The Classical Channel

Quantum Computing

01:08

2

Q: Has anyone analyzed multi-round nonlocal games?

The traditional definition of a nonlocal game is restricted to having two players and one round (e.g., here), but it is natural to consider a more general class of games that may have more than two players and more than one round of questions. While there has been a lot of work dealing with games...

Quantum Computing

01:57

0

Q: Can quantum money be reliably "burned?"

One of the novel features of Bitcoin and other cryptocurrencies is that coins can be irrefutably "burned" or destroyed, by creating a transaction to send the money to a junk burn address. Thinking similarly about quantum money - from knots, or hidden subspaces, Wiesner's currency, BBBW, etc. - h...

quantum-algorithms cryptography

Quantum Computing

03:03

0

Q: Phononic Quantum Computing

Google returns "About 1 results" for Quantum Computing with Sound. The sole result links to an article entitled "Physicists have designed the building blocks of quantum computer that works using sound" From the abstract: Sound can be just as quantum as light. But our toolbox for single quan...

quantum-algorithms quantum-computer resource-request

Quantum Computing

06:39

0

Q: What does negative probability represent?

"Negative energies and probabilities should not be considered as nonsense. They are well-defined concepts mathematically, like a negative of money." -Paul Dirac The abstract from Photon-phonon-photon transfer in optomechanics states: the Wigner function of the recovered state can have ne...

quantum-state photonics contextuality

meowzz

07:14

should cryptocurrency & post-quantum-crypto tags be merged to post-quantum-crypto?

Anonymous

07:47

$$|0\rangle \otimes \sum_{j=1}^{n} \sum_{p=0}^{2^m-1}\sum_{0}^{2^l-1}\beta_j\exp[i\frac{p}{2^{m+l}}t_0(2^l-\lambda_‌j s)]|s\rangle |p\rangle |\lambda_j\rangle |u_j\rangle$$ does indeeed turn out to be the correct state if we use the expression for the controlled-controlled-gate which DaftWullie mentioned.

Anonymous

@Nelimee

Anonymous

Finally verified it :P

Nelimee

Haha, some maths are always good :p

Anonymous

@Nelimee Now just that I don't know how DaftWullie came up with that expression for $U$ :P

Nelimee

I still don't understand the $H_0$ and its hamiltonian simulation though

Anonymous

07:48

Which I can obviously ask him in the comments now

Nelimee

@Blue Which expression?

(link?) ^

Anonymous

$$U=\sum_{k\in\{0,1\}^t}\sum_{s\in\{0,1\}^l}\sum_{p\in\{0,1\}^m}|k\rangle\langle k|_C\otimes|s\rangle\langle s|_L\otimes|p\rangle\langle p|_Me^{-i2\pi p k \frac{f(s)}{2^{t+m+l}}}$$

Anonymous

This ^

Anonymous

And $f(s)=s$

Nelimee

Ok, I'll read

Ha! I upvoted the answer, so I already read it... But I don't remember it ><

Anonymous

07:52

@Nelimee FWIW $H_0$ is defined as $$\text{diag}(1,2,2^2,...,2^{m-1})$$

Anonymous

Where $m$ is the number of qubits in register $M$

Nelimee

Yup! Where is $f(s)$ in the paper?

Anonymous

Anonymous

I don't think $f(s)$ is mentioned in the paper

Nelimee

Ok, that's what I saw also ^^

Anonymous

08:00

@Nelimee BTW how did you implement those $(t,l-k_l+1)$ gates in qiskit? Are those available?

Anonymous

It's a controlled-controlled gate

Nelimee

I did not, I used the circuit they presented for the 4x4 matrix

Anonymous

@Nelimee Which one is that?

Anonymous

Figure number?

Nelimee

With some modifications

Because this circuit is false ^^

Anonymous

08:02

@Nelimee But that one is missing the Hamiltonian simulation part isn't it?

Anonymous

It's not the complete circuit

Nelimee

Nope, look at the bottom

It's the Hamiltonian simulation part :)

Anonymous

$e^{iAt}$ thing?

