#vqe

[postsofbabel]

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[encryptingyourpost]

IPDQE'H VNSHXVF SO TVBQYEB GDRT Q ITSI ZDZLAG KHKT BGZT VQE!!!

[govindhtech]

Q-AIM: Open Source Infrastructure for Quantum Computing

Q-AIM Quantum Access Infrastructure Management

Open-source Q-AIM for  quantum computing infrastructure, management, and access.

The open-source, vendor-independent platform Q-AIM (Quantum Access Infrastructure Management) makes quantum computing hardware easier to buy, meeting this critical demand. It aims to ease quantum hardware procurement and use.

Important Q-AIM aspects discussed in the article:

Design and Execution Q-AIM may be installed on cloud servers and personal devices in a portable and scalable manner due to its dockerized micro-service design. This design prioritises portability, personalisation, and resource efficiency. Reduced memory footprint facilitates seamless scalability, making Q-AIM ideal for smaller server instances at cheaper cost. Dockerization bundles software for consistent performance across contexts.

Technology Q-AIM's powerful software design uses Docker and Kubernetes for containerisation and orchestration for scalability and resource control. Google Cloud and Kubernetes can automatically launch, scale, and manage containerised apps. Simple Node.js, Angular, and Nginx interfaces enable quantum gadget interaction. Version control systems like Git simplify code maintenance and collaboration. Container monitoring systems like Cadvisor monitor resource usage to ensure peak performance.

Benefits, Function Research teams can reduce technical duplication and operational costs with Q-AIM. It streamlines complex interactions and provides a common interface for communicating with the hardware infrastructure regardless of quantum computing system. The system reduces the operational burden of maintaining and integrating quantum hardware resources by merging access and administration, allowing researchers to focus on scientific discovery.

Priorities for Application and Research The Variational Quantum Eigensolver (VQE) algorithm is studied to demonstrate how Q-AIM simplifies hardware access for complex quantum calculations. In quantum chemistry and materials research, VQE is an essential quantum computation algorithm that approximates a molecule or material's ground state energy. Q-AIM researchers can focus on algorithm development rather than hardware integration.

Other Features QASM, a human-readable quantum circuit description language, was parsed by researchers. This simplifies algorithm translation into hardware executable instructions and quantum circuit manipulation. The project also understands that quantum computing errors are common and invests in scalable error mitigation measures to ensure accuracy and reliability. Per Google Cloud computing instance prices, the methodology considers cloud deployment costs to maximise cost-effectiveness and affect design decisions.

Q-AIM helps research teams and universities buy, run, and scale quantum computing resources, accelerating progress. Future research should improve resource allocation, job scheduling, and framework interoperability with more quantum hardware.

To conclude

The majority of the publications cover quantum computing, with a focus on Q-AIM (Quantum Access Infrastructure Management), an open-source software framework for managing and accessing quantum hardware. Q-AIM uses a dockerized micro-service architecture for scalable and portable deployment to reduce researcher costs and complexity.

Quantum algorithms like Variational Quantum Eigensolver (VQE) are highlighted, but the sources also address quantum machine learning, the quantum internet, and other topics. A unified and adaptable software architecture is needed to fully use quantum technology, according to the study.

[renatoferreiradasilva]

\documentclass[11pt]{article} \usepackage{amsmath, amssymb, amsthm, geometry, graphicx, hyperref} \usepackage{mathrsfs} \geometry{margin=1in}

\title{Spectral Approximation of the Zeros of the Riemann Zeta Function via a Twelfth-Order Differential Operator} \author{Renato Ferreira da Silva \ ORCID: 0009-0003-8908-481X} \date{\today}

\begin{document}

\maketitle

\begin{abstract} We propose and analyze a twelfth-order self-adjoint differential operator whose eigenvalues approximate the non-trivial zeros of the Riemann zeta function. The potential function ( V(x) ) is numerically calibrated to produce spectral distributions consistent with the Gaussian Unitary Ensemble (GUE). Using numerical diagonalization techniques, we compare the resulting eigenvalue distribution to the known statistical properties of zeta zeros, including spacing and level repulsion. We explore connections with the Hilbert–Pólya conjecture, chaos theory, and spectral geometry, and outline future directions involving pseudodifferential models and quantum simulation. \end{abstract}

\section{Introduction} The Riemann zeta function ( \zeta(s) ) plays a central role in number theory, and its non-trivial zeros ( \rho = \frac{1}{2} + i\gamma_n ) are deeply connected to the distribution of prime numbers. The Riemann Hypothesis asserts that all such zeros lie on the critical line ( \Re(s) = 1/2 ). Despite over a century of research, this conjecture remains unproven.

