#Stem Cuttings

[philodendronforming]

Cordyline fruticosa

The Cordyline fruticosa plants are most beautiful eye-catching evergreen perennial plants with broad leaves. Plant foliage varies in different colors such as red, pink, yellow, white & other streaks.

Good Luck plant

These cordyline fruticosa plants are commonly called Hawaiian ti plant, good luck plant, ti plant, palm lily, cabbage palm, and miracle plant belonging to Asparagaceae. This plant is often believed to bring good luck to the home.

Hawaiian ti plant

This cordyline plant variety prized & beloved especially for its colorful, long-lasting foliage with attractive stripes. The name Hawaiian ti plant name due to the reason that this croton plant believed to bring positiveness, creation, and blessing during those times in Hawaiian culture.

Benefits

The placement of ti -plant croton plant is believed to bring good luck, peace and positivity to home.

Cordyline Ti plants are pests & diseases resistant plants.

The most beautiful feature of this plant is the colorful foliage & air-purifier.

[theoldkyokodied]

Uploading all my Tomgreg art at once from the past few week before season 4 hits, who knows in what kind of mental state i'm gonna be once it does :')

[sixtyt-en]

I think that like, the major reason why benrey got so mischaracterized by the fandom at hlvrai's peak popularity was because they forgot he acts like a dmv employee

[beebones]

support women’s wrongs or else

[ruvviks]

nathan encounter with obscura 2.0 goes about as well as the day he killed his parents, more at 11

taglist (opt in/out)

@shellibisshe, @florbelles, @ncytiri, @hibernationsuit, @stars-of-the-heart;

@lestatlioncunt, @katsigian, @radioactiveshitstorm, @estevnys, @adelaidedrubman;

@celticwoman, @rindemption, @carlosoliveiraa, @noirapocalypto, @dickytwister;

@killerspinal, @euryalex, @ri-a-rose, @velocitic, @thedeadthree;

@jacobseed

[dustykneed]

what if i drew myself stress relief musical sapphics.... what then....

can you tell i've been. hmmm. stressed this week LMAO (anyways if you recognise these pairs like that's awesome and you're so cool genuinely! but this is so self indulgent who am i kidding xDD)

[teddy-bear-naps-and-random-snaps]

[missingexaltation]

It was one thing remaining from the start of their relationship, but Steve still couldn't get Eddie's hair to behave. He'd tried all sorts of products over the years, all sorts of techniques, but all in vain. It either frizzed up and went all static, or started alright and ended up with more grease than a breakfast pan by the end of the day.

Eddie didn't mind too much. Part of his entire aesthetic was grotty and grungy, and if his hair was a bit frizzy from overwashing, or stiff with mousse, it didn't matter too much to him, as long as he was vaguely clean and could headbang to his music. Whatever tricks they tried lasted maybe a day, and was way too much effort for Eddie to keep up with on a day to day basis.

It bothered Steve though, so Eddie put up with the sighs and new lotions and conditioners (and oh one memorable occasion...rollers, like he was a eighty year old woman) until even 'The Hair' Harrington threw his hands up in defeat and left Eddie to whatever shampoo was on offer at the store that week.

After Eddie started his internship at the tattoo parlour, he stated wearing his hair up, out of the way, as he was literally violating health and safety codes with it down. He only really wore it down for gigs, and despite the growing crowds that he now played for, metal fans weren't the most picky with hygiene, and if he reveled in being a bit gross for the set, Steve wasn't to know.

So the years passed, and despite Steve's occasional attempts, 'the mop', as he called it, remained untamed.

It wasn't until a couple of decades later, until after Eddie's music career had exploded and calmed down, did anything change. His D&D podcast turned streaming sessions with the old Hellfire club, garnered a lot of interest from fellow nerds, old and young.

An offhand comment (Eddie wasn't sure who from), about his lack of proper curls ignited chat into hair care. More specifically the 'curly girl method', that was apparently setting social media on fire.

'We're trying it.' Steve said, excitedly reading chat over his shoulder. 'I'm finally gonna win this one, babe.'

And they do. Eddie even let Steve film the process, and to both of their surprise...it worked! AND it lasts longer than half a day.

More importantly to Steve, Eddie's hair was now properly curly, soft and photoshoot ready. 'You look like someone cares about you now.' He says, pulling on a stray curl from Eddie's temple.

He's so pleased with himself that it makes Eddie's heart ache with adoration. Nearly thirty years but he won the war in the end.

Steve's less fond of their video going viral though. He loves Eddie, is proud of his career, but definitely hates being in the spotlight, especially as his excitement at the result is the thing mentioned in most of the comments.

'Wish my man looked at me like that.'

'Imagine being that happy together after thirty years'

'Awww you can tell they're high school sweethearts.'