Anonymous

That's there

Nelimee

Yup

Anonymous

08:03

I'm talking about the $e^{iH_0t}$ thing

Anonymous

It's surprising that your circuit works without it although it seems like a necessary part of the protocol :P

Nelimee

As I said, the $e^{iH_0t}$ seems to be here only to invert the eigenvalues

But with the matrix they choose, the inversion is much easier

Because the eigenvalues are just powers of 2

Anonymous

@Nelimee Oh, oh. Makes sense now

Anonymous

BTW do you have a circuit diagram of the modified circuit you made for Figure 4?

Nelimee

Nevertheless, their inversion scheme (which is the SWAP gate after the $FT^\dagger$) makes sense to me, but does not work. I tried at random other SWAPs and it finally works, I'm not proud of it :( I need to know why it worked with this "random" SWAP

The corrected circuit?

Anonymous

08:07

(And meanwhile, I just started to learn QISKit properly since yesterday.....so it will take me a while to understand your program)

Anonymous

@Nelimee Yes

Nelimee

No I don't have such a diagram

Anonymous

@Nelimee Okaies. Could you just in brief tell me what changes you made to the circuit and why

Anonymous

(if and when you're free)

Anonymous

Oh, btw, I never asked. What are you doing your masters in? Quantum computing or CS?

Nelimee

08:11

From memory, here are the modification I made:
1. In the hamiltonian simulation part, the last gate is a controlled-Z.
2. The inversion part (the SWAP after the $FT^\dagger$ should be between qubits 2 and 3, index starting at 1).
3. Multiplying the coefficients in the rotation gates does not produce the right Hamiltonian (it should produce the powers, it does not). I used https://github.com/nelimeee/quantum-tools/blob/master/HHL/optim_hamil.py to guess the right coefficients. Again, I tried by brute force without any proof that it will work. I am able to simulate the $e^{iA\frac{t_0}{2}}$ t…

I don't remember other modifications, but if I do I will tell you :)
And I'm making a master in CS and applied mathematics. I started QC during my last semester internship (master thesis) and it's quite nice :)

Anonymous

@Nelimee What do you mean by coefficients. The 0.2 in $R_x$, 0.38 in $R_{zz}$, those ones?

Nelimee

Yup

In the paper they say that multiplying them by 2, 4 and 8 will give the successive powers of the $e^{iA\frac{t_0}{16}}$ but my tests told me otherwise

So I ran an optimisation procedure on the value of these parameters for the 4 powers of the Hamiltonian needed, and the 4 of them converged! I was quite happy with the convergence, as I did not have any proof that it will (or even can) converge :)

github.com/nelimeee/quantum-tools/blob/master/HHL/… is the optimisation procedure I ran. Basically I use scipy.optimize.minimize of the 5 parameters and my cost function is the distance between the real matrix $e^{iA\frac{t_0}{2^n}}$ and the simulated one.

Anonymous

@Nelimee Oh, that's very nice! :D I actually want to do something similar. I'm currently pursuing my undergrad in electronics engineering (in the transition phase between sophomore and freshman now), but I've a growing interest in some of the interdisciplinary areas between mathematics, mathematical physics, and computer science - to name some topology, statistical learning, complexity analysis and GR.

Anonymous

I probably would love to pursue a masters degree where I can take classes in computer science, some areas of mathematical physics (advanced GR and QFT) and mathematics. But well, sort of stuck in EE for the next 3 years (although I enjoy some areas of it like signal processing and communication) :P

Anonymous

What's your specialization in mathematics btw?

Nelimee

08:20

sophomore / freshman is equivalent to what? license? master?

Anonymous

@Nelimee Freshman = 1st year of undergraduate

Nelimee

undergraduate = license?

Anonymous

Just after high school i.e.

Nelimee

Ok! :)

Anonymous

@Nelimee I don't know what license is :P

Nelimee

08:21

Arf

Anonymous

Is it a French term? :P

Nelimee

European ;)

Anonymous

Ah

Nelimee

In Europe we have high school, then in the university it's 3 years of license, followed by 2 years of master and then 3 years for the doctorate

(you don't have to do the 8 years, you can stop at the end of the license :p)

Anonymous

Oh, engineering is a 4 years course here

Anonymous

08:22

@Nelimee True, true

Anonymous

What was your undergraduate degree in?