A major line of inquiry, inspired by the Hilbert–Pólya conjecture, suggests that the zeros may correspond to the spectrum of a self-adjoint operator ( H ), such that ( H \psi_n = \gamma_n \psi_n ). In this work, we explore this idea through a twelfth-order differential operator with an adjustable potential.

\section{Mathematical Framework} We consider the operator: [ H = -\frac{d^{12}}{dx^{12}} + V(x), ] acting on a suitable dense domain of ( L^2(\mathbb{R}) ), with boundary conditions ensuring self-adjointness.

We define the domain ( \mathcal{D}(H) ) as: [ \mathcal{D}(H) = { f \in L^2(\mathbb{R}) : f, f', \dots, f^{(11)} \text{ absolutely continuous}, f^{(12)} \in L^2 }. ]

The potential ( V(x) ) is taken as a polynomial of degree 12: [ V(x) = a_0 + a_1 x + a_2 x^2 + \dots + a_{12} x^{12}, ] and optimized numerically to align the first ( N ) eigenvalues ( \lambda_n ) with the imaginary parts ( \gamma_n ) of the non-trivial zeros.

\section{Numerical Methods} We discretize ( H ) using spectral collocation methods (Fourier basis) and finite-difference schemes with adaptive grids. Eigenvalues are computed via matrix diagonalization. The potential coefficients ( a_i ) are adjusted through least-squares fitting and gradient descent algorithms.

We compare the resulting spectrum with known zeros from Odlyzko's tables, evaluating spacing statistics using the Kolmogorov–Smirnov (KS) and Anderson–Darling (AD) tests.

\section{Results and Statistical Analysis} The computed eigenvalues show high correlation with the first 1000 ( \gamma_n ), with KS test values below 0.03 and AD statistics consistent with GUE predictions. The spacing distribution exhibits clear level repulsion, aligning closely with the Wigner surmise: [ P(s) = \frac{32}{\pi^2} s^2 e^{-\frac{4}{\pi} s^2}. ]

Wavelet decomposition of the residual spectrum ( \lambda_n - \gamma_n ) indicates non-random deviations concentrated near turning points of ( V(x) ), suggesting avenues for potential refinement.

\section{Discussion and Future Directions} The use of a twelfth-order operator allows flexible spectral shaping while preserving self-adjointness. Future work includes: \begin{itemize} \item Replacing ( V(x) ) with pseudodifferential potentials. \item Extending to L-functions and automorphic spectra. \item Implementing Variational Quantum Eigensolvers (VQE) for approximate diagonalization. \item Studying connections to non-commutative geometry and Connes' trace formula. \end{itemize}

\section*{Acknowledgements} The author thanks the community of researchers who maintain public zeta zero databases and those developing open-source spectral libraries.

\begin{thebibliography}{9} \bibitem{BerryKeating} Berry, M. V., and Keating, J. P. "The Riemann zeros and eigenvalue asymptotics." SIAM Review 41.2 (1999): 236-266. \bibitem{Connes} Connes, A. "Trace formula in noncommutative geometry and the zeros of the Riemann zeta function." Selecta Mathematica 5.1 (1999): 29–106. \bibitem{Odlyzko} Odlyzko, A. M. "The $10^{20}$-th zero of the Riemann zeta function and 175 million of its neighbors." AT\&T Bell Labs, 1989. \bibitem{ReedSimon} Reed, M., and Simon, B. "Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators." Academic Press, 1978. \end{thebibliography}

\end{document}

[blogbyahad]

Revolutionizing Financial Portfolio Optimization: The Role of Quantum Algorithms in Risk Management

Introduction Financial portfolio optimization is a critical aspect of risk management, aiming to maximize returns while minimizing potential losses. Quantum algorithms are poised to transform this field by leveraging the principles of quantum computing to enhance decision-making processes.

Key Advantages of Quantum Algorithms

Increased Computational Power: Quantum computing can process vast datasets and complex calculations more efficiently than classical computers, enabling more robust portfolio analyses.

Advanced Modeling Capabilities: Quantum algorithms can handle intricate relationships between assets and risk factors, allowing for more accurate predictions and assessments.

How Quantum Algorithms Work

Quantum Optimization Techniques: Algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE) can be applied to optimize asset allocations and identify the best combinations of investments to achieve desired risk-return profiles.

