Melvin: An algorithm for automatically designing new quantum experiments using SymPy

[Xuemei Gu]

Hello all,

I worked on quantum physics and studied computer science. Using AI to discover new quantum experiments is one of my research interests.  

There is a computer-based design algorithm for seaching new quantum optics experiments -- Melvin (10.1103/PhysRevLett.116.090405), which is implemented in Mathematica. Based on this work, I have reimplemented it in SymPy:

https://github.com/XuemeiGu/MelvinPython

It would great, if this project (https://github.com/XuemeiGu/MelvinPython) could be listed on the SymPy webpage. 

I am looking forward to hearing feedback from the SymPy commuity on this project.

Thank you very much!

best regards,

Xuemei Gu

[David Bailey]

Dear group,

First I would like to say how good it was to discover that the online
SymPy documentation now supports copy/paste operations without
constantly switching to SymPyLive. I think this will make the
documentation considerably more user friendly.

My question is what construct should I use to get variables with
subscripts, and maybe superscripts. I thought at first that indexed
objects were the way to go, but they seem rather obscure. E.g. think of
indexing through the Bessel functions - J0, J1,J2 etc.

Ideally I'd like to loop over the index/indices and also see the
subscripts positioned below the main symbol when using Latex output

Best wishes,

David

[Oscar Benjamin]

On Tue, 19 Oct 2021 at 20:55, David Bailey <da...@dbailey.co.uk> wrote:
>
> Dear group,
>
> First I would like to say how good it was to discover that the online
> SymPy documentation now supports copy/paste operations without
> constantly switching to SymPyLive. I think this will make the
> documentation considerably more user friendly.

I'm not sure what has changed there...

> My question is what construct should I use to get variables with
> subscripts, and maybe superscripts. I thought at first that indexed
> objects were the way to go, but they seem rather obscure. E.g. think of
> indexing through the Bessel functions - J0, J1,J2 etc.
>
> Ideally I'd like to loop over the index/indices and also see the
> subscripts positioned below the main symbol when using Latex output

I'm not completely sure what you want here but is this it:

In [19]: symbols('x:10')
Out[19]: (x₀, x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉)

IndexedBase is for the situation where you want the index to be symbolic e.g.:

In [27]: xi = IndexedBase('x')

In [28]: n, m = symbols('n, m')

In [29]: Sum(xi[n], (n, 1, m))
Out[29]:
m
___
╲
╲
╱ x[n]
╱
‾‾‾
n = 1

--
Oscar

[David Bailey]

On 20/10/2021 12:36, Oscar Benjamin wrote:

On Tue, 19 Oct 2021 at 20:55, David Bailey <da...@dbailey.co.uk> wrote:

Dear group,

First I would like to say how good it was to discover that the online
SymPy documentation now supports copy/paste operations without
constantly switching to SymPyLive. I think this will make the
documentation considerably more user friendly.

I'm not sure what has changed there...

Thanks for replying Oscar. You are right! When I went to the SymPy documentation to prepare the second part of this email I found it behaved in the same old way - maybe the live shell was down last night. The problem is that if you click into a block of SymPy code with the intention of cutting and pasting its contents, it fires up the live shell when you don't want it - at least using Firefox on Windows 10. To cut and paste you have to use a trick - clicking outside the block with the green background and dragging into the block from there. Since there is a dark green tag above each section to invoke the live shell, all that is needed is to disable special trapping the left mouse click.

My question is what construct should I use to get variables with
subscripts, and maybe superscripts. I thought at first that indexed
objects were the way to go, but they seem rather obscure. E.g. think of
indexing through the Bessel functions - J0, J1,J2 etc.

Ideally I'd like to loop over the index/indices and also see the
subscripts positioned below the main symbol when using Latex output

I'm not completely sure what you want here but is this it:

In [19]: symbols('x:10')
Out[19]: (x₀, x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉)

IndexedBase is for the situation where you want the index to be symbolic e.g.:

In [27]: xi = IndexedBase('x')

In [28]: n, m = symbols('n, m')

In [29]: Sum(xi[n], (n, 1, m))

It was the second facility that I was looking for. What fooled me was that in the documentation:

https://docs.sympy.org/latest/modules/tensor/indexed.html

The index variables are created specially:

i, j = symbols('i j', cls=Idx)

However it would seem you can index with any integer variable. What does the Idx class contribute?

David

[Aaron Meurer]

Idx lets you specify a range of values. I think it is also handled
better by the code printers. If you don't need any of those features,
just using a Symbol should work fine.

Aaron Meurer

>
> David
>
>
>
> --
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[David Bailey]

On 20/10/2021 22:51, Aaron Meurer wrote:
> Idx lets you specify a range of values. I think it is also handled
> better by the code printers. If you don't need any of those features,
> just using a Symbol should work fine.
>
> Aaron Meurer

Thanks Aaron,

That clarifies things a lot, but I think if you look at the
documentation, this isn't clear.

That leaves me with one question. Can this be used to index a sequence
of functions (as opposed to values) - think of the conventional notation
J_n for the n'th Bessel function, for example? This test suggests that
such a sequence can't be constructed::

X=IndexedBase('X')

x[3]=sin

Generates an error:

TypeError: 'IndexedBase' object does not support item assignment

David

[Aaron Meurer]

On Thu, Oct 21, 2021 at 2:37 PM David Bailey <da...@dbailey.co.uk> wrote:
>
> On 20/10/2021 22:51, Aaron Meurer wrote:
> > Idx lets you specify a range of values. I think it is also handled
> > better by the code printers. If you don't need any of those features,
> > just using a Symbol should work fine.
> >
> > Aaron Meurer
>
> Thanks Aaron,
>
> That clarifies things a lot, but I think if you look at the
> documentation, this isn't clear.
>
> That leaves me with one question. Can this be used to index a sequence
> of functions (as opposed to values) - think of the conventional notation
> J_n for the n'th Bessel function, for example? This test suggests that
> such a sequence can't be constructed::

You would have to represent that as the index being an argument of the
function. For example, J_n(x) is besselj(n, x).

Aaron Meurer

>
> X=IndexedBase('X')
>
> x[3]=sin
>
> Generates an error:
>
> TypeError: 'IndexedBase' object does not support item assignment
>
> David
>
>

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[Oscar Benjamin]

Hi Xuemei,

I'm sure we can list this on the webpage. I think you can just open a
PR to add this.

Oscar

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