marekgluza - Network

Reflections by Liebhttps://youtu.be/kwn8ySt0vH8

Reflections by Lieb
https://youtu.be/kwn8ySt0vH8

Double-bracket #quantum imaginary-time evolution (see arxiv.org/abs/2412.04554 orhttps://scirate.com/arxiv/2412.04554) provide rigorous...

Double-bracket #quantum imaginary-time evolution (see arxiv.org/abs/2412.04554 or

https://scirate.com/arxiv/2412.04554) provide rigorous circuit synthesis approximating imaginary-time evolution.

In the process of analysis we derived this lemma which didn't make it into the final draft but is mind-bogglingly neat 😊

Normally when assessing the distance of two unitaries we *should* use the operator norm while other norms such as the Hilbert-Schmidt norm are 'wrong'.

The problem is that the estimates in norms other than the operator norm will be untight, with constants growing exponentially with the number of qubits.

In contrast, the operator norm grows polynomially, so it 'should' be used.

It turns out that the unitaries implementing imaginary-time evolution can be analyzed using a 'wrong' norm, the Hilbert-Schmidt norm.

This is because the bounding constant will be proportional to energy fluctuations which grow polynomially with the number of qubits so suddenly for tasks related to QITE the 'should' criteria are fulfilled for the Hilbert-Schmidt norm. If I wanted to die on pointless hill, I'd even argue that for our QITE approach the Hilbert-Schmidt is better than the operator norm.

So, normally using the Hilbert-Schmidt norms for unitaries is a very (very, very, very) bad idea. Here, not.

As the screenshots of the deleted lemma show, the energy fluctuation sets a good quantitative bound an unitary approximation, which effectively behaves like the operator norm that grows polynomially and not exponentially with the number of qubits.

Imaginary-time evolution is a solution to Brockett's double-bracket flow which has direct implications for #quantum circuit...

Imaginary-time evolution is a solution to Brockett's double-bracket flow which has direct implications for #quantum circuit synthesis.

https://arxiv.org/abs/2412.04554
https://scirate.com/arxiv/2412.04554

Me next to the #chess world champion trophy that likely will belong to #Gukesh thanks to Qxc6!

Me next to the #chess world champion trophy that likely will belong to #Gukesh thanks to Qxc6!

A programming job to develop the fullstack quantum computing package #qibo with many possibilities to develop #opensource #software and...

A programming job to develop the fullstack quantum computing package #qibo with many possibilities to develop #opensource #software and learn #physics and learn first hand about #qubit fabrications and calibration.

Basically you will learn about all levels of running a #quantum computer and your work will influence the capacities for academic quantum computing in the foreseeable future.

If you identify with an underrepresented group and that makes you hesitate whether to apply - feel free to inquire or simply do apply.

https://github.com/qiboteam/qibo/discussions/1436

Talk by Aleks Kissinger later in the same day

Talk by Aleks Kissinger later in the same day

John van de Wetering just finished his talk at #IWQC6 by live on the stage changing to public the github repo of his new book written with...

John van de Wetering just finished his talk at #IWQC6 by live on the stage changing to public the github repo of his new book written with Aleks Kissinger about --- #quantum compilation ---

https://github.com/zxcalc/book

Posted today: strategies for how to go about optimising double-bracket #quantumAlgorithmshttps://scirate.com/arxiv/2408.07431We compare with...

Posted today: strategies for how to go about optimising double-bracket #quantumAlgorithms
https://scirate.com/arxiv/2408.07431

We compare with cases inspired by Brockett's #doubleBracketFlow which have rigorous global convergence guarantees and found that departing from them and at every step optimising the involved generators gives faster diagonalization.

This motivates our upcoming work on training our double-bracket circuits on single-shot samples: today we posted that 1) within the class of #doubleBracket #quantum algorithms it's worthwhile to variationally train the parametrisations at every step, last week we posted that 2) warm-starts from #VQE facilitate very high ground state preparation fidelity and so 3) training on shot-noise limited data will give an idea how to use our approach on future large-scale quantum hardware.

Have a look in case you are among those who have been using wrongly variational #quantum get-stuck-in-barren-nowhere-for-more-than-5-qubits...

Have a look in case you are among those who have been using wrongly variational #quantum get-stuck-in-barren-nowhere-for-more-than-5-qubits eigensolver circuits?

After a VQE gets stuck --- double-bracket circuits can be used to continue lowering the energy.

https://scirate.com/arxiv/2408.03987

Among the circuits that we compiled my favorite has 55 CZ gates per qubit and gives 99.5% fidelity to the 10 qubit XXZ ground state.

