# Tag Info

Accepted

### What kinds of objects are Liouvillian, Lindbladian, and Davies generator?

Much like how the Hamiltonian $H$ determines the dynamics of a closed system via $\dot\rho=-i[H,\rho]$, the Lindbladian (or Liouvillian${}^1$) is an extension of Hamiltonian generators to model the ...
• 2,613

### Will quantum computers of the future be operational under room temperatures (above 0 Celsius)?

It is extremely hard to talk with certainty about the future when talking about quantum computation. Nevertheless, there are fair things we can say about the closely related question Is it ...
• 2,377
Accepted

### What are kraus operators of a qubit interacting a thermal environment?

One way to model interaction with a thermal environment (of some temperature $T$) is through so-called thermal operations. Given some system's Hamiltonian $H_S$ they're all channels $\Phi$ of the form ...
• 2,613
Accepted

Accepted

### What properties do Kraus operators of Markovian processes have?

I think this question is generally difficult because there is no standard metric for non-Markovianity, for example this paper would suggest you try to express the evolution in a time-local canonical (...
• 1,416
Accepted

### How to formulate the master equation for three systems?

To be clear: You have a Hilbert space $\mathcal{H}_A\otimes\mathcal{H}_B\otimes\mathcal{H}_C$. The initial state is $\rho_\text{tot}(0)=\rho_A\otimes\rho_B\otimes\rho_C$. There is a Hamiltonian ...
• 60.3k

### Show that if the Lindblad satisfy $\sum_\mu L_\mu L_\mu^\dagger=\sum_\mu L_\mu^\dagger L_\mu$ then $\rho\propto I$ is a fixed point of an evolution

Go back to the Lindblad master equation: $$\frac{d\rho}{dt}=i[H,\rho]+\sum_nL_n^\dagger\rho L_n-\frac12\sum_nL_nL_n^\dagger \rho-\frac12\sum_n\rho L_nL_n^\dagger.$$ The statement that the maximally ...
• 60.3k
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### What does it mean for a channel to be independent of the input state?

The given form of the Kraus operators, though not unique, tells us what is physically happening. In the case of pure-state outputs, each Kraus operator takes one of the possible basis states and ...
• 4,529
Accepted

### Do all Hermiticity-preserving maps generate completely positive maps?

First a basic observation: if all Hermitian preserving $\mathcal L$ gave rise to completely positive dynamics $e^{t\mathcal L}$ for all $t\geq 0$, then so would $-\mathcal L$ (still Hermitian ...
• 2,613
Accepted

The notation is perhaps a little lazy. There ar two distinct sets of Lindblad operators: $\{L_i\}$ and $\{L_t\}$ and you need both. One does not over-write the other. Yes, it's unfortunate that if you ...
• 60.3k
Accepted

### how to fix error 'QiskitBackendNotFoundError'

Unfortunately, ibmq_16_melbourne was retired. You can see the list of all the retired systems in this website. You can list of all the backends in your provider ...
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• 7,543

### What are the singular values of a quantum channel?

As usual, the singular values of an operator $\phi$ are the square roots of the eigenvalues of the positive semi-definite operator $\phi^\dagger \phi$ (or $\phi^*\phi$ if you prefer the $*$ for the ...
• 5,267
1 vote

### Simulate dual Lindblad master equations in the Heisenberg picture in QuTiP

The function mesolve (see here) takes in an array of collapse operators (c_ops) which, if given as superoperators, will be ...
• 1,416
1 vote

### Will quantum computers of the future be operational under room temperatures (above 0 Celsius)?

Most of the quantum computers developed worldwide work with so-called qubits. These only work at temperatures close to absolute zero. A degree above absolute zero is boiling hot for a quantum computer....
• 157
1 vote

### Deriving Bloch vector $dr$ from master equation

While I'm of course 4 years late I'd like to answer this question for the sake of posterity. tl;dr: Your calculations for the $Z$-measurement ($X=\sqrt{2\kappa}\sigma_z$) are correct and for the ...
• 2,613
1 vote

### Why do quantum computation models based on open quantum systems receive so little attention?

I know this isn't really what you're thinking of with your question, but measurement-based quantum computing is pretty well studied. Under the many-worlds interpretation, the system counts as open for ...
• 2,861
1 vote

### Plotting Bloch sphere in QuTiP

That is a very old paper, corresponding to version one of the software. It is now on version 4.x. It is best to see the current documentation for how to use the Bloch sphere: http://qutip.org/docs/...
• 2,249
1 vote

### Only assuming the universe evolves according to a positive trace-preserving map, is there a proof that all subsystem evolution must be CPTP?

There are two possible answers. Let's say the universe evolves from $t=0$ to $t_f$ then the unitary evolution $U$ from $0$ to $t_f$ induces a CP evolution on the subsystem. To see this, note that ...

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