Questions tagged [algorithms]
For questions about an algorithm as it relates to physics. DO NOT ask how to implement an algorithm, questions like that belong on Stack Overflow or Computational Science. DO NOT ask about the efficiency of an algorithm, or other such questions, questions like that belong on Computational Science.
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References for Numerical Solutions of the Feynman Path Integral
I am looking for references that discuss numerical approaches to evaluating the Feynman path integral.
Specifically, I would like references (books, papers, or reviews) that cover:
Discretization ...
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How to define an equitable success event in quantum-walk-based multiple-targets search algorithm?
In quantum search algorithms (on a 2D grid or other setting), when there are multiple targets, a "successful search" event is often defined in following:
$$P_{success}=\max_{t\in [0,T]} \...
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Go a step further and get the both results of $f(x)$ in Deutsch algorithm
The Deutsch-Josza algorithm gives the result in one operation of the type of a $(0,1) \mapsto (0,1)$ function $f(x)$, i.e. if $f(x)$, is constant or balanced. With the parallel computing power of a ...
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Doubt in Verlet's Algorithm
In studying the temporal evolution of a system according to the deterministic model, we begin by considering a Taylor series expansion for the displacement $r$. First, we consider a positive variation ...
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Neglected Term in the energy gradient for Variational Monte-Carlo
I'm looking into variational Monte-Carlo to determine the optimal variational parameter that corresponds to the ground state of a Hamiltonian. In general I am interested in tight binding models where ...
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Multilateration of a light source in a medium whose index of refraction varies with position
Background
I have a set of $N$ receivers whose locations in $3D$ space are well-known. These receivers are immersed in a medium whose index of refraction (and thereby the velocity of light propagation)...
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Checking inverse metric and Christoffel symbols for the Kerr metric against references
I am trying to cross-check the Christoffel symbols and other very laborious geometric components in several metrics. In particular the Kerr metric is notoriously complex and results in expressions ...
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Force-simulation for graph layout: How to avoid particle collapsing into a single point?
In a force-based graph-layout simulation using Barnes-Hut, what are the conditions for collapse? With collapse I mean multiple (or even all) nodes "collapsing" into a single point.
Is there ...
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Any quantum Monte-Carlo algorithm for calculating the lowest eigenenergy in each symmetry sector?
Suppose we have a hamiltonian which has the parity symmetry (e.g., the Heisenberg model with the open boundary condition). Is there any quantum Monte-Carlo algorithm which can be used to calculate the ...
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About how to calculate observables in Quantum Monte Carlo with complex weights
I'm rewriting a Diagrammatic Quantum Monte Carlo algorithm following Werner, P., Oka, T., & Millis, A. J. (2009). Diagrammatic Monte Carlo simulation of nonequilibrium systems. Physical Review B, ...
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Is there a proof for critical slow-down in Monte Carlo?
It is physically understood why the standard Metropolis-Hasting algorithm slows down near the critical temperature, since it doesn’t utilize the divergence of the correlation length. However, I’m ...
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Is Quantum State Tomography (QST) an inherently supervised or unsupervised problem in Machine Learning?
I am studying how to apply neural networks to the problem of Quantum State Tomography (QST) and I got confused when it comes to decide if this is a supervised or unsupervised learning problem.
At ...
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Understanding chapter 3.1 (Laplace's equation) in Introduction to electrodynamics Griffiths 4 ed [duplicate]
I really need help to understand chapter 3.1.
What is the method of relaxation?
How can I use the method of relaxation to solve Laplace's equation?
How can I use the first and second uniqueness ...
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How to efficiently calculate the inverse of the overlap matrix?
Now, we consider a non-orthonormal basis:
$$\mathcal{S}_N=\{|\alpha\rangle,a^\dagger|\alpha\rangle,a^{\dagger 2}|\alpha\rangle,\ldots,a^{\dagger N}|\alpha\rangle\},$$
where $|\alpha\rangle$ is the ...
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Can I find quantum circuit drawing of BB84 protocol somewhere?
Quantum algorithms and protocols are often expressed as circuit diagrams. But I have not been able to find the circuit diagram of BB84 protocol. Has anyone seen one?
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Fringe pattern and ripples in the fringe visibility plot from interferograms
I am using a lens testing interferometer, where I record 4 to 5 interferograms with a 90$^{\circ}$ phase step between consecutive interferograms. In addition to the interferometer, I have also created ...
