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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Sampling Theorem01:15

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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.
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Sampling Methods: Overview01:06

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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. 
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Sampling Methods: Sample Types01:18

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Sampling materials are classified into three main types: solid, liquid, and gas.
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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Random Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Continuous-Variable Instantaneous Quantum Computing is Hard to Sample.

T Douce1,2, D Markham2,3, E Kashefi2,3,4

  • 1Laboratoire Matériaux et Phénomènes Quantiques, Sorbonne Paris Cité, Université Paris Diderot, CNRS UMR 7162, 75013 Paris, France.

Physical Review Letters
|March 4, 2017
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Summary
This summary is machine-generated.

We demonstrate that instantaneous quantum computing is hard to simulate classically in continuous-variable systems. This involves using squeezed states and homodyne detection, with error suppression for robust quantum computation.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Complexity Theory

Background:

  • Instantaneous quantum computing (IQC) is a subuniversal quantum complexity class.
  • IQC circuits are classically hard to simulate in the discrete-variable (DV) domain.

Purpose of the Study:

  • Extend the classical hardness proof of IQC to the continuous-variable (CV) domain.
  • Investigate the role of postselection in CV quantum computation.

Main Methods:

  • Utilized squeezed states and homodyne detection for CV systems.
  • Employed finitely resolved homodyne detectors to model realistic postselection.
  • Applied a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding for error suppression.

Main Results:

  • Established the classical hardness of simulating IQC circuits in the CV domain.
  • Showed that logarithmic squeezing parameter scaling is necessary for meaningful postselected CV computational classes.
  • Demonstrated polynomial scaling of input energy with circuit size.

Conclusions:

  • CV quantum computation with postselection is classically intractable.
  • Error suppression techniques are crucial for fault-tolerant CV quantum computation.
  • The findings have implications for understanding the power and limitations of quantum computers.