Nelimee

Haha, this is 100% specific to France

In France we have what I described you in university and we have what is called "Grandes Écoles" (literally "great schools" but it's also called engineering schools).

Anonymous

I see. Some of the Ecoles are famous

Nelimee

In order to integrate these schools, you have to pass an exam and to be in the bests. The preparation is two-years long and oriented in theoretical maths, physics, chemistry and a little of side-lessons (foreign languages, philosophy, ...)

So I did a 2 year preparation, did not pass any exams (because I was in something even more specific :p), and I continued in a so-called engineering school.

Anonymous

Heh, sounds somewhat like the JEE exams in India :P We too spend two years during high just for preparation to get into unis

Anonymous

08:27

Some of the Ecoles are famous I know

Nelimee

And for the third year of my engineering school (fifth year after high school) I choose to replace my engineering courses by a master oriented in research :)

In the famous schools you have "école polytechnique" or "école nationale supérieure (ENS)"

The first one is also called "X"

Anonymous

Nice!

Anonymous

Yeah, I heard of those

Nelimee

And about my speciality in mathematics... I did plenty of things :p

Anonymous

I personally would like to switch to a more math-heavy area for my masters but one of the restrictions is that most schools don't consider engineering course-work to be even close to sufficient for a mathematics masters

Nelimee

08:29

I did a course on Machine Learning. For me it was more for my culture, but it was great! I also did plenty of courses in numerical methods (PDEs analysis, numerical scheme analysis, theory behind finite element method, Fourier transform, distribution theory, wavelets, ...)

Anonymous

@Nelimee Sounds good...do tell ;)

Nelimee

Arf, maybe you could do a master abroad? :p

But my school/master is more into CS, so I did even more CS courses ;)

Anonymous

@Nelimee Great. I'm personally very interested in machine learning too and have been studying neural networks for a while :)

Nelimee

If I have an advice, start by studying the "old" methods

Perceptron is really interesting and it's easier to understand

Anonymous

@Nelimee Yes, I'm looking forward to the European countries for masters

Anonymous

08:32

I'm not exactly aware of their admission criteria for math-heavy masters' degrees, but it seems to be a bit more relaxed compared to my country

Nelimee

If you are interested in Data-Science / Machine learning: iam.imag.fr/doku.php

The courses are 100% taught in english :p

Anonymous

@Nelimee Haha, that's another big problem, lol xD

Nelimee

Why? You seems to have a nice english no?

Anonymous

@Nelimee Oh, English is fine. Problem is that many of the good master's courses (in European countries) are in languages other than English. For example yesterday I was looking at the Scientific Computing courses at University of Heidelberg, Germany but it is taught in "partly German" :/

Anonymous

So, basically I need to filter for "English" courses

Nelimee

08:36

Ha! Look at the international masters maybe

In France, all the courses in the international masters are in english I think

Anonymous

True, yeah. The international master's degrees seem to be in English but a bit rarer. I'm still collecting data about the universities and courses which I like. Still, 3 years to go before undergrad is over though :P

Nelimee

Good luck! =)

Anonymous

Thanks :)

Anonymous

Okay, I guess I gotta go now. See you around!

Nelimee

Bye! :)

Anonymous

11:29

@Nelimee I just installed QISKit on Ubuntu, following this. However, the source activate QISKitenv command doesn't seem to work. It says bash: activate: No such file or directory

Anonymous

Any idea what's the problem?

Anonymous

These are the current files in the directory ~/quantum/qiskit-tutorial

Nelimee

Here are the command I would type:
python3 -m venv qiskit # This will create a 'qiskit' directory in your current working directory.
source qiskit/bin/activate # Activate the virtual environment.
pip3 install -U pip # Update pip
pip3 install qiskit # Install qiskit

Are you familiar with Python's virtual environments or with Python?

Anonymous

@Nelimee I already have pip and qiskit installed it seems

Anonymous

11:33

@Nelimee Not much

Nelimee

Downloading the git repository is only for advanced users, when you want to contribute to the project

Can you C-P the output of pip3 freeze?