In short: See that training plateaux? A
Double-bracket circuits don't. This completely different, algorithmic, approach doesn't see the same limitations and just goes straight through to the ground state.

Why should a paper have 15 coauthors? If you provide explicit CZ gate compilation for a completely new quantum algorithm type and showcase functioning by applying to the state of the art plus code matches Qibo software development standards then... We learned a great deal along the way!

Matteo Robbiati, Edoardo Pedicillo and Andrea Pasquale on the lead contributed equally.

Most of #TeXLaTeX compiling errors appear for me when editing a draft and merging comments of coauthors in color.You always cut some { block...

Most of #TeXLaTeX compiling errors appear for me when editing a draft and merging comments of coauthors in color.
You always cut some { block }.

The fastest way to find it where you missed it is to do binary search by going up in the document, adding

\end{document}

and compiling.

The first position where it compiles is your friend.
The first position where it doesn't compile singles out the block where the stray { is hidden.

@TeXhackse is there a way for latex to suggest the line number where an open { appears?

When applying for a job, this advice saved me grief:- 'Oh, login to the webpage early. I had everything ready and then they ask you much...

When applying for a job, this advice saved me grief:

- 'Oh, login to the webpage early. I had everything ready and then they ask you much more in the form.'

Ryuji Takagi, then a fellow postdoc at NTU and kow professor in Tokyo, told me this when I asked him the catch all question if there is anything else to keep in mind. Turned out the form asked for additional information on impact, prior works, popular summary, summary for experts and what not. Serious writing might be required and not listed in the required documents which would have been a serious issue had I not known ahead that hidden workload is coming up.

- 'If you will invest time into writing the grant, then begin by loging into the ststem.'

Following Ryuji's advice earlier this year I logged in to a grant application Web page 1 week before the deadline. The login system was archaic and while I was working on the draft I had time to troubleshoot and not be daunted by added stress.

- 'Write to the email listed and ask a dummy question'

I realised that when I was troubleshooting the archaic login system, I had a chance to ask other questions. Today I was preparing another application and early on I asked a question without hesitation. A follow up question had an answer thar resolves a constraint and I clarified what is needed for reference letters. This speeds up preparation because I asked 1 month before applying. If anything pops up I can #quickly bounce back even two weeks later with oh one more question thanks - when stressed I will be able to be fast and no need to write context anymore because the contact is established and I know if a reliable response can be expected.

What I check in incoming drafts:State 1.- what's the ratio of formulas and text? Too little text means not enough storyline- are samoled...

What I check in incoming drafts:

State 1.

- what's the ratio of formulas and text? Too little text means not enough storyline

- are samoled equations intuitively clear? Are all symbols discussed?

- is the order of introducing things harmonious?

Stage 2.

- what is the key section introducing new things?

- does it read quickly so someone in a rush will comprehend it?

- what are the results following the key section? Are they harmonizing with the main premise?

- change passive sentences to active

State 3.

- read intro and throw out all adjectives. Important is not. Famous is not. It's all relative fluff that means the intro needs to be rewritten to pivot on things that really matter.

- in this work... is it really saying the key things in this work without being convoluted?

- is the abstract representing what is in the paper?

- is the title correct? Cannit be shorter?

Stage 4.

- rewrite conclusions, they always are weak. Weak in the sense of weak words, passive form, encyclopedic listings without structuring that highlights what matters

- go back to intro and make it reasonable, again

- check main results as part of the whole

Stage 5.

- read through once in one go looking for fiction or tension

- fall back in stack if issues bigger than typo

Stage 6.

- check title, affiliations, acknowledgments

- search for question marks which are broken links

- check optically if there are any hanging paragraphs

I realised that, if anything, I have 10 years of professional experience in writing #quantum papers in #TeXLaTeXSo much for for-profit...

I realised that, if anything, I have 10 years of professional experience in writing #quantum papers in #TeXLaTeX
So much for for-profit journals being helpful - but that's not my point:

1. When you finish a sentence with a fullstop - break the line.
Then continue to next one.
Even though you break the line they will appear connected.
Version tracking like git will be more helpful.

2. When you write an outlined equation space the punctuation with backslash-space like that \ , to avoid cluttered formulas
\( a=b_1.\)
becomes
\( a=b_1\ .\)
(Mathstodon.xyz typesets latex in Web browsers)

3. I don't believe anything was done in [3]. However: In Ref.~\cite{a} the proof of Eq.~\eqref{b} suggested an algorithm to compute results shown in Fig.~\ref{c} discussed in Sec.~\{d}. The tilde will prevent ugly line breaks. The convention Ref, Eq, Fig, Sec is handy and will allow you to write direct sentences naturally.