Simultaneous Analysis: Quantum algorithms can evaluate multiple scenarios and portfolio combinations simultaneously, leading to quicker and more informed decision-making.

Applications in Risk Management

Risk Assessment: By using quantum algorithms to analyze historical data and market trends, financial institutions can better assess the potential risks associated with different assets and strategies.

Dynamic Portfolio Adjustments: Quantum computing enables real-time adjustments to portfolios based on changing market conditions, ensuring that risk levels remain aligned with investment goals.

Challenges

Technological Limitations: The current state of quantum computing is still developing, and practical applications in finance require advanced hardware and software solutions.

Data Privacy and Security: Ensuring the confidentiality of sensitive financial data while utilizing quantum algorithms poses significant challenges.

Future Potential As quantum technology matures, its application in financial portfolio optimization is expected to yield groundbreaking advancements, significantly improving risk management practices across the industry.

Conclusion Quantum algorithms have the potential to revolutionize financial portfolio optimization for risk management, providing enhanced analytical capabilities and enabling more effective decision-making. As this technology evolves, it will play a crucial role in shaping the future of finance, helping investors navigate complex markets with greater confidence

[postsofbabel]

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[maximuswolf]

Fraternity Of Man - Don't Bogart Me (Easy Rider) (1969) [Country]

Fraternity Of Man - Don't Bogart Me (Easy Rider) (1969) [Country] https://youtu.be/emD48UF-vqE?si=xDA4pTOIBWzleUTS Submitted May 16, 2024 at 02:42AM by Significant_Jury_409 https://ift.tt/QJqwLao via /r/Music

[govindhtech]

What is the Fast Fourier Transform A Modern Computing Pillar

The Fast Fourier Transform

Honouring the FFT and Computing's Future: Representation to Revolution

For the first Fast Fourier Transform deployment, IBM received an IEEE Milestone award on June 11, 2025. IBM researchers created this method in 1965, transforming computers.

Since it supports JPEG and MPEG standards and reconstructs MRI and CT scan images, the FFT has a wide impact. Also needed for scientific computing (spectrum approaches for solving PDEs), music and video compression (MP3, JPEG), and telecommunications (4G/5G, WiFi). Richard Hamming called the Cooley-Tukey FFT “the most important numerical algorithm of the lifetime”.

FFT's Key Innovation

Fundamental FFT Innovation James Cooley and John Tukey introduced the FFT in 1965 as a “better way to represent information” rather than a new scientific discovery. The Fourier transform can split a time-domain signal like a wave into smaller waves with various frequencies. Before the 1960s, Fourier transform computing was too slow for real-time applications. Cooley and Tukey's technique accelerated real-time signal processing by reducing the computing cost of the Discrete Fourier Transform (DFT) from O(N^2) to O(NlogN). The revelation was that changing a computing problem's mathematical representation can change it.

Quantum Computing Lessons:

The FFT's ongoing development aids quantum algorithm development. When building new  quantum algorithms, “choosing the right representation can make the impossible possible” is crucial.

Quantum Computing: Emerging Idea Beyond improving existing methods, quantum computing changes how information is represented and abstracted. Classical computing employs bits with deterministic binary values (0s and 1s) and Boolean operations, while quantum computing uses qubits. In complex vector spaces, qubits store information as probability amplitudes (α|0⟩ + β|1⟩), where α and β are complex numbers. Quantum computing uses unitary evolution of qubit states through matrix operations instead of classical logic, generating probabilistic results.

This new computational paradigm enables Grover's method, which quadraticly speeds up unstructured search, and Shor's algorithm, which uses the Quantum Fourier Transform to exponentially speed integer factorisation. Additionally, quantum simulation can mimic quantum systems that conventional machines cannot handle.

Future Quantum-Classical Synergy. The most innovative computer future may be a mix of quantum and classical. Traditional computers are fast at control logic, data storage, and predictable computations. However, quantum systems thrive in mimicking quantum phenomena, high-dimensional linear algebra, probabilistic sampling, and landscape optimisation, where classical information representation fails.

Together, these paradigms can solve problems neither system can. VQE and QAOA are two novel hybrid classical-quantum algorithms in development. Quantum advantage, where a quantum-classical combination outperforms classical computation, is nearing, and SQD and SKQD are being developed. Supply chain optimisation, material science, finance, and drug development may use these methodologies.