Anonymous

apturl==0.5.2
backcall==0.1.0
beautifulsoup4==4.4.1
bleach==2.1.3
blinker==1.3
Brlapi==0.6.4
chardet==2.3.0
checkbox-support==0.22
command-not-found==0.3
cryptography==1.2.3
decorator==4.3.0
defer==1.0.6
entrypoints==0.2.3
feedparser==5.1.3
guacamole==0.9.2
html5lib==1.0.1
httplib2==0.9.1
idna==2.0
ipykernel==4.8.2
ipython==6.4.0
ipython-genutils==0.2.0
ipywidgets==7.2.1
jedi==0.12.1
Jinja2==2.8
jsonschema==2.6.0
jupyter==1.0.0
jupyter-client==5.2.3
jupyter-console==5.2.0
jupyter-core==4.4.0
language-selector==0.1

Anonymous

@Nelimee Here ^

Nelimee

Ok, you don't have qiskit. Are you on your personal computer? Do you have admin rights?

Anonymous

@Nelimee Yes, it's my personal computer

Nelimee

11:36

sudo pip3 install -U pip first to upgrade pip to its last version

Then sudo pip3 install qiskit and you are done :)

Anonymous

Successfully installed pip-10.0.1

Anonymous

phew

Nelimee

The list of command I wrote before were if you wanted a virtual environment, but you seems to be fine with everything in your main Python install

If you want to submit something online, you also need to complete the Qconfig.py file and to be able to import it (put it under your PYTHONPATH)

Anonymous

@Nelimee What's the use of a virtual environment?

Nelimee

@Blue It allows you to isolate your Python/module installs

With this, it's easy to switch between environment with multiple (possibly incompatible modules)

Anonymous

11:39

Successfully installed IBMQuantumExperience-1.9.6 asn1crypto-0.24.0 cffi-1.11.5 cryptography-2.2.2 cycler-0.10.0 idna-2.7 kiwisolver-1.0.1 matplotlib-2.2.2 mpmath-1.0.0 networkx-2.1 ntlm-auth-1.2.0 numpy-1.14.5 pillow-5.2.0 ply-3.11 pycparser-2.18 pytz-2018.5 qiskit-0.5.5 requests-ntlm-1.1.0 scipy-1.1.0 sympy-1.1.1

Anonymous

Looks okay? ^

Anonymous

@Nelimee I see. Didn't know that!

Nelimee

Image you have a website that needs version 3.X of module XXX to run and an other one that cannot work with 3.X and needs 2.X, this can be solver with virtual environments

If you plan to use Python more than just a little, you need to use virtual environments

It's ok

Anonymous

@Nelimee Gotcha, makes sense

Anonymous

What's next?

Nelimee

11:40

python3 -c "import qiskit" works fine?

Anonymous

Unknown option: -C
usage: python3 [option] ... [-c cmd | -m mod | file | -] [arg] ...
Try `python -h' for more information.

Nelimee

(it's little "c", my bad)

If you don't have any error message, then you can use qiskit

Anonymous

Well, it's just showing a >

Anonymous

in the next line

Nelimee

Seems OK

Anonymous

11:42

After I typed in
python3 -c "import qiskit

Nelimee

Try to import qiskit from your python interpreter and see :)

Some of my script will not work (because of the Qconfig.py step), but HHL should work fine :)

Anonymous

@Nelimee So, umm, how to run the scripts from here now? Or I just type them in an external text editor?

Nelimee

@Blue python3 [script_name.py]

You may need to install other packages, but I don't think so

You are on Windows?

Linux?

Anonymous

@Nelimee And that script should be located in the same directory where qiskit was installed?

Anonymous

@Nelimee Yes, Ubuntu

Anonymous

11:45

Lol, and it's stuck at this ">"

Anonymous

Do I close the terminal?

Nelimee

Try Ctrl-C

Anonymous

Ah, done :P

Anonymous

Looks okay now

Nelimee

Then you'll need to re-clone my quantum-tool repository with
`git clone https://github.com/nelimeee/quantum-tools.git utils`

You need to clone it in a directory named utils :/

Anonymous

11:47

@Nelimee Should I create a new one using mkdir?

