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Related Concept Videos

The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
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Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

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Related Experiment Video

Updated: Jun 2, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

A precise error bound for quantum phase estimation.

James M Chappell1, Max A Lohe, Lorenz von Smekal

  • 1School of Chemistry and Physics, University of Adelaide, Adelaide, South Australia, Australia. james.m.chappell@adelaide.edu.au

Plos One
|May 17, 2011
PubMed
Summary
This summary is machine-generated.

Researchers derived an exact formula for quantum phase estimation error probability by ensuring symmetry. This precise quantum computing formula aids in validating simulations and optimizing qubit requirements.

Related Experiment Videos

Last Updated: Jun 2, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum Computing
  • Quantum Algorithms
  • Computational Complexity

Background:

  • Quantum phase estimation is a fundamental algorithm in quantum computing.
  • Previous derivations of error probability for this algorithm were approximate.
  • Accurate error estimation is crucial for reliable quantum computation design.

Purpose of the Study:

  • To derive an exact formula for the probability of error in quantum phase estimation.
  • To explore the applicability of this new approach to related quantum computing problems.
  • To provide a tool for validating simulations and optimizing qubit allocation.

Main Methods:

  • Revisiting existing derivations of error probability.
  • Introducing symmetry into error definitions to achieve an exact formula.
  • Developing expressions for special cases in limiting qubit scenarios.

Main Results:

  • An exact formula for quantum phase estimation error probability was successfully derived.
  • The formula was validated for two limiting cases: infinite qubits and infinite auxiliary qubits.
  • The derived formula proves useful for validating computer simulations.

Conclusions:

  • The new exact error formula enhances precision in quantum computer design.
  • It helps avoid overestimation of required qubits for desired reliability.
  • This methodology may extend to other quantum computing error calculation problems.