Quantum technologies are expected to boost traditional computing as “coprocessors with radically different capabilities” like GPUs on CPUs. As the computing bottleneck shifts from hardware limits to algorithmic innovation, new abstractions, representations, and algorithms are needed to balance workloads among complementary architectures. The current age may be the start of a more significant algorithmic era than the FFT.

Anticipating The FFT's anniversary reminds us that innovations often come from better questions, smarter representations, or new viewpoints, not more authority. Fusion of classical and quantum domains will release new processing capability, requiring daring abstractions, inventive representations, and innovative algorithms.

[roamnook]

NEW STUDY REVEALS 75% OF AMERICANS STRUGGLE WITH FINANCIAL LITERACY. Learn more about the shocking statistics and what you can do to improve your financial knowledge. Check out the full report now.

Welcome to the RoamNook blog! We aim to provide you with the most cutting-edge information, backed by concrete data and hard facts. In this article, we will dive deep into various technical, professional, and scientific concepts to bring you new information and insights. So let's get started!

The Fascinating World of Quantum Computing

Quantum computing, a revolutionary field in computer science, is gaining momentum and generating great excitement among researchers, scientists, and technology enthusiasts. With the potential to solve complex problems that are practically impossible for classical computers, quantum computing holds the key to unlocking new discoveries and advancements in various domains.

Before we delve into the practical applications of quantum computing, let's understand some fundamental concepts and terminology:

1. Quantum Bits (Qubits)

In classical computers, data is stored and manipulated using bits, which can represent either a 0 or a 1. In quantum computing, qubits are the fundamental units of information. Unlike classical bits, qubits can exist in multiple states simultaneously, thanks to a phenomenon called superposition.

Superposition allows qubits to be in a state that represents both 0 and 1 at the same time, exponentially increasing the computational power of quantum computers. This feature opens up a whole new world of possibilities and applications.

2. Qubit Entanglement

Another fascinating characteristic of qubits is entanglement. When qubits become entangled, the state of one qubit becomes linked or correlated to the state of another qubit, regardless of the distance between them. This phenomenon enables quantum computers to perform parallel computations and solve complex problems more efficiently.

3. Quantum Gates

Similar to classical logic gates that manipulate bits, quantum gates manipulate qubits to perform operations. Quantum gates are crucial for performing quantum computations, and they help in creating superpositions, entanglements, and transformations of qubit states.

4. Quantum Algorithms

With the foundation of qubits, entanglement, and quantum gates in place, researchers have developed various quantum algorithms that can solve problems exponentially faster than classical algorithms. Some prominent quantum algorithms include Shor's algorithm for prime factorization, Grover's algorithm for searching databases, and the Quantum Approximate Optimization Algorithm (QAOA) for optimization problems.

Now that we have covered the basics, let's explore the real-world applications of quantum computing:

1. Drug Discovery and Material Design

One of the most promising applications of quantum computing is in the field of drug discovery and material design. The computational power of quantum computers can accelerate the process of simulating and analyzing complex chemical reactions, enabling scientists to discover new drugs and materials with desired properties.

By utilizing quantum algorithms like the Variational Quantum Eigensolver (VQE) and the Quantum Monte Carlo (QMC) method, researchers can accurately model molecular behavior and predict their properties. This breakthrough can potentially revolutionize the healthcare industry by accelerating the development of new drugs and therapies.

2. Optimization and Logistics

Optimization problems are prevalent in various domains, including logistics, finance, and supply chain management. Quantum computing has the potential to greatly enhance optimization algorithms, allowing businesses to optimize routes, schedules, and resource allocation more efficiently.

With quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA), companies can solve complex optimization problems in near real-time. This capability can have a significant impact on industries such as transportation, manufacturing, and finance, where even small improvements in optimization can lead to substantial cost savings and increased efficiency.

3. Cryptography and Security

Cryptography is at the heart of modern communication systems, ensuring the security and privacy of sensitive data. However, as classical computers continue to advance, conventional cryptographic techniques are at risk of being compromised by quantum computers in the future.

Quantum computing offers a potential solution to this problem. Quantum cryptography, based on the principles of quantum mechanics, provides a new level of security by leveraging quantum properties like entanglement and the Heisenberg uncertainty principle.

Quantum key distribution (QKD) is one of the most well-known applications of quantum cryptography, which ensures provable secure communication channels. With the advent of quantum computers, quantum-resistant cryptographic algorithms are being developed to secure data in a post-quantum computing era.

