Physics, Electronics and Programming
Introduction According to EPR, an acronym for Einstein-Podolsky-Rosen, a physical theory must contain elements of reality and be local. This argument was presented in a famous 1935 paper, where the authors questioned whether quantum mechanics was a complete theory, suggesting the existence of hidden variables that could deterministically explain the behavior of quantum particles. However, … Read more
Introduction The Variational Quantum Eigensolver (VQE) algorithm is a hybrid quantum-classical method developed to estimate the ground-state energy of a quantum system, described by a Hamiltonian \( H \). It leverages the variational principle and quantum computing to prepare trial wavefunctions and evaluate their energy expectation values efficiently, making it a key algorithm for near-term … Read more
Introduction Simulating the dynamics of the Schrödinger equation on quantum computers is a foundational task for exploring quantum systems. This requires efficient representations and approximations of the Hamiltonian \( H \) and its associated time evolution operator. Two key techniques are Pauli decomposition and Trotter-Suzuki decomposition, which together enable the practical implementation of quantum simulations. … Read more
Introduction Lie groups and Lie algebras form the backbone of modern physics and mathematics, particularly in areas such as quantum mechanics, particle physics, and differential geometry. A Lie group is a continuous group with a smooth structure, where elements can be parameterized by continuous variables. These groups encapsulate symmetries of physical systems and are often … Read more
The group discussed here, also known as the Lorentz group in one dimension, describes the symmetries of special relativity with one spatial and one temporal dimension. The metric is defined as: \[\eta = \begin{pmatrix}1 & 0 \\0 & -1\end{pmatrix}\] The position vector is given by: \[x = \begin{pmatrix}ct \\x\end{pmatrix}\] If \(x\) transforms as \(x’ = … Read more
Gauge theories play a central role in modern physics, providing a unified framework for describing the fundamental interactions of nature. The introduction of local gauge invariance to the Dirac Lagrangian leads to the coupling of fermionic fields with gauge fields, paving the way for the development of quantum electrodynamics (QED) and other gauge theories. This … Read more
Quantum computing continues to advance, offering groundbreaking opportunities to solve complex problems. If you’re a developer or researcher seeking tools to simulate quantum algorithms with ease, LogicQubit is a versatile library designed for numerical and symbolic simulations. Here, we’ll explore the features and capabilities of LogicQubit and show you how to get started with this … Read more
Universal Gravitation Two bodies are mass \( m \) and \( M \), where the first body is a circular orbit with respect to the second. The centripetal force that acts on \(m\) is:\[F\_{m} = m\frac{v^{2}}{r}\] We know that for a circular orbit \(v = \frac{2\pi r}{T}\), using this expression in the third law of Kepler … Read more