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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...
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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...
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Digital System Design for Quantum Error Correction Codes.

Othman O Khalifa1, Nur Amirah Bt Sharif1, Rashid A Saeed2

  • 1Electrical and Computer Engineering Department, International Islamic University, Gombak, Malaysia.

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|January 7, 2022
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Summary

Quantum error correction protects quantum information transmitted via qubits from environmental noise. This study details digital system designs for encoding and decoding nine-qubit error correction codes to enhance quantum communication reliability.

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Area of Science:

  • Quantum Information Science
  • Computer Engineering
  • Error Correction Theory

Background:

  • Quantum computing leverages quantum mechanics for advanced computation.
  • Quantum information transmission is vulnerable to environmental interactions and noise.
  • Quantum error correction is crucial for reliable quantum communication and storage.

Purpose of the Study:

  • To discuss the digital system design of quantum error correction codes.
  • To explain three qubit codes and nine-qubit codes for quantum error correction.
  • To design and configure systems for encoding and decoding nine-qubit error correction codes.

Main Methods:

  • Digital system design implementation for quantum error correction.
  • Explanation and application of three qubit codes and nine-qubit codes.
  • System configuration for encoding and decoding operations.
  • Design of a modified circuit with Hadamard gates for comparison.

Main Results:

  • Successful design and configuration of systems for encoding and decoding nine-qubit error correction codes.
  • Demonstration of quantum error correction code designs.
  • Comparison of a modified circuit with added Hadamard gates.

Conclusions:

  • Quantum error correction is essential for mitigating noise in quantum channels.
  • The digital system designs presented offer a pathway to protect qubits from decoherence.
  • Further research can explore enhanced error correction strategies using modified circuits.