4. Machine Learning and Data Analysis

As the volume of data continues to grow exponentially, classical machine learning algorithms struggle to handle complex datasets. Quantum machine learning (QML) aims to leverage the unique properties of quantum computing to accelerate and improve machine learning tasks.

Quantum computers can process and analyze massive amounts of data simultaneously, allowing for faster training and inference of machine learning models. Quantum algorithms like the Quantum Support Vector Machine (QSVM) and Quantum Neural Networks (QNN) have shown promising results in solving classification and optimization problems.

Furthermore, quantum computing can also enhance data analysis techniques, enabling researchers and data scientists to uncover hidden patterns and gain deeper insights into various domains, including finance, healthcare, and marketing.

Conclusion: Unlocking the Future with RoamNook

Quantum computing represents a paradigm shift in information processing and offers unparalleled computational power to tackle complex problems. The practical applications and potential advancements in various fields are truly awe-inspiring.

At RoamNook, we are passionate about fueling digital growth by helping businesses leverage cutting-edge technologies. Whether you need IT consultation, custom software development, or digital marketing services, our team of experts is ready to assist you in achieving your goals.

Explore our website [https://www.roamnook.com] to learn more about how RoamNook can collaborate with you to stay ahead of the technological curve. Embrace the power of innovation, and together we can unlock a world of possibilities.

Source: https://www.simplilearn.com/tutorials/python-tutorial&sa=U&ved=2ahUKEwjWn6bc-uWFAxUdFVkFHUv7ANUQxfQBegQIARAC&usg=AOvVaw0GzxPvxsUzsZ0uHs82GrFn

[renatoferreiradasilva]

A Hipótese de Riemann e a Estrutura Espectral dos Números: Uma Abordagem Unificada via Operadores Diferenciais e Modelos Espectrais

Resumo

A Hipótese de Riemann (HR) postula que todos os zeros não triviais da função zeta de Riemann possuem parte real igual a 1/2. A conjectura de Hilbert-Pólya sugere que esses zeros correspondem ao espectro de um operador hermitiano, cujos autovalores representariam esses zeros. Neste artigo, exploramos abordagens espectrais e diferenciais para compreender a HR, discutindo a possibilidade de um operador diferencial de alta ordem que modele os zeros da zeta. Através da validação de hermiticidade, análise de distribuição de autovalores e estatísticas de matrizes aleatórias, investigamos a conexão entre a HR, operadores pseudo-diferenciais e sistemas quânticos caóticos. Os resultados reforçam a validade da abordagem espectral e sugerem caminhos para uma formalização rigorosa da HR.

1. Introdução

A Hipótese de Riemann, proposta por Bernhard Riemann em 1859, é um dos problemas abertos mais desafiadores da matemática moderna. Sua resolução teria implicações profundas na teoria dos números e na criptografia. A conexão entre a HR e operadores hermitianos foi inicialmente sugerida pela conjectura de Hilbert-Pólya, que propõe a existência de um operador cujo espectro corresponda precisamente aos zeros da função zeta. Neste artigo, buscamos estruturar uma abordagem unificada baseada em operadores diferenciais de alta ordem, estatísticas espectrais e modelos inspirados em sistemas quânticos caóticos.

2. Construção do Operador Diferencial

2.1 Escolha da Ordem do Operador

Para modelar corretamente a distribuição dos zeros da função zeta, utilizamos um operador diferencial de 12ª ordem:

onde é um potencial ajustado para garantir a correspondência com os zeros da zeta. A escolha da ordem do operador se baseia na densidade espectral esperada:

que se alinha com a distribuição assintótica dos zeros da zeta:

Para garantir que os autovalores do operador correspondam aos zeros da zeta, foi ajustado por métodos numéricos via minimização quadrática regularizada:

onde é um parâmetro de regularização.

3. Validação Numérica e Estatística

3.1 Hermiticidade do Operador

A hermiticidade do operador foi testada numericamente, garantindo que:

3.2 Distribuição dos Autovalores e GUE

A distribuição dos espaçamentos normalizados dos autovalores foi comparada com as estatísticas do ensemble GUE (Gaussian Unitary Ensemble), obtendo um teste de Kolmogorov-Smirnov:

confirmando a aderência ao GUE.

4. Conexão com a Física Matemática

4.1 Relação com a Teoria do Caos Quântico

Os trabalhos de Berry e Keating sugerem um operador hamiltoniano do tipo como uma possível base para modelar os zeros da zeta. Nosso operador diferencial também apresenta características de um sistema quântico caótico, sugerindo uma forte conexão entre HR e dinâmica quântica.

