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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How can the depolarizing channel be a quantum operation?

In Quantum Computing: From Linear Algebra to Physical Realizations it states that A quantum operation maps a density matrix to another density matrix linearly But let $\rho\in M_2$ be a density ...
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Depolarizing channel on GHZ-state

Consider a GHZ-state $|\psi\rangle =\frac{1}{\sqrt{2}}(|0\rangle^{n}+|1\rangle^n)$, and consider a depolarizing channel that maps a density matrix $$\rho\to(1-\lambda)\rho + \frac{\lambda}{2^d}I.$$ ...
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Trouble in Depolarizing Error Simulation with Qiskit

I'm currently attempting to simulate depolarizing errors using Qiskit, but I'm encountering an issue where it appears that no errors are being introduced into my simulation. After running the ...
Byeongyong Park's user avatar
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Decoding the Steane Code

The $[[5,1,3]]$ code is a perfect code basically meaning that the weight-0 and weight-1 error spaces completely fill out the $32$-dimensional Hilbert space. On the other hand, the $[[7,1,3]]$ Steane ...
Eric Kubischta's user avatar
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Is the "unitary twirling operation" physically realizable?

In this neat answer by Markus Heinrich, it is shown that twirling an arbitrary quantum channel $\Lambda$ over the unitary group $U(d)$ yields a depolarizing channel $\tilde{\Lambda}$ given by $$ \...
Eric Kubischta's user avatar
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Partial decoherence of a general one-photon state

Let $\rho_1$ be the pure one-photon state described by the ket $$|\psi_1\rangle = \int dk\ A(k)a^\dagger(k)|0\rangle$$ for a complex amplitude function $A(x)$ and an empty ket $|0\rangle$. This state ...
Bentanglement's user avatar
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Why does depolarising channel shrinks Bloch vectors?

Let's start with $Tr_{\Omega}[U|0,\Omega_{0}\rangle\langle0,\Omega_{0}|U^{\dagger}] = \sum_{\alpha}E_{\alpha}|0\rangle\langle0|E_{\alpha}^{\dagger}$ where $U$ be a unitary operator. The trace operator ...
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Physical description of trace of ancilla state yields a depolarising channel

Let's start with $Tr_{\Omega}[|0,\Omega_{0}\rangle\langle0,\Omega_{0}|U^{\dagger}] = \sum_{\alpha}E_{\alpha}|0\rangle\langle0|E_{\alpha}^{\dagger}$ where $U$ be a unitary operator. The trace operator ...
Physkid's user avatar
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How does depolarization error accumulate?

Here's my code to define the depolarization error using Qiskit, which included both one and two-qubit errors: ...
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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 ...
Sami Farrag's user avatar
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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 ...
Christian Bunker's user avatar
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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. ...
Michael.Andy's user avatar
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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 ...
Frederik vom Ende's user avatar
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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 ...
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Representing 1 qubit pauli-channels as an averaging effect of random rotations in the bloch sphere. Basic literature?

I am looking into 1 qubit pauli channels, e.g. the dephasing channel $$\mathcal{E}(\rho)=(1-p)\rho+p\sigma_z\rho\sigma_z.$$ I found out it could be represented as $$\mathcal{E}(\rho)=\int p(\lambda)\...
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Prove that the twirling operation on a channel gives a decomposition $\int dU\, U^\dagger\mathcal E(U\rho U^\dagger)U=\alpha P+\beta Q$

The twirled operation of a quantum channel $\mathcal E$ is defined as \begin{align} \mathcal E_T(\rho) &= \int dU U^\dagger \mathcal E(U \rho U^\dagger)U, \end{align} where the integral is over ...
Michael.Andy's user avatar
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Prove the invariance upon change of variables in the definition of twirled channel

The twirled operation of a quantum channel $\varepsilon$ is defined as \begin{align} \varepsilon_T(\rho) &= \int dU U^\dagger \varepsilon(U \rho U^\dagger)U, \end{align} where the integral is over ...
Michael.Andy's user avatar
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How do Hashing bound, entanglement purification, and QECC, relate to each other?

