Editing of algorithms sections causes the deletion of previously edited sections.

[DeanEmmettSmith]

I cannot complete editing the algorithm I am assigned to (QPE) as if there was a limit of characters used for all sections together. Currently, the Input section has been "deleted" recently when having updated another section.

[VasStoneone]

Hi @DeanEmmettSmith this is a very unusual behavior, can you provide us with a little more details, so we can reproduce the issue, were you editing two sections at the same time?

Feel free to use this template

Problem Description:

(Summarize the bug encountered concisely)

Steps to Reproduce:

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Current bug behavior:

(What actually happens)

Expected Behaviour:

(What you should see instead)

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[DeanEmmettSmith]

Hello PlanQK platform team

This is the link to the QPE algorithm: https://platform.planqk.de/algorithms/ba4c50e3-7429-4471-a250-1762ed4c556a/

Current bug behavior: If I add text to a section such as Intent and save the updates, another section gets deleted such as Input Format, we suspect I may be exceeding some kind quota reserved for the text sections.

Screenshot 224 indicates the section, I updated.

Screenshot 255 indicates the section which was deleted.

If I update (actually add) the content section for Input Format, I assume the text will get deleted for a random other section.

I am avoiding to reproduce the bug because Jonas is reviewing the text. We can schedule an appointment to do this together.

Expected Behaviour:

If I update any text section, the other text sections should not change at all. Please check the text sections stored in the attachment (qpe_text.txt).

Relevant logs and/or screenshots

(Paste any relevant logs - please use code blocks (```) to format console output, logs, and code as it's very hard to read otherwise.) I have not had the time to troubleshoot the problem in this depth. We can schedule an appointment to inspect this. I hope the information clarified the situation a bit. Feel free to reach out to me for a call.

Best regards, Dean

From: VasStoneone @.> Sent: Donnerstag, 11. November 2021 13:13 To: PlanQK/platform @.> Cc: Smith, Dean Emmett @.>; Mention @.> Subject: [External] Re: [PlanQK/platform] Editing of algorithms sections causes the deletion of previously edited sections. (Issue #60)

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@DeanEmmettSmithhttps://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_DeanEmmettSmith&d=DwMCaQ&c=eIGjsITfXP_y-DLLX0uEHXJvU8nOHrUK8IrwNKOtkVU&r=FGnubJHiCPr_aFTE65ze_6F08DZuxd-p3HzAokSzFeA&m=Hu1iF8Z7YcbWVMe7rhFjn96L0yEOf6nivWv6-NyKpAM&s=EVnnoFV2J8B8Gdq3O1QAzoN37fRsMacaxPr63KFYr34&e= this is a very unusual behavior, can you provide us with a little more details, so we can reproduce the issue, were you editing two sections at the same time?

Feel free to use this template

Problem Description:

(Summarize the bug encountered concisely)

Steps to Reproduce:

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Acronymns

QPE, PEA

Quantum Advantage

Exponential speedup of resource by determining the (lowest typically) eigenvalue of a $2^N \times 2^N$ unitary matrix with $O(N)$ qubits.

Intent

Arbitrary approximation of the phase of an eigenvalue of an unitary operator. I.e. for an eigenvalue $\lambda=\mathrm{e}^{2\pi i \phi}$ one computes $\phi$.

Problem

Determine phase $\phi$ of an eigenvalue $\lambda=\mathrm{e}^{2\pi i \phi}$ associated to unitary operator $U$.

Solution

• $m$: accuracy of the solution

• $\phi$: Desired phase for the given eigenstate

• $\vert \Phi \rangle$: Output ancilla register at the beginning consisting of $m$ qubits.

• ${\vert \Phi \rangle}^{'}$: Output register at the end containing $\phi$. If $\phi$ is the reciprocal of an integer smaller than $2^m -1$, one measures ${\vert \Phi \rangle}^{'} = \vert 2^m \phi \rangle$ with probability 1. Else ${\vert \Phi \rangle}^{'}= \frac{1}{2^m} \sum{k=0}^{2^m -1} \sum{k=1}^{2^m -1} \mathrm{e}^{-2 \pi i \frac{j(x-2^m)}{2^m}} \vert k \rangle$ and one measures the closest integer to $2^m \phi$ with probability $> \frac{4}{{\pi}^2}$.

