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Writerside/topics/How-the-Solvers-work.md

@@ -1,173 +1,5 @@
 # How the Solvers work
-
-## Grover's algorithm
-using the Qiskit library in Python. Grover's algorithm is a quantum algorithm that finds with high probability the unique input to a black box function that produces a particular output value, using just O(sqrt(N)) evaluations of the function, where N is the size of the function's domain.
-The first part of the code imports necessary libraries from Qiskit, loads the IBM Q account, and selects the least busy backend device that has at least 3 qubits and is operational.
-
-```python
-from qiskit import QuantumCircuit, execute, Aer, IBMQ
-from qiskit.providers.ibmq import least_busy
-from qiskit.visualization import plot_histogram
-
-provider = IBMQ.load_account()
-backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and
-                                   not x.configuration().simulator and x.status().operational))
-```
-
-Next, a quantum circuit is created with 3 qubits and 3 classical bits. The Hadamard gate is applied to all qubits to create a superposition of all possible states.
-
-```python
-qc = QuantumCircuit(3, 3)
-qc.h(range(3))
-```
-
-The Oracle is then applied. This part of the code flips the sign of the state we are searching for. In this case, the Oracle is hard-coded to flip the sign of the state `|111>`.
-
-```python
-qc.x(range(3))
-qc.h(2)
-qc.ccx(0, 1, 2)
-qc.h(2)
-qc.x(range(3))
-```
-
-The Grover diffusion operator is applied next. This part of the code amplifies the probability of the state we are searching for.
-
-```python
-qc.h(range(3))
-qc.x(range(3))
-qc.h(2)
-qc.ccx(0, 1, 2)
-qc.h(2)
-qc.x(range(3))
-qc.h(range(3))
-```
-
-The qubits are then measured and the results are stored in the classical bits.
-
-```python
-qc.measure(range(3), range(3))
-```
-
-Finally, the quantum circuit is executed on the selected backend, the results are retrieved, and a histogram of the results is plotted.
-
-```python
-job = execute(qc, backend, shots=1024)
-result = job.result()
-counts = result.get_counts(qc)
-plot_histogram(counts)
-```
-
-In summary, this code is a complete implementation of Grover's algorithm for 3 qubits using the Qiskit library. It creates a quantum circuit, applies the Oracle and Grover diffusion operator, measures the qubits, and plots the results.
-
-##  Shor's algorithm 
-
-Shor's algorithm is a quantum algorithm for integer factorization, which underlies the security of many cryptographic systems.
-The first part of the code imports necessary libraries from Qiskit, loads the IBM Q account, and selects the least busy backend device that has at least 3 qubits and is operational.
-
-```python
-from qiskit import QuantumCircuit, execute, Aer, IBMQ
-from qiskit.providers.ibmq import least_busy
-from qiskit.visualization import plot_histogram
-import numpy as np
-
-provider = IBMQ.load_account()
-backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and
-                                                           not x.configuration().simulator and x.status().operational))
-```
-
-Next, a quantum circuit is created with 3 qubits and 3 classical bits. The Hadamard gate is applied to all qubits to create a superposition of all possible states.
-
-```python
-qc = QuantumCircuit(3, 3)
-qc.h(range(3))
-```
-
-The Oracle is then applied. This part of the code flips the sign of the state we are searching for. In this case, the Oracle is hard-coded to flip the sign of the state `|111>`.
-
-```python
-qc.x(range(3))
-qc.h(2)
-qc.ccx(0, 1, 2)
-qc.h(2)
-qc.x(range(2))
-```
-
-The Shor's algorithm is applied next. This part of the code amplifies the probability of the state we are searching for.
-
-```python
-qc.h(range(3))
-qc.measure(range(3), range(3))
-```
-
-Finally, the quantum circuit is executed on the selected backend, the results are retrieved, and a histogram of the results is plotted.
-
-```python
-job = execute(qc, backend, shots=1024)
-result = job.result()
-counts = result.get_counts(qc)
-plot_histogram(counts)
-```
-
-In summary, this code is a complete implementation of Shor's algorithm for 3 qubits using the Qiskit library. It creates a quantum circuit, applies the Oracle and Shor's algorithm, measures the qubits, and plots the results.
-
-##  Variational Quantum Eigensolver (VQE) 
-The variational quantum eigensolver (VQE) is a quantum algorithm that can be used to find the ground state energy of a molecule or other quantum system. It combines a quantum circuit with a classical optimizer to minimize the energy of the system.
-The first part of the code imports necessary libraries from Qiskit and numpy. It also loads the IBM Q account and selects the least busy backend device that has at least 3 qubits and is operational.
-
-```python
-from qiskit import QuantumCircuit, execute, Aer, IBMQ
-from qiskit.visualization import plot_histogram
-from qiskit.aqua.algorithms import VQE
-from qiskit.aqua.components.optimizers import COBYLA
-from qiskit.aqua.components.variational_forms import RY
-from qiskit.aqua.operators import WeightedPauliOperator
-import numpy as np
-
-provider = IBMQ.load_account()
-backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and
-                                       not x.configuration().simulator and x.status().operational))
-```
-
-Next, a quantum circuit is created with 3 qubits and 3 classical bits. The Hadamard gate is applied to all qubits to create a superposition of all possible states. An Oracle is then applied which flips the sign of the state we are searching for.
-
-```python
-qc = QuantumCircuit(3, 3)
-qc.h(range(3))
-qc.x(range(3))
-qc.h(2)
-qc.ccx(0, 1, 2)
-qc.h(2)
-qc.x(range(3))
-```
-
-The VQE algorithm is then applied. This part of the code defines the Hamiltonian, the variational form, and the optimizer. The Hamiltonian is defined using a dictionary of Pauli operators, the variational form is defined using the RY gate, and the optimizer is defined using the COBYLA method.
-
-```python
-pauli_dict = {
-    'paulis': [{"coeff": {"imag": 0.0, "real": -1.052373245772859}, "label": "II"},
-              {"coeff": {"imag": 0.0, "real": 0.39793742484318045}, "label": "ZI"},
-              {"coeff": {"imag": 0.0, "real": -0.39793742484318045}, "label": "IZ"},
-              {"coeff": {"imag": 0.0, "real": -0.01128010425623538}, "label": "ZZ"},
-              {"coeff": {"imag": 0.0, "real": 0.18093119978423156}, "label": "XX"}]
-}
-qubit_op = WeightedPauliOperator.from_dict(pauli_dict)
-var_form = RY(qubit_op.num_qubits, depth=3, entanglement='linear')
-optimizer = COBYLA(maxiter=1000)
-vqe = VQE(qubit_op, var_form, optimizer)
-```
-
-Finally, the quantum circuit is executed on the selected backend, the results are retrieved, and a histogram of the results is plotted. The VQE algorithm is then executed on the backend.
-
-```python
-job = execute(qc, backend, shots=1024)
-result = job.result()
-counts = result.get_counts(qc)
-plot_histogram(counts)
-result = vqe.run(backend)
-```
-
-In summary, this code is a complete implementation of the VQE algorithm for 3 qubits using the Qiskit library. It creates a quantum circuit, applies the Oracle and VQE algorithm, measures the qubits, plots the results, and executes the VQE algorithm.
+This contains the explanation of how the solvers work.
 
 ##  Boson Sampling
 Boson Sampling is a type of quantum computing algorithm that is used to simulate the behavior of photons in a linear optical system.