I have been working on quantum machine learning by implementing gradient descent for optimized parametrized circuits using pennylane and qiskit, this can tremendously improve the cost and also simplify the quantum gate. The Jupyter Notebook file may be too large so you need to reload it again.
Implement a circuit that returns |01> and |10> with equal probability. Requirements :The circuit should consist only of CNOTs, RXs and RYs. Start from all parameters in parametric gates being equal to 0 or randomly chosen. You should find the right set of parameters using gradient descent (you can use more advanced optimization methods if you like). Simulations must be done with sampling (i.e. a limited number of measurements per iteration) and noise. Compare the results for different numbers of measurements: 1, 10, 100, 1000. Bonus question: How to make sure you produce state |01> + |10> and not |01> - |10> ? (Actually for more careful readers, the “correct” version of this question is posted below: How to make sure you produce state |01⟩ + |10⟩ and not any other combination of |01> + e(i*phi)|10⟩ (for example |01⟩ - |10⟩)?)
The task tells us that we need to create a two-qubit Bell State of 1/2(|01> + |10>) and not 1/2(|01> - |10>).
Analytically, I try to caculate how to get to the state. I make use of the Qiksit to verfiy if my calculation is correct.
Numerically, we need the following:
two qubits: q0, q1 a set of operations on Rx, Ry, CNOT only Initial parameters for the gates Rx, Ry corresponding to their parameters: thetaRx, thetaRy A circuit that applies the operations to thte qubits: circuit A simulator that runs the circuit fora specified numbdr of repetitions: reps, simulator We introdue coding Gradient Descent on Task 2 for optimized parametrized circuit using pennyLane and qiskit.