4. Latex understands that \frac 12 is 1/2 and that H_\text{TFIM} has the whole word as subscript. You don't need to celebrate movember every day...

5. Never \begin{equation} because there are always equations that you might want to try to split with \\ which is much faster if you \begin{align}.

6. You can trim margins of pdf files using include graphics options. For example, you can take a 2 panel figure and see how each panel would function as a standalone figure without modifying the file.

7. You can \def\a{a_3} anywhere in the text. If you put { around a text } then inside that block you can overload that command.

8. \bigl( will force a regular parenthesis to be slightly bigger and boost clarity

9. In align write =& and then if you break with \\ write &+ then + will appear correctly below =

|struggle>+|satire>+|too much Hamilton(ians)>Experiments of this type would herald the ascendancy of #quantum field simulation.

|struggle>+|satire>+|too much Hamilton(ians)>

Experiments of this type would herald the ascendancy of #quantum field simulation.

Did any of you #computerScience and #mathematics folks have any success explaining to your partners/parents/roommates that your way of...

Did any of you #computerScience and #mathematics folks have any success explaining to your partners/parents/roommates that your way of organizing your living space is not #messy but #smart in that it involves a quick access data structure with a one-way function as the hashing method?

https://en.wikipedia.org/wiki/Hash_table#Performance

yes, they got startled and walked away
yes, we wrote a good paper together
no, they told me I'm like Sheldon but more annoyin

In the surrender to the reality of things, I find a pathway to effect change.I like the idea of #interbeing. This holistic stance is a...

In the surrender to the reality of things, I find a pathway to effect change.

I like the idea of #interbeing. This holistic stance is a curious characteristic of quantum states in a different way than I mean here. In general, I like it as a dialectic concept. And simply: It's chilled :)

Group commutators have curious exchange #symmetry propertiesWrite\[ V(A,B) = e^{iA}e^{iB}e^{-iA}e^{-iB} \] We have\[ V(A,B)\approx...

Group commutators have curious exchange #symmetry properties

Write
\[ V(A,B) = e^{iA}e^{iB}e^{-iA}e^{-iB} \]
We have
\[ V(A,B)\approx e^{[A,B]} \]
But also
\[ V(-A,-B)\approx e^{[-A,-B]}= e^{[A,B]}\]
So
𝑉(𝐴,𝐵)≈𝑉(−𝐴,−𝐵)

This is not intuitive: Here we inverted all constituent evolutions and nothing much happened.

The right way to invert is in fact
\[ V(A,B) = V(B,A)^\dagger \]
with equality and
\[ V(A,B) \approx V(-A, B)^\dagger \]
with approximation via both being in proximity to an approximate commutator exponential.

If we bring these two together we get one more approximate symmetry
𝑉(𝐴,𝐵)≈𝑉(𝐵,−𝐴)
or
\[ V(A,B) \approx V(-B,A) \]

I added a disclaimer explaining the choice of the background for my slides on #quantum compiling:It's a bricklayer...

I added a disclaimer explaining the choice of the background for my slides on #quantum compiling:

It's a bricklayer 😂

https://slides.com/marekgluza/lecture-quantum-compiling

"Why 8? It's an auspicious number!"It literally came from bounding a double bracket in an 'auspicious' way:4<8 so I...

"Why 8? It's an auspicious number!"

It literally came from bounding a double bracket in an 'auspicious' way:
4<8 so I usually additionally multiply in a factor 2 here and there in case I had missed a factor 2 when bounding a commutator on the way 😅😂

We can generalize this by considering the group commutator \[ e^{iA}e^{iB}e^{-iA}e^{-iB} \approx e^{[A,B]} \] Applied to the above we get\[...

We can generalize this by considering the group commutator

\[ e^{iA}e^{iB}e^{-iA}e^{-iB} \approx e^{[A,B]} \]

Applied to the above we get
\[ e^{-it^2[H_{k+1},D]} \approx e^{itH_{k+1}}e^{itD}e^{-itH_{k+1}}e^{-itD}\]

\[ e^{-t^2[H_{k+1},D]} \approx U_k^\dagger e^{itH_{k}} U_k e^{itD}U_k^\dagger e^{-itH_{k}}U_ke^{-itD}\]

Which is a second step if 𝐷 is diagonal.