# OQS Project 1: Depolarizing channel

(01/04/2021)

The following series of posts combine projects from Open Quantum Systems with Qiskit with Strangeworks to allow readers to quickly explore and apply concepts with real quantum code using the free community edition of the Strangeworks platform.

In this project we will implement the depolarizing channel in qiskit and test it with state tomography on the simulator and on a real device.

Clone the project to your account to get started. Don't have an account? No problem! You can sign up for our free account and the project will be waiting for you in your dashboard.

We introduced the depolarizing channel in Chapter 5 where we showed the circuit that implements it.

Here it is again:

Create a function that returns a quantum circuit implementing depolarizing channels with parameter $p$​ on a specified qubit system, using three ancillary qubits ancillary = [a1, a2, a3].

Write a circuit prepared_state that prepares the system qubit in an initial state that has non-zero populations and coherences (both real and imaginary parts).

For different values of $p \in [0,1]$​:
1. Concatenate prepare_state and depolarizing_channel in a circuit and create the corresponding tomography_circuits (check the preliminaries for help with the tomography).
2. Execute the tomography_circuits in the simulator and collect the results.

1. Process the results of the simulation by performing the tomographic reconstruction.
2. Find analytically what is the density matrix of the system qubit after the depolarizing channel as a function of $p$​.
3. Plot the values of $\rho_{11}, \rho_{22}, \mathfrak{R}\rho_{12},\mathfrak{F}\rho_{12}$​ as function of $p$​​ and compare them to the analytical prediction.

Up to the statistical errors due to the finite number of shots, the simulated points should match the analytical prediction.

## Homework

Perform Tasks 3-5 on a real device, and include error mitigation (check the preliminaries for instructions). Compare the results with the simulation.