# Codercise H.4.1a Potential Mistake

**URL:** <https://discuss.pennylane.ai/t/codercise-h-4-1a-potential-mistake/8721>\
**Category:** Codebook\
**Created:** [July 4, 2025, 10:31am UTC](https://discuss.pennylane.ai/t/codercise-h-4-1a-potential-mistake/8721 "2025-07-04T10:31:36Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![cyyoung](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/cyyoung/32/3821_2.png) [@cyyoung](https://discuss.pennylane.ai/u/cyyoung)\
**Post date:** [July 4, 2025, 10:31am UTC](https://discuss.pennylane.ai/t/codercise-h-4-1a-potential-mistake/8721/1 "2025-07-04T10:31:36Z")

</div>

Hi. Under the Energy levels and time evolution section in the theory section, equation (1) seems to only hold true for odd powers of (Z@Z) (i.e. (Z@Z)^2m+1). That is, when it is to an even power, (Z@Z)^2m = (I@I), so (Z@Z)^2m |xy\> = (I@I)|xy\> = |xy\>.

---

<div class="post-metadata">

**Author:** ![daniela.murcillo](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/daniela.murcillo/32/3612_2.png) [@daniela.murcillo](https://discuss.pennylane.ai/u/daniela.murcillo)\
**Post date:** [July 4, 2025, 9:26pm UTC](https://discuss.pennylane.ai/t/codercise-h-4-1a-potential-mistake/8721/2 "2025-07-04T21:26:38Z")

</div>

Hi @cyyoung  
Thanks for your question.  
I’ll check the math and get back to you next week.

---

<div class="post-metadata">

**Author:** ![daniela.murcillo](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/daniela.murcillo/32/3612_2.png) [@daniela.murcillo](https://discuss.pennylane.ai/u/daniela.murcillo)\
**Post date:** [July 7, 2025, 1:51pm UTC](https://discuss.pennylane.ai/t/codercise-h-4-1a-potential-mistake/8721/3 "2025-07-07T13:51:39Z")

</div>

Hi!  
I checked your statement and it is true. However, why is this a potential mistake in the Codebook? The section is making an assumption at the beginning about the form of the Hamiltonian H=\alpha Z \otimes Z and at any stage it claims to be general.  
Let me know! Thanks!

---

<div class="post-metadata">

**Author:** ![cyyoung](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/cyyoung/32/3821_2.png) [@cyyoung](https://discuss.pennylane.ai/u/cyyoung)\
**Post date:** [July 7, 2025, 5:58pm UTC](https://discuss.pennylane.ai/t/codercise-h-4-1a-potential-mistake/8721/4 "2025-07-07T17:58:29Z")

</div>

Oh. Thank for your reply. I thought the codebook was taking  
 ![image](https://canada1.discourse-cdn.com/flex012/uploads/pennylane/original/2X/5/574e2bdd9f86ed84d582f44d94b5c95c7098c849.png)  
for granted and just putting it into the exponent.  
Because of this  
 ![image](https://canada1.discourse-cdn.com/flex012/uploads/pennylane/original/2X/d/df5f5a3752aea14855c23ba45d0f2415ece33c4e.png)  
I assumed that the Hamiltonian (Z@Z) is just following this.

Thanks alot!