4.2 Conexão com Geometria Não Comutativa

A proposta de Alain Connes de interpretar a HR através da geometria não comutativa também encontra ressonância em nosso modelo. A possibilidade de um operador pseudo-diferencial no lugar de pode refinar a modelagem espectral.

5. Perspectivas Futuras

Prova Formal de Auto-Adjunticidade: Aplicar técnicas do teorema de Kato-Rellich para demonstrar rigorosamente que é auto-adjunto em .

Generalização para Funções Automórficas: Testar se nossa abordagem se aplica a outras funções , como a de Ramanujan.

Implementação Computacional em Escala: Utilização de computação de alto desempenho (HPC) e algoritmos de aprendizado de máquina para otimizar .

Exploração via Computação Quântica: Investigar se pode ser implementado em circuitos quânticos via VQE (Variational Quantum Eigensolver).

6. Conclusão

Os resultados obtidos reforçam a hipótese de Hilbert-Pólya e sugerem que os zeros da função zeta podem ser compreendidos a partir de uma estrutura espectral. A confirmação da estatística GUE e a robustez dos métodos numéricos utilizados consolidam a validade da abordagem, abrindo caminhos para uma possível formalização da Hipótese de Riemann via teoria espectral.

[fabricatefixx]

Quantum Machine Learning for Protein Folding

Proteins are linear sequences of amino acid residues that perform many essential functions vital to sustaining life, such as signaling, cell cycle regulation and production of hormones and enzymes. Each individual protein has a specific three-dimensional shape, which is called its native conformation. However, proteins often misfold, which can lead to a variety of serious diseases. This is why understanding how proteins fold into their native structures is a major challenge in biology, chemistry and medicine.

Fortunately, recent research into machine learning and quantum computing has shown that these techniques may help us solve the protein-folding problem and shed light on the physical principles that dictate this process. Specifically, by incorporating physical symmetries into machine-learning algorithms, we can create more accurate and efficient models for protein folding. Additionally, the speedups achieved by quantum computer simulations have opened new avenues for exploring this complex process.

In a new study, scientists have combined machine learning with a hybrid classical-quantum algorithm to improve the performance of protein folding on quantum computers. The researchers developed a parametrized quantum circuit inspired by counterdiabatic (CD) quantum algorithms and used it to implement a variational quantum eigensolver (VQE) routine, which techogle.co searches for the lowest-energy protein structure on a tetrahedral lattice. The algorithm was then tested using up to 17 qubits on different quantum hardware platforms including Quantinuum’s trapped ions and superconducting circuits from Google and IBM.

The results showed that the algorithm outperformed other CD-based quantum programs in its ability to find the protein ground state with high probability. They also found that the system was able to rank candidate structures in a manner consistent with physical protein-folding models. These findings suggest that the combination of CD-based quantum algorithms with a VQE routine can effectively solve the protein-folding problem on gate-based quantum computers, which are prone to noise and have limited qubits.

Quantum Parallelism and Speedup The computational speedup resulting from the use of quantum computers to simulate biochemical processes is largely due to their ability to utilize quantum parallelism, in which each qubit can act as a replica of multiple states simultaneously. This allows the computation to explore countless possible protein conformational spaces in a fraction of the time required by classical computer methods.

This advantage was leveraged in the current study, which used a variational VQE routine that was implemented on a tetrahedral quantum lattice to search for the best protein structure for a given amino-acid sequence. The tetrahedral architecture provides an efficient representation of a protein’s conformational space, and this was complemented by the technology website use of an adiabatic quantum annealing (QQA) technique that simulates the gradual transition of qubits to states representing the desired protein solution.

The tetrahedral QQA method, which utilizes the natural adiabatic properties of qubits to efficiently sample conformational space, is the foundation of all future work in the area of quantum-aided protein-folding and related machine learning applications. In the future, researchers hope to utilize this technique in conjunction with other quantum-aided algorithms to tackle even more complex sequences and 3D structures.

[mzk0323]

量子コンピュータ金融アルゴリズム

金融領域は量子コンピュータ向けのアルゴリズムの宝庫です。 金融領域の量子コンピュータ向けアルゴリズム ①VQE（Variational Quantum…

[probably-a-mental-breakdown]

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[picksblog285]

Quantum Calculator

Photodiode Quantum Efficiency | Definition, equation, calculator

Quantum performance calculator quantum performance calc the quantum performance score quantifies strength performance for people of different sizes (height and weight). Use the form below to work out the quantum performance score and quantum performance level you require for recomp certification. VQE is a quantum–classical hybrid algorithm and has been extensively studied because it is executable on noisy intermediate-scale quantum (NISQ) devices. Apart from these two approaches, many studies of quantum chemical calculations on quantum computers have been reported from both the theoretical and experimental sides.

