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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
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Commercial applications of quantum computing.

Francesco Bova1,2, Avi Goldfarb1,2, Roger G Melko2,3,4

  • 1Rotman School of Management, University of Toronto, Toronto, Canada.

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Quantum computing is advancing, offering solutions for cybersecurity, materials, finance, and manufacturing. Near-term opportunities include quantum-safe encryption, drug discovery, and quantum-inspired algorithms.

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Area of Science:

  • Quantum computing applications
  • Combinatorics in industry

Background:

  • Quantum computing faces scientific and engineering challenges.
  • Progress is being made in applying quantum technology to commercial use cases.

Purpose of the Study:

  • Discuss solutions companies are developing using quantum hardware.
  • Illustrate applications in cybersecurity, materials/pharmaceuticals, banking/finance, and advanced manufacturing.
  • Identify near-term opportunities from quantum computing advancements.

Main Methods:

  • Framing commercial applications as combinatorics problems.
  • Analyzing four industry verticals: cybersecurity, materials and pharmaceuticals, banking and finance, and advanced manufacturing.

Main Results:

  • Quantum hardware is being used to build solutions for specific industry problems.
  • Three key near-term opportunities are identified: quantum-safe encryption, material and drug discovery, and quantum-inspired algorithms.
  • Current quantum computers are not yet at the scale to solve all combinatorics problems.

Conclusions:

  • Quantum computing offers significant potential across various industries.
  • Near-term applications focus on quantum-safe encryption, drug discovery, and quantum-inspired algorithms.
  • Continued development is crucial for realizing the full potential of quantum solutions.