9 votes
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 ...
Frederik vom Ende's user avatar
7 votes

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 ...
R.W's user avatar
  • 2,337
5 votes
Accepted

Show that if the Lindblad satisfy $\sum_\mu L_\mu L_\mu^\dagger=\sum_\mu L_\mu^\dagger L_\mu$ then the von Neumann entropy increases monotonically

I'll show you how to do it by brute force, since this will demonstrate a lot of techniques that will be useful for you if you have to derive something more complicated. The Lindblad evolution: $$ \...
user1271772 No more free time's user avatar
5 votes
Accepted

What does "generator" mean in the master equation?

The idea is that $$ \frac{d}{dt}\rho=\mathcal{L}\rho\qquad \Leftrightarrow\qquad \rho(t)=\exp(t\mathcal{L})\rho(0). $$ In that sense, the Lindbladian $\mathcal{L}$ generates evolution through $$\rho(...
Quantum Mechanic's user avatar
4 votes
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 ...
DaftWullie's user avatar
  • 58.1k
4 votes
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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 (...
chrysaor4's user avatar
  • 1,376
4 votes
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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 ...
Quantum Mechanic's user avatar
4 votes

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 ...
DaftWullie's user avatar
  • 58.1k
3 votes

Is it overestimating noise in a QPU if we use infidelities and also quantum channel such as depolarising or amplitude damping?

First of all, it should be intuitively clear that if you combine two noise models with similar "strength" that this results in a "noisier" model. The noise model should fit to your ...
Markus Heinrich's user avatar
3 votes
Accepted

Notation for Lindblad operators

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 ...
DaftWullie's user avatar
  • 58.1k
3 votes
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 ...
luciano's user avatar
  • 5,763
3 votes

What properties do Kraus operators of Markovian processes have?

I guess from the operator sum representation $\rho(t) = \sum_k K_k \rho(t_0) K_k^\dagger$ alone you won't be able to make any statement about non-Markovianity, since you are missing interesting ...
Quantum Quentin's user avatar
2 votes
Accepted

General Master Equation with Decoherence Query

It's fundamentally similar to/the same as Baker–Campbell–Hausdorff (BCH). Generally, in quantum physics, this is most often used (or at least taught) with commuting Hamiltonians: $$e^{-i\left(H_1+H_2\...
Mithrandir24601's user avatar
  • 3,686
2 votes

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 ...
Markus Heinrich's user avatar
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 ...
chrysaor4's user avatar
  • 1,376
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....
Z0OM's user avatar
  • 157
1 vote
Accepted

Questions about the Hamiltonian of a decay

This is a very generic description that captures essentially all possibilities of describing the Hamiltonian with a decay process (I supposed one should allow for a general $H_{1,2}$ rather than a ...
DaftWullie's user avatar
  • 58.1k
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 ...
tparker's user avatar
  • 2,751
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/...
Paul Nation's user avatar
  • 2,239
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 ...
Aharon Brodutch's user avatar

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