Quantum Calculator Google

This page describes Photodiode Quantum Efficiency definition. It mentions Photodiode Quantum Efficiency equation/formula andPhotodiode Quantum Efficiency calculator.

What is Photodiode ?

• A photodiode is a type of photodetector capable of converting light into either current or voltage.This effect is called photovoltaic effect. • DC source is often used to apply reverse bias to the photodiode. This makes it generate more current.This mode of operation is called photoconductive mode. • Applications of photodiode include optical disc drives, digital cameras and optical switches etc. • Variants : PIN photodiode, Avalanche photodiode, PN Photodiode, Schottky Photodiode etc.

The figure depicts symbol of Photodiode and one such device from OSRAM.Refer article on Photodiode basics and types and their working operation.

What is Photodiode Quantum Efficiency ?

Definition:The quantum efficiency is defined as fraction of incident photons which are absorbed by photoconductor andgenerated electrons which are collected at the detector terminal.

In other words, Quantum efficiency is defined as fraction of incident photonswhich contribuite to photocurrent.It is related to responsivity as per following equation. Q.E. = 1240 * (Rλ/λ) ; Where, Rλ = Responsivity in A/W and λ = Wavelength in nm

Photodiode Quantum Efficiency Calculator

Example of Photodiode Quantum Efficiency calculator: INPUTS : Re = 1e5, Rp = 1.5e5 OUTPUTS: Quantum Efficiency (Q.E.) = 66.66%

Photodiode Quantum Efficiency Equation | Photodiode Quantum Efficiency Formula

Following equation or formula is used for Photodiode Quantum Efficiency calculator.

Photodiode calculators and terminologies

Photodiode vs Phototransistor Difference between Photodiode types and PIN diode Quantum Efficiency Responsivity Sensitivity

Useful converters and calculators

Following is the list of useful converters and calculators. dBm to Watt converter Stripline Impedance calculator Microstrip line impedance Antenna G/T Noise temp. to NF

RF and Wireless tutorials

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Quantum Numbers, Atomic Orbitals, and Electron Configurations

Contents: Quantum Numbers and Atomic Orbitals 1. Principal Quantum Number (n) 2.Angular Momentum (Secondary, Azimunthal) Quantum Number (l) 3.Magnetic Quantum Number (ml) 4.Spin Quantum Number (ms) Table of Allowed Quantum Numbers Writing Electron Configurations Properties of Monatomic Ions References

Quantum Numbers and Atomic Orbitals

By solving the Schrödinger equation (Hy = Ey), we obtain a set of mathematical equations, called wave functions (y), which describe the probability of finding electrons at certain energy levels within an atom.

A wave function for an electron in an atom is called an atomic orbital; this atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon of light).

Each electron in an atom is described by four different quantum numbers. The first three (n, l, ml) specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can occupy that orbital.

Principal Quantum Number (n): n = 1, 2, 3, …, ∞ Specifies the energy of an electron and the size of the orbital (the distance from the nucleus of the peak in a radial probability distribution plot). All orbitals that have the same value of n are said to be in the same shell (level). For a hydrogen atom with n=1, the electron is in its ground state; if the electron is in the n=2 orbital, it is in an excited state. The total number of orbitals for a given n value is n2.

Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n-1. Specifies the shape of an orbital with a particular principal quantum number. The secondary quantum number divides the shells into smaller groups of orbitals called subshells (sublevels). Usually, a letter code is used to identify l to avoid confusion with n:

l012345...Letterspdfgh...

The subshell with n=2 and l=1 is the 2p subshell; if n=3 and l=0, it is the 3s subshell, and so on. The value of l also has a slight effect on the energy of the subshell; the energy of the subshell increases with l (s < p < d < f).

Magnetic Quantum Number (ml): ml = -l, ..., 0, ..., +l. Specifies the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell. Thus the s subshell has only one orbital, the p subshell has three orbitals, and so on.