Anonymous

Within ~/quantum/qiskit-tutorial?

Nelimee

The directory does not matter

Clone it wherever you want

Anonymous

1 min ago, by Nelimee

You need to clone it in a directory named utils :/

Nelimee

Yup

Anonymous

But you said ^ :P

Anonymous

11:48

I don't have a utils directory

Nelimee

Wait

Go wherever you want in your computer, where you want to have the utils directory. You don't have to create the utils directory

Then clone the quantum-tool directory BUT name it `utils`:
`git clone [quantum-tool URL] utils`

Then you need to update your PYTHONPATH:
`export PYTHONPATH=directory/where/you/cloned/without/utils/at/the/end/:${PYTHONPATH}`

If you want that to be persistent, write the export ... line in ~/.bashrc

Anonymous

So, I'm currently in the ~/quantum/qiskit-tutorial directory. I use cd .. to get to the ~quantum directory, and I want to clone the quantum-tool directory using git clone [quantum-tool URL] utils. That will download your quantum-tool directory within the quantum directory, with the name utils?

Nelimee

Yes exactly :)

And it needs to be named utils

Anonymous

Okay, trying the cloning first!

Nelimee

Tell me the results :)

Wait, do you want a full script to install?

Anonymous

11:55

@Nelimee How'll that help?

Anonymous

Full script for?

Nelimee

For the installation

But yeah, I'll just tell you how you need to do :)

Anonymous

Cloning into 'utils'...
remote: Counting objects: 59, done.
remote: Compressing objects: 100% (44/44), done.
remote: Total 59 (delta 14), reused 59 (delta 14), pack-reused 0
Unpacking objects: 100% (59/59), done.
Checking connectivity... done.

Anonymous

qiskit-sdk-py qiskit-tutorial utils

Anonymous

These are the three folders under ~quantum now

Nelimee

11:57

Nice!

Anonymous

What next? :P

Nelimee

Type pwd and save the output

Anonymous

done

Anonymous

copied to clipboard

Nelimee

Type echo "export PYTHONPATH=\"[path copied]:${PYTHONPATH}\"" >> ~/.bashrc

This will just append to ~/.bashrc the export... command

So that you don't have to execute it at each new session

Anonymous

12:01

@Nelimee Are those " symbols to be included? Ran that command, but it doesn't show any output. Is that expected?

Nelimee

Nope, it's OK if there is no output

Anonymous

Nope is for which part of the statement? I ran with " included

Nelimee

You can check with cat ~/.bashrc and verify that the last line is `export PYTHONPATH="...:${PYTHONPATH}"

" included is good

Anonymous

`export PYTHONPATH="/home/<name>/quantum:"
export PYTHONPATH="/home/<name>/quantum:"
`

Anonymous

Looks okay?

Anonymous

12:04

Last 2 lines

Anonymous

After cat ~/.bashrc

Anonymous

<name> is a placeholder for my name

Nelimee

Yup! Or just remove the 2 and replace them with export PYTHONPATH="/home/<name>/quantum/:${PYTHONPATH}"

With the "

Then, either your close and re-open your terminal or you type source ~/.bashrc

Anonymous

@Nelimee How do I remove them? That's the printed output (not editable)

Nelimee

Open ~/.bashrc with a text editor

Anonymous

12:07

Oh, okay :P

Anonymous

Doing the change

Nelimee

Then, either your close and re-open your terminal or you type source ~/.bashrc
And you are fine, you can go in `/home/<name>/quantum/utils/HHL/` and type `python3 test.py`. It should display a bunch of floating-points values

Anonymous

# ~/.bashrc: executed by bash(1) for non-login shells.
# see /usr/share/doc/bash/examples/startup-files (in the package bash-doc)
# for examples

# If not running interactively, don't do anything
case $- in
*i*) ;;
*) return;;
esac

# don't put duplicate lines or lines starting with space in the history.
# See bash(1) for more options
HISTCONTROL=ignoreboth

# append to the history file, don't overwrite it
shopt -s histappend

# for setting history length see HISTSIZE and HISTFILESIZE in bash(1)

Anonymous

Done. Looks good?

