating the feasibility of QKD (quantum key distribution) networks and their related integration in current telecommunications infrastructures towards the quantum internet.
{"title":"The Rise of Quantum Information and Communication Technologies","authors":"Antonio Manzalini, Luigi Artusio","doi":"10.3390/quantum6010003","DOIUrl":"https://doi.org/10.3390/quantum6010003","url":null,"abstract":"Today, we are already using several-component devices and systems based on the technologies developed during the first quantum revolution. Examples include microchips for servers, laptops and smartphones, medical imaging devices, LED, lasers, etc. Now, a second quantum revolution is progressing fast, exploiting technological advances for the ability to engineer and manipulate other quantum phenomena such as superposition, entanglement and measurement. As a matter of fact, there is an impressive increase in research and development activities, innovation, public and private investments in a new wave of quantum services and applications. In this scenario, quantum information and communication technologies (QICTs) can be defined as a set of technological components, devices, systems and methods for elaborating, storing and transmitting/sharing quantum information. This paper addresses the challenges and opportunities enabling the rise of QICTs. In order to provide a concrete example, the paper describes an overview of the European project EQUO (European Quantum ecOsystems) dealing with ongoing innovation activities in the QICT avenue; in fact, EQUO aims at developing and demonstrating the feasibility of QKD (quantum key distribution) networks and their related integration in current telecommunications infrastructures towards the quantum internet.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"41 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139533830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marco Maronese, Massimiliano Incudini, Luca Asproni, Enrico Prati
The Quantum Amplitude Estimation (QAE) algorithm is a major quantum algorithm designed to achieve a quadratic speed-up. Until fault-tolerant quantum computing is achieved, being competitive over classical Monte Carlo (MC) remains elusive. Alternative methods have been developed so as to require fewer resources while maintaining an advantageous theoretical scaling. We compared the standard QAE algorithm with two Noisy Intermediate-Scale Quantum (NISQ)-friendly versions of QAE on a numerical integration task, with the Monte Carlo technique of Metropolis–Hastings as a classical benchmark. The algorithms were evaluated in terms of the estimation error as a function of the number of samples, computational time, and length of the quantum circuits required by the solutions, respectively. The effectiveness of the two QAE alternatives was tested on an 11-qubit trapped-ion quantum computer in order to verify which solution can first provide a speed-up in the integral estimation problems. We concluded that an alternative approach is preferable with respect to employing the phase estimation routine. Indeed, the Maximum Likelihood estimation guaranteed the best trade-off between the length of the quantum circuits and the precision in the integral estimation, as well as greater resistance to noise.
{"title":"The Quantum Amplitude Estimation Algorithms on Near-Term Devices: A Practical Guide","authors":"Marco Maronese, Massimiliano Incudini, Luca Asproni, Enrico Prati","doi":"10.3390/quantum6010001","DOIUrl":"https://doi.org/10.3390/quantum6010001","url":null,"abstract":"The Quantum Amplitude Estimation (QAE) algorithm is a major quantum algorithm designed to achieve a quadratic speed-up. Until fault-tolerant quantum computing is achieved, being competitive over classical Monte Carlo (MC) remains elusive. Alternative methods have been developed so as to require fewer resources while maintaining an advantageous theoretical scaling. We compared the standard QAE algorithm with two Noisy Intermediate-Scale Quantum (NISQ)-friendly versions of QAE on a numerical integration task, with the Monte Carlo technique of Metropolis–Hastings as a classical benchmark. The algorithms were evaluated in terms of the estimation error as a function of the number of samples, computational time, and length of the quantum circuits required by the solutions, respectively. The effectiveness of the two QAE alternatives was tested on an 11-qubit trapped-ion quantum computer in order to verify which solution can first provide a speed-up in the integral estimation problems. We concluded that an alternative approach is preferable with respect to employing the phase estimation routine. Indeed, the Maximum Likelihood estimation guaranteed the best trade-off between the length of the quantum circuits and the precision in the integral estimation, as well as greater resistance to noise.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"389 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139160870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Chernega, Mariia Martsinkiv, Taras Vasylyshyn, Andriy Zagorodnyuk
We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for ℓ1(Z0), induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semi-ring structures into this set and discuss their possible physical interpretations.
{"title":"Applications of Supersymmetric Polynomials in Statistical Quantum Physics","authors":"I. Chernega, Mariia Martsinkiv, Taras Vasylyshyn, Andriy Zagorodnyuk","doi":"10.3390/quantum5040043","DOIUrl":"https://doi.org/10.3390/quantum5040043","url":null,"abstract":"We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for ℓ1(Z0), induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semi-ring structures into this set and discuss their possible physical interpretations.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"7 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139011545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vi D. Ao, Duy V. Tran, Kien T. Pham, Duc M. Nguyen, Huy D. Tran, Tuan K. Do, Van H. Do, Trung V. Phan
We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh–Ritz variational method and the Rayleigh–Schrödinger perturbation theory, allowing us not only the conduct of reasonable quantitative assessments but also exploration of fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis—a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in an unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations.
{"title":"A Schrödinger Equation for Evolutionary Dynamics","authors":"Vi D. Ao, Duy V. Tran, Kien T. Pham, Duc M. Nguyen, Huy D. Tran, Tuan K. Do, Van H. Do, Trung V. Phan","doi":"10.3390/quantum5040042","DOIUrl":"https://doi.org/10.3390/quantum5040042","url":null,"abstract":"We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh–Ritz variational method and the Rayleigh–Schrödinger perturbation theory, allowing us not only the conduct of reasonable quantitative assessments but also exploration of fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis—a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in an unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"98 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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