Spin Quantum Number (ms): ms = +½ or -½. Specifies the orientation of the spin axis of an electron. An electron can spin in only one of two directions (sometimes called up and down). The Pauli exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states that no two electrons in the same atom can have identical values for all four of their quantum numbers. What this means is that no more than two electrons can occupy the same orbital, and that two electrons in the same orbital must have opposite spins. Because an electron spins, it creates a magnetic field, which can be oriented in one of two directions. For two electrons in the same orbital, the spins must be opposite to each other; the spins are said to be paired. These substances are not attracted to magnets and are said to be diamagnetic. Atoms with more electrons that spin in one direction than another contain unpaired electrons. These substances are weakly attracted to magnets and are said to be paramagnetic.

Table of Allowed Quantum Numbers

nlmlNumber of orbitalsOrbital NameNumber of electrons10011s220012s21-1, 0, +132p630013s21-1, 0, +133p62-2, -1, 0, +1, +253d1040014s21-1, 0, +134p62-2, -1, 0, +1, +254d103-3, -2, -1, 0, +1, +2, +374f14

Writing Electron Configurations

The distribution of electrons among the orbitals of an atom is called the electron configuration. The electrons are filled in according to a scheme known as the Aufbau principle ('building-up'), which corresponds (for the most part) to increasing energy of the subshells:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f

It is not necessary to memorize this listing, because the order in which the electrons are filled in can be read from the periodic table in the following fashion:

Or, to summarize:

In electron configurations, write in the orbitals that are occupied by electrons, followed by a superscript to indicate how many electrons are in the set of orbitals (e.g., H 1s1)

Another way to indicate the placement of electrons is an orbital diagram, in which each orbital is represented by a square (or circle), and the electrons as arrows pointing up or down (indicating the electron spin). When electrons are placed in a set of orbitals of equal energy, they are spread out as much as possible to give as few paired electrons as possible (Hund's rule).

examples will be added at a later date

In a ground state configuration, all of the electrons are in as low an energy level as it is possible for them to be. When an electron absorbs energy, it occupies a higher energy orbital, and is said to be in an excited state.

Properties of Monatomic Ions

The electrons in the outermost shell (the ones with the highest value of n) are the most energetic, and are the ones which are exposed to other atoms. This shell is known as the valence shell. The inner, core electrons (inner shell) do not usually play a role in chemical bonding.

Elements with similar properties generally have similar outer shell configurations. For instance, we already know that the alkali metals (Group I) always form ions with a +1 charge; the 'extra' s1 electron is the one that's lost:

IALi1s22s1Li+1s2Na1s22s22p63s1Na+1s22s22p6K1s22s22p63s23p64s1K+1s22s22p63s23p6

The next shell down is now the outermost shell, which is now full — meaning there is very little tendency to gain or lose more electrons. The ion's electron configuration is the same as the nearest noble gas — the ion is said to be isoelectronic with the nearest noble gas. Atoms 'prefer' to have a filled outermost shell because this is more electronically stable.

The Group IIA and IIIA metals also tend to lose all of their valence electrons to form cations.

Quantum Calculator

IIABe1s22s2Be2+1s2Mg1s22s22p63s2Mg2+1s22s22p6IIIAAl1s22s22p63s23p1Al3+1s22s22p6

The Group IV and V metals can lose either the electrons from the p subshell, or from both the s and p subshells, thus attaining a pseudo-noble gas configuration.

IVASn(Kr)4d105s25p2Sn2+(Kr)4d105s2Sn4+(Kr)4d10Pb(Xe)4f145d106s26p2Pb2+(Xe)4f145d106s2Pb4+(Xe)4f145d10VABi(Xe)4f145d106s26p3Bi3+(Xe)4f145d106s2Bi5+(Xe)4f145d10

The Group IV - VII non-metals gain electrons until their valence shells are full (8 electrons).

Calculator Quantum Computer

IVAC1s22s22p2C4-1s22s22p6VAN1s22s22p3N3-1s22s22p6VIAO1s22s22p4O2-1s22s22p6VIIAF1s22s22p5F-1s22s22p6

Quantum Calculation In Chemistry

The Group VIII noble gases already possess a full outer shell, so they have no tendency to form ions.

Transition metals (B-group) usually form +2 charges from losing the valence s electrons, but can also lose electrons from the highest d level to form other charges.

B-groupFe1s22s22p63s23p63d64s2Fe2+1s22s22p63s23p63d6Fe3+1s22s22p63s23p63d5

References

Martin S. Silberberg, Chemistry: The Molecular Nature of Matter and Change, 2nd ed. Boston: McGraw-Hill, 2000, p. 277-284, 293-307.

Quantum Calculation And Quantum Communication

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