Anonymous

Last 2 lines changed

Nelimee

12:09

You should have the line only one time

2 times will not hurt, but it is useless

Anonymous

@Nelimee Trying!

Anonymous

@Nelimee Oh, okaies

Anonymous

Changing

Nelimee

And on a new line

Not in the continuation of an other line

Anonymous

Done

Anonymous

12:11

And when I run

Anonymous

/home/<name>/quantum/utils/HHL/

Anonymous

I get:

Anonymous

bash: /home/<name>/quantum/utils/HHL/: Is a directory

Anonymous

Fair?

Nelimee

cd /home/<name>/quantum/utils/HHL/

I said "go in" :p

Anonymous

12:12

Oh, lol

Anonymous

Okaies

Nelimee

And then python3 test.py

Anonymous

[0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j
0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j
0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j
0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j
0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j
0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j 0.1767767+0.j
0.1767767+0.j 0.1767767+0.j]

Anonymous

Done!

Nelimee

It worked

Anonymous

12:14

What are these values? :P

Nelimee

Hummm

np.ones((2**qubit_number,)) / np.sqrt(2**qubit_number)

Just the quantum state after Hadamard gates

test.py is this script: quantumcomputing.stackexchange.com/questions/2439/…

Anonymous

Oh, it's here: github.com/nelimeee/quantum-tools/blob/master/HHL/test.py

Nelimee

Yup

The HHL algorithm is github.com/nelimeee/quantum-tools/blob/master/HHL/4x4_system.py

Anonymous

@Nelimee So you mean 0.1767767+0.j is equivalent to $(|0\rangle+|1\rangle)/\sqrt{2}$ ?

Anonymous

I don't know how to interpret those numbers

Anonymous

12:18

@Nelimee Right, right I noticed

Nelimee

@Blue equivalent to $$\frac{1}{\sqrt{2^5}}$$

Anonymous

Oh, the coefficient of tensor product of 5 qubits in Hadamard state?

Nelimee

So equivalent to $$ \left(\frac{\left|0\right> + \left|1\right>}{\sqrt{2}}\right)^5$$

Yes :)

Anonymous

I can see 32 of those ` 0.1767767+0.j `

Anonymous

What does it mean? There are 32*5 qubits? :P

Nelimee

12:20

$32 = 2^5$

There are 5 qubits, so $2^5 = 32$ amplitudes

Anonymous

Ooooooh

Anonymous

Nice!

Anonymous

Okay, now I'll try to read and decipher your code myself. Thanks a ton for the help ! :D

Nelimee

But it's not really an easy code

Maybe start with QISKit's tutorials

Anonymous

@Nelimee Which one?

Nelimee

12:21

As you want, I commented a little the code, but it may be hard to understand from scratch

github.com/QISKit/qiskit-tutorial

Anonymous

Yeah, seems so. I don't have any previous experience with QISKit. But then, I'm not in a hurry either

Nelimee

github.com/QISKit/qiskit-tutorial/tree/master/reference/tools

You have 4 notebooks here that cover the basics

You can skip on the "quantum" part, but try to understand the QISKit part :p

Anonymous

Gotcha. Okay, I'll try to cover them by today :)

Anonymous

Heh, yeah

Anonymous

Okay, see you later then !:D

Nelimee

12:23

And don't worry about the Qconfig.py, it's only needed when you want to communicate with IBM Q quantum chips

Anonymous

I see, gotcha

Mithrandir24601

@Blue heads up - Area 51 stats are fully functioning again :)

Nelimee

@Blue I'm still around if you have questions, don't hesitate ;)

Nelimee

14:34

@Blue An other error in their article is that they start their HHL implementation with the Quantum Phase Estimation of $e^{-iAt}$ instead of $e^{iAt}$

Honestly I don't know how they missed errors like that... Either it was intentional or they gave the writing work to someone else x)

Anonymous

17:53

@Nelimee Heh, strange

Anonymous

Holla, chat time!

Anonymous

So we have a lot of new tags:

Anonymous

quantumcomputing.stackexchange.com/tags?tab=new

Anonymous

Without any wiki

Anonymous

It would be nice if people make suggestions regarding them

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