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Related Concept Videos

Sampling Methods: Overview01:06

Sampling Methods: Overview

663
A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of...
663
Sampling Theorem01:15

Sampling Theorem

872
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
872
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

566
Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
566
Upsampling01:22

Upsampling

361
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
361
Aliasing01:18

Aliasing

296
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
296
Sampling Plans01:23

Sampling Plans

334
Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Quantum Sampling Algorithms for Near-Term Devices.

Dominik S Wild1, Dries Sels2,3, Hannes Pichler4,5

  • 1Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany.

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|September 17, 2021
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Summary
This summary is machine-generated.

Quantum algorithms offer efficient sampling from Gibbs distributions, outperforming classical methods for tasks like the Ising model. This quantum approach provides a physical interpretation of speedup and is suitable for near-term quantum devices.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Machine Learning

Background:

  • Efficient sampling from classical Gibbs distributions is crucial for statistical physics, Monte Carlo methods, optimization, and machine learning.
  • Classical Markov chain algorithms are commonly used but can be computationally intensive.

Purpose of the Study:

  • To introduce a family of quantum algorithms for unbiased sampling from Gibbs distributions.
  • To demonstrate quantum speedup over classical sampling algorithms.
  • To provide a physical interpretation of quantum speedup and explore applications on near-term quantum devices.

Main Methods:

  • Preparation of a quantum state encoding the entire Gibbs distribution.
  • Development of quantum algorithms for sampling from specific distributions, including the Ising model and weighted independent sets.
  • Comparison of quantum algorithm performance against classical Markov chain algorithms.

Main Results:

  • The proposed quantum algorithms achieve unbiased sampling from Gibbs distributions.
  • A demonstrable speedup is observed compared to classical Markov chain algorithms for the Ising model and sampling independent sets on graphs.
  • A connection is established between computational complexity, phase transitions, and quantum speedup.

Conclusions:

  • Quantum algorithms offer a powerful and efficient alternative for sampling from Gibbs distributions.
  • The approach provides a physical insight into quantum speedup and its relation to phase transitions.
  • The developed algorithms are promising for implementation on near-term quantum hardware, such as Rydberg atom arrays.