Tool

 Back on math, for the day...

                                                    *     *     *

Just installed the Merlin extension on Chrome. It allows me to use ChatGPT4 free of

charge. Asked for an image:

                                                           

                                                                   *     *     *

Saving the statevector early in the code was troubling to me. Below:

                                                            

Chat Gpt4 code help:

                                                    

Refs

 For topics in linear algebra:

University of Waterloo Math Online - Linear Algebra 1 (uwaterloo.ca)

                                                      *     *     *

Went off caffeine on March 12, 2024 and still holding. I have

found a new energy equilibrium during the day. I allow myself 

peiods away from the computer throughout the day. I get stuck on

something; I take a break. I do my housework in small chunks every

day rather than on chore days. I get tired but not so much mentally

tired as I did in my coffee days.

One surprising effect: I am less hungry and eat smaller meals. In fact,

I often leave portions of my main meal because I experience an overwhelming

sense of fullness, out of the blue. I am also less tempted by sweets!!

The really unexpected effect: I dream and remember my dreams. A lot

of these are about stressful events in my adolescence or young adulthood. 

I guess I was suppressing all that, and need to work through it now.

I don't really expect to ever go back to my dependency days. My mind feels 

so much freer. I don't dare even a small relapse because getting off caffeine 

was so unpleasant in the initial stages. Like who wants to go on another diet!! 

                                                          *     *     *

Oh!, and I was really delighted to read the other day that we may be getting

closer to solving the extra-terrestial life problem. Why aren't we seeing 

extra-terrestials!? Just maybe, they are just like us: stuck on their home-worlds. 

The difficulties of space travel are real for them as well as for us.  And - dare I say it -

those first forays of ours with selfies and descriptions of our reproductive

activity were kinda cringe then, and they are now. 

Seriously, we need to get serious. Extra-terrestial life may be very different and

needs to be looked for in a very specific way.We won't get far with the Tinder 

dating approach 🙄

                                               *     *     *

What...

 

Here is Gemini's explanation on the second Y and Z equations:

https://g.co/gemini/share/7ef6912ac473

                                                                           *     *     *

The standard definition of Pauli Gates.

                                       

                                                                               

From someone who works at Goole:

                                                                         

On IBM composer:

                                                                               

In both cases, the Pauli gates are reversible ie two X gates in a row takes on back to the

initial position.

But the implementation seems a bit different on the X,Y sequence. Might have to do with

how the conputers work...

                                                           *     *     *

From Meta:

 
   

Global

 Making my peace with the Y-Gate issue. The Bloch sphere shows

us we are in a geometrical perspective:

 Applying an X-gate:                                                 

Applying a Y-gate:

                                                      

                                     

Requesting a positive 180 rotation around the y-axis:

Two y-gates in a row:

A y-gate following a Hadamard gate; the phase shift appears.

Indeed, the phase shift was always there. 

                                                                

Sharma explanation...

                                                                        

                    

                                                                         *     *     *

                                                                              

Gemini:

In the context of the Bloch sphere and your quantum circuit, the phase refers to an additional property of the qubit's state along with its probability of being in |0⟩ or |1⟩. Here's a breakdown:

1. Chance Amplitude and Probability: The Bloch sphere uses complex numbers to represent the qubit's state. The absolute value squared of this complex number gives the probability of finding the qubit in the state |0⟩ or |1⟩ when measured. In your example, the chance amplitude for |1⟩ was smaller, resulting in a lower probability (around 14.6%) of finding the qubit in the |1⟩ state.

2. Phase and Interference: The complex number representing the state also has a phase term, which doesn't directly affect the probability of measurement. This phase information becomes crucial when considering superpositions and interference between different states.

Imagine two waves (representing two possible qubit states) overlapping. Their peaks and troughs can line up constructively (reinforcing each other) or destructively (canceling each other). The phase difference between the waves determines this interference behavior.

3. Phase in Your Circuit: The 22.5° phase reading indicates a specific rotation of the qubit's state vector on the Bloch sphere. This rotation, caused by the Y-axis rotation gate, influences how the qubit would interfere with other qubits in a multi-qubit system.

While the individual phase itself might not hold a physical meaning on its own (since it doesn't affect the immediate measurement probability), it becomes significant when considering the relative phases of multiple qubits and their combined behavior in a quantum circuit. These relative phases can be manipulated by quantum gates to achieve specific desired outcomes in quantum computations.

Difference

 I was getting a little mystified by the fact that applying an X-Gate to

a |0> seems to have the same effect as applyting an X-gate: things go from

0 to 1 on the Bloch shere. Yet these are different matrices...

                                                           

Qutip

 Been looking at how-to use python qutip. Below:

                                                 

                                                                              

Qutip works better for me if I clear the cache...

Magic

 Getting through Sharma lesson 5. 

The code sdegment below is somewhat magical; one can run it a few times

and get different results. sometimes 0, sometimes 1. 

That is because we are using a simulator. On a real quantum computer, measurement

collapses a state( albeit for a very short moment). It is no longer usable for computation.

It either carries on, or it doesn't!!

                                                                   

                                      

                                                                     *     *     *

Finished Sharma 5 with using the Qiskit/matplolib Bloch sphere. One has a choice

on how to code this:

                                                                      

Spherical:

                                                                             

XYZ:

                                                                                 

https://www.perplexity.ai/search/quantum-Computing-use-.E0vjMpwQm2_KthONSlnmA