- Classical Lagrangian
- Captures the dynamics of the system.
- Involves an electromagnetic wave and qubits.
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Simulation of Lagrangian System
- Solves a simplified version of the Lagrangian system using Python.
- Simulates the evolution of
$$\Phi_n$$ over time.
-
$$c$$ (Speed of light) -
$$L$$ (Inductance) -
$$n_{\text{points}}$$ (Number of qubits)
-
$$\Phi_n$$ ,$$\dot{\Phi}_n$$ ,$$\Psi_n$$ ,$$\dot{\Psi}_n$$
-
$$dt$$ (Time step) -
$$time_{\text{steps}}$$ (Number of time steps)
- Kinetic term:
$$\left(\frac{{\dot{\Phi}_n}}{{2c}}\right)^2$$ - Potential term:
$$\frac{{(\Phi_n - \Phi_{n-1} - \tilde{\Psi}_n)^2}}{{2L}}$$
- Update
$$\dot{\Phi}_n$$ by adding random noise - Update
$$\Phi_n$$ and$$\Psi_n$$ based on their derivatives
- Store the values of
$$\Phi_n$$ at each time step
- Plot the evolution of
$$\Phi_n$$ over time
- Progress in experimental and theoretical fields.
- Quantum coherent solid-state qubits as building blocks.
- Explores quantum-classical boundary.
- Distinct from nanotechnology and quantum computing.
- Addresses the quantum effects in engineering.
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Miniaturization and Nanotechnology
- Momentum behind nanotechnology from miniaturization.
- Quantum effects important in mesoscopic physics.
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Quantum Computing
- Algorithms like Shor's and Grover's.
- DiVincenzo criteria for scalable quantum computer.
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Criteria for Quantum Computer
- Initialize qubit states.
- Long decoherence times.
- Universal quantum gates.
- Qubit-specific measurements.
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Solid-State Devices
- Superconducting devices and quantum dots.
- Decoherence times and scalability.
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Macroscopic Schrödinger Cat States
- Testing the limits of quantum mechanics.
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Quantum Engineering as a Branch
- Large systems of interacting qubits.
- Quantum coherence in large systems