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Simplest quantum Monte-Carlo method for the Bose-Hubbard model
I want to use quantum Monte-Carlo results to benchmark an algorithm for the Bose-Hubbard model. There are so many QMC methods in the market, so which one is the simplest one? I want the ground state ...
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How are the boundary conditions given in the SIMPLE algorithm on a forward staggered grid for a lid driven cavity flow?
I have a code given by my professor in which he applies the boundary conditions for the lid driven cavity flow. All the enforcement of boundary conditions I have seen elsewhere completely differ from ...
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Numerically computing induced magnetic field from current density
Let's say we have current density $J_i$ on a discretized grid with $(N_x \times N_y \times N_z)$ points. What is the best procedure to compute the induced magnetic field $(B_i)$ from the current ...
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What are the advantages of tensor network algorithms over monte-carlo simulations in terms of time-evolution?
I understand that tensor networks and monte carlo simulations are based on completely different principles. However, to my knowledge both are used to simulate the time evolution of a system. Is there ...
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An example problem to solve using 100 qubits?
Suppose we have in our possession 100 pairs of electrons.
Each electron A1 - A100 is entangled with its respective twin B1 - B100. Each entangled electron pair has been set up to have opposite spins (...
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Grover's algorithm & using wave interference for computing
Grover's quantum search algorithm contends that it is possible to search for a specific item in an N-sized unsorted database in only $\sqrt N$ attempts. Classically, it takes N/2 attempts on average ...
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Sensor Array Position Calibration in Anisotropic Media
Problem.
I have a sensor array consisting of $n \gg 4$ receivers at unknown locations $\langle x_n, y_n, z_n\rangle$ embedded in an anisotropic medium whose index of refraction varies as a known ...
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Why are time-reversible integration algorithms in molecular dynamics simulations favorable?
I read that integration algorithms that are not time-reversible tend to be less "stable". Where stable means that the total energy stays constant (is conserved). I'd like to know what it ...
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Are there ways to find representations of matrices given an algebra?
Given an equation (or a set of equations) involving matrices, is there an algorithm to find possible representations of these matrices?
For example, we can consider a matrix $A$ such that
$A^2=\begin{...
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Applying Divergence to query moving points
Problem statement :- There is a moving source($s$) and other moving points ($p_{1}.... p_{n}$). There are fixed obstacles and a fixed destination point($d$). In each time step I have to query "Is ...
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Reference request: Numerical techniques, Monte-Carlo (MC), Density Matrix Renormalization Group (DMRG), Dynamical Mean-Field Theory (DMFT)
I am an undergraduate student and my previous learning in physics is more on theory instead of numerics. I would be very grateful if you can point me to good introductory lecture notes/lecture videos ...
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Could we have a quantum algorithm that have the quantum speed-up, but don’t need universal gates?
When it comes to building a quantum computer, it's like we need to consider how to perform universal gates fault-tolerantly, which is an unsolvable problem so far. While Clifford gates may be easier ...
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Algorithm for solving Poisson's equation numerically
I need an algorithm to solve Poisson's equation for gravitational potential.
$$ \nabla^2\phi = 4\pi G\rho $$
where, $\phi$ is Gravitational Potential.
I am trying PDE for the first time so, I need ...
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Numerical solutions to the 3D wave equation
I am doing a research to explore the existing numerical schemes that are used to solve the $3$D wave equation.
The standard form of the problem in $3$ dimensional setting is : $$\Delta u= \frac{1}{c^2}...
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Dynamic Programming and legendre transformation?
I read once (I can't find it anymore:( ), that the Legendre transformation from the Lagrange formalism to the Hamilton formalism can be seen as dynamic programming.
I have never seen it like this and ...
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Compressing the Hilbert Space in Traditional DMRG
The traditional, non Matrix Product State, formulation of the Density Matrix Re-normalization Group (DMRG) algorithm can be coded in python. Such a code can be found in the following link:
https://...
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Algorithm that checks if a subspace of states contains a product state
Suppose I have two identical qudits, the full Hilbert space is $\mathcal{H}=(\mathbb{C}^{d})^{\otimes 2}$. Say I'm given a supspace of states $\Lambda\subset \mathcal{H}$. What is the fastest ...
