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Second-Order Circuits

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Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
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An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
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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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Calculations of Electric Potential I01:15

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Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
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The Quantum-Mechanical Model of an Atom02:45

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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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First-Order Circuits01:15

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First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
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Measurement-Based Infused Circuits for Variational Quantum Eigensolvers.

Albie Chan1, Zheng Shi1, Luca Dellantonio1,2

  • 1Institute for Quantum Computing and Department of Physics and Astronomy, <a href="https://ror.org/01aff2v68">University of Waterloo</a>, Waterloo, Ontario, N2L 3G1, Canada.

Physical Review Letters
|July 1, 2024
PubMed
Summary
This summary is machine-generated.

Variational quantum eigensolvers (VQE) now integrate measurement-based quantum computing concepts for enhanced quantum simulations. This approach enables novel Hamiltonian simulations on superconducting quantum hardware.

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Area of Science:

  • Quantum Computing
  • Quantum Simulation
  • Computational Physics

Background:

  • Variational quantum eigensolvers (VQE) are established algorithms for quantum computation.
  • Quantum simulation has been extended to the measurement-based model, utilizing graph states.
  • This extension introduces advantages for simulating quantum systems.

Purpose of the Study:

  • To integrate measurement-based quantum computing concepts into traditional VQE algorithms.
  • To develop novel, problem-informed designs for VQE circuits.
  • To enable versatile implementations of many-body Hamiltonians using VQEs.

Main Methods:

  • Incorporation of measurement-based quantum computing ideas into VQE circuits.
  • Development of problem-informed circuit designs.
  • Implementation of VQE simulations on superconducting quantum hardware.

Main Results:

  • Demonstrated novel VQE designs for quantum simulation.
  • Successfully simulated various testbed systems, including perturbed planar code, Z2 lattice gauge theory, 1D quantum chromodynamics, and the LiH molecule.
  • Showcased versatile implementations of many-body Hamiltonians.

Conclusions:

  • The integration of measurement-based quantum computing enhances VQE capabilities.
  • The proposed approach allows for flexible and efficient quantum simulations.
  • This work advances the application of VQEs on real quantum hardware for complex physical systems.