• $\vert \Psi \rangle$: Given eigenstate

• $U^{2^k}$: ${2^k}$-th power of input operator U

• ${IQFT}$: Inverse Quantum Fourier Transform

• $H = \frac{1}{\sqrt{2}}\left(\begin{array}{cc} 1 & 1\ 1 & -1 \end{array}\right) $: Hadamard-Gate

 

The circuit consists of two parts. The first one, known as Kitaev's Algorithm [K95], extracts the eigenvalue into an additional register (here $\vert \Psi \rangle$) as a coefficient, whereas the extension of Abrams and Cleves [CEM+98] transforms it further to an $m$-bit representation.

At the beginning, output/ancilla register $\vert \Psi \rangle$ is set to ${\vert 0 \rangle}^{\otimes m}$, whereas the eigenstate is present as register $\vert \Phi \rangle$. At first, one extracts the corresponding eigenvalue $\lambda$ as coefficient into register $\vert \Psi \rangle$; namely in such as way that, after expressing $\lambda=\mathrm{e}^{2\pi i \phi}$ through its phase $\phi$, the result of this step resembles that of the QFT. Therefore, one case use the inverse Quantum Fourier Transform (IQFT) to restore at least an approximation of $\phi$ in bit representation.

Superposition Targeting a QFT-similar state an equally weighted superposition of $\vert \Psi \rangle$ is produced by applying the Hadamard-Gate to each qubit:

$$ {\vert 0 \rangle}^{\otimes m} \mapsto \bigotimes_{i = 1}^{m} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle}+ {\vert 1 \rangle}}\right) $$

 

Phase-Kickback Exploiting the bilinearity of the tensor products and eigenstate property of ${\vert \Phi \rangle}$, one moves eigenvalue $\lambda$ to $\vert \Psi \rangle$ through applying operator $U$ to $\vert \Phi \rangle$ controlled by the last qubit register of $\vert \Psi \rangle$:

$$ \begin{aligned} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle}+ {\vert 1 \rangle}}\right) \otimes \vert { \Phi} \rangle = &\frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle}\otimes \vert { \Phi} \rangle+ {\vert 1 \rangle} \otimes \vert { \Phi} \rangle}\right) \ \mapsto &\frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle}\otimes \vert { \Phi} \rangle + {\vert 1 \rangle} \otimes U \vert { \Phi} \rangle} \right) \ = &\frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle}\otimes \vert { \Phi} \rangle+ {\vert 1 \rangle} \otimes \lambda \vert { \Phi} \rangle}\right) \ = &\frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle}\otimes \vert { \Phi} \rangle+ \lambda {\vert 1 \rangle} \otimes \vert { \Phi} \rangle}\right) \ = &\frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + \lambda {\vert 1 \rangle} }\right) \otimes \vert { \Phi} \rangle \end{aligned} $$

Notice that $\vert \Psi \rangle$ has not changed, so one can reuse it.

 

Obtaining QFT Shape In this step a QFT-like state is prepared to extract $\phi$ easily in an m-bit representation. However, this is not possible without further ado because one usually interprets a bit register as a natural number, whereas $\phi \in \left[0,1\right[$. Hence, measuring $\vert { \Phi^{'}} \rangle$ does not return $\phi$ itself but $2^{m}\Phi$. So the QFT-like state to be created looks the following way:

$$ \bigotimes{k = 1}^{m} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + \mathrm{e}^{2 \pi i \frac{ 2^m \phi}{2^k}} {\vert 1 \rangle} }\right) = \bigotimes{k = 1}^{m} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + \left({\mathrm{e}^{2 \pi i \phi}}\right)^{2^{m-k}} {\vert 1 \rangle} }\right) $$

