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Related Concept Videos

State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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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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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Reconstructing Quantum States With Quantum Reservoir Networks.

Sanjib Ghosh, Andrzej Opala, Michal Matuszewski

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    We present a novel quantum state tomography platform using reservoir computing. This quantum neural network reconstructs arbitrary quantum states efficiently with simple measurements.

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    Area of Science:

    • Quantum information science
    • Quantum computing and technology

    Background:

    • Quantum state tomography is crucial for quantum technologies but conventionally challenging.
    • Existing methods often require state-specific protocols and complex measurements.

    Purpose of the Study:

    • To develop a universal and efficient quantum state tomography platform.
    • To overcome the limitations of conventional tomography techniques.

    Main Methods:

    • Utilizing a reservoir computing framework to create a quantum neural network.
    • Implementing a comprehensive device for reconstructing arbitrary quantum states.

    Main Results:

    • Demonstrated reconstruction of both finite-dimensional and continuous variable quantum states.
    • Achieved state reconstruction using only average occupation number measurements.

    Conclusions:

    • The reservoir computing approach offers a unified and simplified method for quantum state tomography.
    • This platform advances the development of practical quantum technologies by simplifying state reconstruction.