Results

 My results are in. For the two output graphs:

GEMINI:

The two matplotlib output graphs in this video show the results of running two different quantum circuits on a quantum computer. The circuits are inspired by a recent paper by IBM that studied the dynamics of a kicked Ising model on 127 qubits.

The first graph (Figure 1) shows the survival probability of the all-zero bit string as a function of the two-qubit gate depth. The survival probability is the probability of the circuit ending in the same state that it started in. In this case, the circuit starts in the all-zero bit string state, and the two-qubit gate depth is a measure of how many times two-qubit gates have been applied. The graph shows that the survival probability starts at 1 and then drops down close to 0.2 as the two-qubit gate depth increases. This is because noise in the quantum computer causes the circuit to deviate from the ideal state.

The second graph (Figure 2) shows the expectation value of the single-qubit Z operator in the middle of the chain as a function of the RX angle. The expectation value is a measure of the average value of a particular observable. In this case, the observable is the Z operator, which measures whether a qubit is in the state |0> or the state |1>. The RX angle is a parameter of the circuit. The graph shows that the expectation value starts at close to 1 and then goes towards zero as the RX angle increases. This is the expected behavior for this particular circuit.

Overall, the two graphs show that the quantum circuits can be used to study the dynamics of the kicked Ising model, but that noise in the quantum computer limits the accuracy of the results.

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BING/CHAT:

The kicked Ising model is a quantum system that combines elements of the Ising model (a classical statistical mechanics model) with periodic external perturbations. Here's a brief overview:

1. **Ising Model**:

   - The Ising model describes the behavior of spins (quantum or classical) on a lattice. Each spin can be in one of two states: up or down.

   - Spins interact with their nearest neighbors, and the goal is to understand the collective behavior of the entire system.

   - The Hamiltonian for the Ising model includes terms related to spin-spin interactions and an external magnetic field.

2. **Kicked Ising Model**:

   - The kicked Ising model extends the Ising model by periodically perturbing the system.

   - The perturbation is typically a "kick" or sudden change in the external magnetic field.

   - The system evolves under the combined influence of the Ising interactions and the periodic kicks.

   - It exhibits rich dynamical behavior, including quantum chaos and localization.

3. **Quantum Chaos and Localization**:

   - Quantum chaos refers to the complex, unpredictable behavior observed in quantum systems with classically chaotic counterparts.

   - Localization occurs when quantum states become localized (confined) in certain regions of the lattice due to interference effects.

   - The kicked Ising model provides insights into these phenomena.

In summary, the kicked Ising model is a fascinating quantum system that combines features from classical statistical mechanics and quantum dynamics, making it an interesting area of study in both physics and quantum computing. 🌟

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Certainly! Let's explore the differences between the **Sampler** and **Estimator** primitives in the context of IBM Quantum's Qiskit framework:

1. **Sampler**:

   - The **Sampler** primitive is responsible for obtaining bit strings (samples) from the probability distribution of a quantum state prepared on a device.

   - It directly returns the sampled outcomes without additional post-processing.

   - Useful for tasks like quantum approximate optimization algorithms (QAOA) and variational quantum eigensolvers (VQE).

   - You can run the Sampler with any provider using `qiskit.primitives.BackendSampler`.

2. **Estimator**:

   - The **Estimator** primitive computes expectation values of observables with respect to states prepared by quantum circuits.

   - It takes one or more Pauli observable objects (PUBs) as input and returns computed expectation values along with their standard errors.

   - Estimators are essential for VQE and other quantum algorithms.

   - You can run the Estimator with any provider using `qiskit.primitives.BackendEstimator`.

In summary, the **Sampler** provides raw samples, while the **Estimator** calculates expectation values. Both are crucial for quantum computations! 🚀 ²³

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Usingthe web

The kicked Ising model is a quantum system that combines elements of the Ising model (a classical statistical mechanics model) with periodic external perturbations. Here’s a brief overview:

1. Ising Model:

   • The Ising model describes the behavior of spins (quantum or classical) on a lattice. Each spin can be in one of two states: up or down.
   • Spins interact with their nearest neighbors, and the goal is to understand the collective behavior of the entire system.
   • The Hamiltonian for the Ising model includes terms related to spin-spin interactions and an external magnetic field.

2. Kicked Ising Model:

   • The kicked Ising model extends the Ising model by periodically perturbing the system.
   • The perturbation is typically a “kick” or sudden change in the external magnetic field.
   • The system evolves under the combined influence of the Ising interactions and the periodic kicks.
   • It exhibits rich dynamical behavior, including quantum chaos and localization.

3. Quantum Chaos and Localization:

   • Quantum chaos refers to the complex, unpredictable behavior observed in quantum systems with classically chaotic counterparts.
   • Localization occurs when quantum states become localized (confined) in certain regions of the lattice due to interference effects.
   • The kicked Ising model provides insights into these phenomena.

In summary, the kicked Ising model is a fascinating quantum system that combines features from classical statistical mechanics and quantum dynamics, making it an interesting area of study in both physics and quantum computing. 🌟

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