Notice that for the k-th qubit one can rewrite $\left( \mathrm{e}^{2 \pi i \phi} \right)^{2^{m-k}}=\lambda^{2^{m-k}}$. Thus one can achieve the target state by applying phase-kickback for each k-th qubit with controlled $U^{2m-k}$. Combining this and the last step, the following mappings are performed:

$$ \begin{aligned} \bigotimes{k = 1}^{m} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + {\vert 1 \rangle} }\right) \;\; &{{\text{C-}{U}}{\mapsto}} \bigotimes{k = 1}^{m-1} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + {\vert 1 \rangle} }\right) \otimes \left( {{\vert 0 \rangle} + \lambda {\vert 1 \rangle} }\right) \ \;\; &{{\text{C-}{U}^{2}}{\mapsto}} \bigotimes{k = 1}^{m-2} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + {\vert 1 \rangle} }\right) \otimes \left( {{\vert 0 \rangle} + \lambda {\vert 1 \rangle} }\right) \otimes \left( {{\vert 0 \rangle} + \lambda^2 {\vert 1 \rangle} }\right) \ &\vdots \ \;\; &{{\text{C-}{U}^{2^{m-1}}}{\mapsto}} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + \lambda^{m}{\vert 1 \rangle} }\right) \otimes \bigotimes{k = 2}^{m} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + \lambda^{m-k} {\vert 1 \rangle} }\right) \ &= \bigotimes{k = 1}^{m} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + \lambda^{2^{m-k}} {\vert 1 \rangle} }\right) = \bigotimes_{k = 1}^{m} \frac{1}{\sqrt{2}} \left( {{\vert 0 \rangle} + \mathrm{e}^{2 \pi i \phi \frac{2^m \phi}{2^k}} {\vert 1 \rangle} }\right) \end{aligned} $$

The last term is exactly the result of QFT for the basis state.

Apply IQFT If $2^{m} \phi$ is a natural number, i.e. $\phi$ is a reciprocal of a natural number $<2^m$, then measuring $\vert {\Phi}^{'} \rangle$ after applying IQFT results with probability $1$ in $2^m\phi$ which is the desired outcome. Otherwise one receives the closest integer to $2^m\phi$ with probability $>\frac{4}{\pi^{2}} \approx 0.41$.

References

• [K95] Alexei Yu. Kitaev. 1995. Quantum measurements and the Abelian Stabilizer Problem. arXiv: https://arxiv.org/abs/quant-ph/9511026.
• [CEM+98] R. Cleve A. Ekert, C. Macchiavello and M. Mosca. 1998. Quantum Algorithms Revisited. Proc. R. Soc. Lond. A. 454: 339–354. DOI: 10.1098/rspa.1998.0164. arXiv: https://arxiv.org/abs/quant-ph/9708016.
• [3] N. Hatano and M. Suzuki, Quantum Annealing and Other Optimization Methods, pp. 37–68, (Springer Berlin Heidelberg, 2005), arXiv:math-ph/0506007

Input format

Input built in circuit: unitary operator (⇔ quantum gate). Input via register: associated eigenstate.

Algorithm Parameter

Hyperparameter: Accuracy of solution, i.e. amount of bits to store the phase.

[VasStoneone]

Hi @DeanEmmettSmith lets schedule an appointment, so you can show me the issue. We are not able to reproduce it and I don't even have access to the algorithm in question.

Regards

VAS valentin.aponte.sarmientos@stoneone.de

[DeanEmmettSmith]

Hello PlanQK support team,

Please schedule a teams appointment for us. My agenda should be relatively flexible.

Best regards, Dean

From: VasStoneone @.> Sent: Freitag, 3. Dezember 2021 13:45 To: PlanQK/platform @.> Cc: Smith, Dean Emmett @.>; Mention @.> Subject: [External] Re: [PlanQK/platform] Editing of algorithms sections causes the deletion of previously edited sections. (Issue #60)

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Regards

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[VasStoneone]

Hi @DeanEmmettSmith can you write me to valentin.aponte.sarmientos@stoneone.de I don't have your contact details

[DeanEmmettSmith]

Thanks for the information. I will do so!

From: VasStoneone @.> Sent: Dienstag, 7. Dezember 2021 15:14 To: PlanQK/platform @.> Cc: Smith, Dean Emmett @.>; Mention @.> Subject: [External] Re: [PlanQK/platform] Editing of algorithms sections causes the deletion of previously edited sections. (Issue #60)

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[VasStoneone]

Hi we couldn't reproduce this issue and we will close, please open a new issue if you still encounter this problem