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Why does the chain be at equilibrium in the MH algorithm?
I'm implementing the Metropolis algorithm to solve the 2D Ising model. I've understood how to implement it and now I'm trying to understand a bit of how the algorithm works. In the site I'm reading it ...
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Is Shor's algorithm for factoring still efficient in the presence of small phase noise
Quantum Fourier transform of $|a\rangle\in H_N$
$$|a\rangle\longrightarrow\sum_{l=0}^{N-1}e^{\frac{i2\pi a l}{N}}|l\rangle$$
where $N=2^n$ and $H_N$ is $N$-dimensional Hilbert space.
The ...
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Which is more accurate: Euler's method or modified Euler's method?
I was solving a differential equation, the equation being,
$$\frac{dv}{dt} = g-\frac{c_d}{m}v^2,$$
which can be solved analytically to give
$$v = \sqrt{\frac{mg}{c_d}}\left(\frac{e^{2t\sqrt{\frac{c_dg}...
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How Do Quantum Computers Work, Like Really [closed]
I understand in plain terms superposition and entanglement, but I'm very unclear how either of these could work as a means to increase computation power.
A helpful metaphor is that of the maze. A ...
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Number of qubits required in Shor's algorithm
People say that the number of qubits required in Shor's algorithm for factorizing $N$ should be
$2\log N$ for control register and $\log N$ for target register.
What is the reason why these numbers of ...
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Is there a comparison table for quantum algorithms like VQE, QPE, QAOA, and so on?
I have one question: Recently, I studied about several algorithms like VQE, QPE, QAOA and so on. I would like to make some comparison tables about those algorithms, their strengths and weaknesses. If ...
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Why use Crank-Nicolson over Matrix Exponential when solving Schrödinger's equation?
For Schrödinger's equation,
$$\psi(x,t+\Delta t)=e^{-i H\Delta t}\psi(x,t)\approx\frac{1-\frac{1}{2}i H\Delta t}{1+\frac{1}{2}i H\Delta t}\psi(x,t).$$
The right-most expression is the Crank-Nicolson ...
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Final Hamiltonian for Adiabatic Grover
X-Posted on Quantum-Computing Stack Exchange
In quantum computation, there is a famous algorithm to search a marked item in an unstructured database called Grover's algorithm. It achieves a quadratic ...
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Why is the boundary of friends-of-friends (FOF) halo corresponding to iso-density contour?
The friends-of-friends algorithm (hereafter FOF) is commonly used to find halos in cosmological simulations. (For more information, please refer to here and here)
I found that some literature argues ...
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Is the universe's Kolmogorov complexity growing over time?
The Kolmogorov complexity of a deterministic universe is constant.
The Kolmogorov complexity of a nondeterministic universe grows over time. It grows whenever something happens that is not ...
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Bell State Measurement Algorithm
I'm relatively new to quantum computation and am taking a course in it. I was wondering if it is possible to code an algorithm which would be able to take an input of a 2 qubit state and perform a ...
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Modeling curved light in media with "complex" indices of refraction
I've written an algorithm to solve the Time Difference of Arrival (TDoA) localization problem, using Bancroft's method (see). Given the coordinates of $n$ nodes in ...
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How to calculate acceleration due to gravity in a 3D $N$-Body system?
How do you calculate acceleration due to gravity for objects in 3D space?
My current understanding for the force due to gravity on object $i$ from object $j$ is
$$\mathbf{F}_g=(\mathbf{r}_j-\mathbf{r}...
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Novikov self-consistency and computability
The Wikipedia article on the Novikov self-consistency principle has a section on time loop logic, where it discusses using time travel to solve any NP problem by finding an algorithm where the only ...
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Is the only difference between tDMRG and TEBD the way the central sites are shifted?
I have been reading up on time evolution methods using matrix product states. Reading from Schollwoeck's notes on the density matrix renormalization group, (https://arxiv.org/abs/1008.3477), I looked ...
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Github for Physicists
I am wondering if there is a platform to which researchers share or publish the code they used in their research. I noticed that many researchers explain their algorithm and math and present the ...
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Numerical renormalization of 2D Ising lattice
I'm trying to make some toy computations on the $2D$ Ising model on a square lattice. I want to apply a renormalization transformation, and try to estimate observables on the renormalized lattice ...
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