# Questions tagged [depolarizing-channel]

A model for noise in quantum systems such as a decohering qubit that has particularly nice symmetry properties. The depolarizing channel is a “worst-case scenario” channel. It assumes that we just completely lose the input qubit with some probability, i.e., it replaces the lost qubit with the maximally mixed state.

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### Qiskit Aer Noise Module

I am trying to use the following single qubit depolarizing channel (on a GHZ state for example) but the simulation histogram counts are not affected ...
53 views

### How to see the effects of the depolarizing channel in qiskit?

I am playing around with adding noise to quantum circuit simulation using qiskit_aer.noise.NoiseModel(). My code creates a quantum circuit and simulates it with ...
1 vote
40 views

### What does adding depolarizing error on a Hadamard gate mean mathematically?

I have a quantum circuit as the following picture. Now I add the depolarizing error on the Hadamard gate using the following code in Qiskit. ...
159 views

### Diamond norm distances between some channel and the identity

I'm currently working with the continuity result by Kretschmann-Schlingemann-Werner (arXiv version) for Stinespring isometries (more precisely, the following corollary to their result, cf. Appendix C ...
1 vote
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### Recover the noisy POVMs of Bell basis measurement

Considering Bell basis measurement, we have that the ideal POVMs are four Bell states, which can be obtained by reversing the following quantum circuits. Now, we add depolarizing errors to CX gate and ...
32 views

1 vote
186 views

### Does applying a random Pauli matrix to a density matrix result in the identity?

Nielsen and Chuang's textbook, Equation 8.101 (section 8.3.4 'Depolarizing Channel') shows that applying a random Pauli to a density matrix representing one qubit equals the identity (times one half): ...
145 views

### How to calculate the action of a channel on part of a quantum state?

As the title shows, but I think we can restrict ourselves into a more specific example. Let's consider depolarizing channel $\varepsilon$: $$\varepsilon(\rho)\equiv p\frac{I}{d}+(1-p)\rho\tag{1}$$ ...
1 vote
234 views

### Given a list of stabilizers (or parity check matrix), find an encoding circuit

I am trying to study Quantum LDPC code and have generated the A matrix by taking the hypergraph product of a classical LDPC code. Now my aim is to study those matrices by implementing the same on ...
178 views

### Qiskit NoiseModel.from_backend gives wrong gate error

According to the Qiskit documentation, a gate error is simulated by a thermal relaxation channel followed by a depolarisation channel, where the parameter of the depolarisation channel is adjusted so ...
1 vote
708 views

### what is Pauli twirling approximation?

In this video, Artur Ekert shows that for a single qubit, 4 Kraus operators can be chosen such that the action on state $\rho$ is given as $\rho \rightarrow \sum_m p_m A_m \rho A_m^\dagger$. We can ...
1 vote
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### What is a realistic model for simulating physical tampering of a channel? (ex: nearby vibrations)

Somewhat related to this question. Imagine a fully functioning quantum network, where qubits are transported via fiber optic cable. If vibrations were to physically tamper with a channel in such a ...
1k views

### Why does the twirl of a quantum channel give a depolarizing channel?

I would like to understand in detail why the twirl of a quantum channel gives depolarizing channel, which is the starting point of randomized benchmarking. To be self-contained, let me set up the ...
184 views

### How to differientate the noise functions in qiskit?

In Qiskit, there are many different Quantum Error Functions. From my understanding, pauli_error represents the error rate of $X, Y, Z$ independently, and ...
197 views

### What is an algorithm to generate random error in depolarizing channel

The Qunatum Depolarizing Channel is parametrized by a single real variable $\lambda, 0 \leq \lambda \leq 1$. I have a system of $n$ qubits. I'd like to generate random errors from that channel. These ...
171 views

### Qiskit noise model question (from textbook)

I'm reading the chapter Introduction to Quantum Error Correction using Repetition Codes and a code example demonstrates how to add depolarizing and pauli error. I have several questions. Is it not ...
978 views

### Inverting the depolarizing channel

I have a depolarizing channel acting on $2^n \times 2^n$ Hermitian matrices, defined as $$\tag{1} \mathcal{D}_p (X) = p X + (1-p) \frac{\text{Tr}(X)}{2^n} \mathbb{I}_{2^n}$$ where $\mathbb{I}_{d}$ is ...
431 views

### How to find the operator-sum representation of the depolarizing channel?

Consider a circuit built as follows: take two ancilla states and an operator $U$ made of a series of controlled gates which act on a pure state $\rho$ as follows: $X$ if the ancilla is in $|00\rangle$...
I suppose a quantum state with density matrix like the following is not valid. $$\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}.$$ Now, let's say I have a valid density operator representing ...