Could anyone elaborate on how these three concepts relate to each other? According to Charlie Bennett's original paper BDSW96, EPP is equivalent to QEC in the sense that both have the hashing bound as ...
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Deriving the choi matrix definition of the quantum depolarizing channel

I was reading up on the quantum depolarizing channel (Preskill's Notes) (stack exchaange explanation), and I'm failing to see how the form \begin{align} \sigma &= (\mathcal E \otimes \mathbb I)(|\...
Apple Meson's user avatar
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What is the adjoint of the depolarizing channel?

Consider the single qubit depolarizing noise channel given by $$\Phi(\rho) = \frac{\lambda}{d} \mathbb{I} + (1- \lambda) \rho.$$ What might be the adjoint $\Phi^{*}(\cdot)$ of this channel? In ...
Tom Clancy's user avatar
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What is an instruction when we `add_all_qubit_quantum_error`?

I'm trying to understand how the noise model works in Qiskit Aer noise simulator. From this information page, add_all_qubit_quantum_error() has two required ...
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What do quantum noise models have in common?

Let us see the one-qubit case of different noise channel, the depolarizing channel is $\Lambda_1^{depol}(\rho_1)=(1-\frac{4}{3}\epsilon_1)\rho_1+\frac{1}{3}\epsilon_1\sum_{i=0}^{3}\sigma_i\rho_1\...
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How do I apply depolarization error on 2 qubits using Qiskit?

I'm trying to apply depolarization error on a 2-qubit circuit using the Qiskit Aer noise module. My question is how can I apply the depolarization error to each of the qubits in my circuit? Does the ...
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Why use conjugate not transpose complex conjugate in superoperator?

For the n-qubit depolarizing noise, I want to know why it uses $\sigma_{0}^{i*}$ instead of $\sigma_{0}^{i}$ or $\sigma_{0}^{i\dagger}$.
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Depolarizing channel for $n$ qubits: why is there a trace term?

The depolarizing channel for an n-qubit quantum circuit is defined as $$ \mathcal{E}(\rho) = \frac{pI}{2^n}\text{Tr}(\rho)+(1-p)\rho,\quad\text{where} \quad\rho \equiv\sum_ip_i|\psi_i\rangle\langle\...
IGY's user avatar
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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): ...
Quantum Guy 123's user avatar
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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 $\varepsilon$: $$\varepsilon(\rho)\equiv p\frac{I}{d}+(1-p)\rho\tag{1}$$ ...
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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 ...
Harsh Wadhwa's user avatar
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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 ...
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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 ...
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Entanglement-assisted communication ability of a quantum depolarizing channel vs. a classical binary symmetric channel

Consider a quantum qubit depolarizing channel which takes a quantum state $\rho$ to output $$N(\rho) = (1-p)\rho + p\frac{\mathbb{1}_2}{2}.$$ If I restrict $\rho$ to be either $\vert0\rangle\langle 0\...
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What is the actual probability of not losing information (in a depolarizing channel)

The probability that a depolarizing channel doesn't affect the information is usually assumed to be $1-3p$, while, for convenience, it is affected with same probability $p$ by any Pauli operator $X,Y,...
Daniele Cuomo's user avatar
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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 ...
Quantum Guy 123's user avatar
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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 ...
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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 ...
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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 ...
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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 ...
Ahmed Malik's user avatar
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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 ...
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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 $|00\rangle$...
Oilobobolus's user avatar
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Two qubit state + Depolarizing channel = Bell diagonal state?

In multiple sources, e.g. RGK, KGR, it is stated (without proof) that if you take any two qubit state and send it through a depolarizing channel, the resulting state would be a Bell-diagonal state. ...
QuestionEverything's user avatar
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Depolarization of density operator with zeros in diagonal

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 ...
QuestionEverything's user avatar