'Get me a man that looks at me like Eddie's husband looks at him.'

'Love my gay rock dads.'

[solargeist]

grian we will keep u AWAY from flora after that 😭

Right 💥💥💥 she is not able to gauge how weak or strong players are, she’s very much like, I can do it, why can’t you do it ? 🤔🤔🤔

not a good mindset to have..

she comes from a twilight forest server, shes survived on her own for a long time as a player, but grian comes from a community of friends, so there’s an obvious difference in their abilities.

she’s not gonna kill him or cause ~severe physical harm, but they don’t get along, u can see Why 😭

[nashvillethotchicken]

I wish there were more black people who were into iwtv so I can talk about how Louis's class and race interests intersected

[twilightarcade]

if I was a character I would've gotten non binary headcannoned so hard

[freaky-flawless]

“You trust me?”

Toralei glanced up at the ghoul before her. Clawdeen Wolf had placed her hands on the werecat’s shoulders, and was staring very intensely into her eyes. Her expression was serious, but her golden eyes shimmered with unrestrained glee. That both delighted, and terrified Toralei.

She’d expressed to her ghoulfriend not too long ago about wanting to cut her hair. It had grown out considerably in the last few months, to the point where it started to graze her shoulders. It had been fun for a while to experiment with different styles, and finally being able to put it all up into a ponytail was interesting, but now she was over it. She typically cut it herself, much to her adoptive mother’s dismay, but upon hearing Toralei’s desire for a new hairdo, Clawdeen insisted upon cutting it for her. Unable to find a justified reason to decline, Toralei hesitantly agreed.

And so there they were, in Toralei’s bedroom, a small tarp laid out on the floor, courtesy of Mr. Stripe, and Toralei in her desk chair in the middle of it. Clawdeen stood before her, the gold hairdressing clippers in her hand looking particularly menacing as they glinted in the sunlight streaming through her window.

Forcing a smile, Toralei answered her with a less than confident, “Yes?”

Clawdeen threw her head back and laughed. “You should! As if I’d be caught alive dating someone with a busted head of hair anyway!”

            “You have been for the last few months,” Toralei quipped back. Then bit her tongue upon realizing she'd just roasted herself. Clawdeen erupted into laughter once more.

            “You said it, not me,” she agreed. She ran her fingers through Toralei’s red-orange locks. They had already washed and conditioned it, leaving it damp. The werecat’s scalp tingled at her touch, and she let out a low purr. Clawdeen smiled at the sound of it. “Your hair is super uneven. The left side is choppy, and it’s a lot longer in the back than on top. You could probably rock a killer mullet if you wanted.”

            Toralei scoffed. “And be called a Holt Hyde wannabe? No thank you.” She paused. “…Well maybe after graduation.”

            “That’s not my vision for you anyway,” Clawdeen announced, that determined expression returning to her face.

            “What is your vision?” Toralei asked warily.

            “It’s a surprise. You ready?”

Toralei did not like surprises. Cats rarely reacted well to be surprised. But she liked Clawdeen, and the feeling of her clawed fingers running through her hair. So, uneasy as she may have felt, she forced a smirk and nodded. “Ready!”

[mysteriousquantumphysics]

Circuit Cutting for Efficient Quantum Circuit Simulation

In previous blog posts [1, 2] we talked about quantum circuit cutting - a technique to "cut" quantum circuits into pieces to run them on smaller quantum devices. In particular, for NISQ devices this is a nice method to run larger quantum circuits than usually possible with the limited number of qubits as well as diminishing the effects of noise during the computation [3]. However, such techniques come with the cost of having an exponential sampling overhead in the number of cut wires or gates. Thus, such methods are limited in applicability - namely they work best for shallow, easy to partition, circuits.

"Cutting" for Classical Simulation

No matter the (dis)advantages, the idea of "cutting" circuits into pieces cannot only be applied as a "compilation" step to run cut algorithms on real quantum devices. In contrast, "cutting" can also make classical simulations of quantum circuits of suitable classes more efficient. Why might it be desirable to simulate smaller circuits on a classical computer? The simple answer is that storing statevectors on classical computers requires an exponential amount of RAM, i.e., 2^n amplitudes for n qubits. As only limited RAM is available - similar to the limited number of qubits in NISQ devices - running smaller simulations/computations is desirable. However, there is no free lunch here as well, since cutting also induces an exponential overhead in the classical simulation case - meaning that an exponential amount of smaller subcircuits has to be run and subsequently reassembled again. Thus, the reason why one wants to cut circuits for classical simulations is a bit more intricate: Reducing the RAM requirements can also decrease the runtime of simulating gates (i.e. by matrix-vector multiplication) but as pointed out before, one has to run an exponential amount of circuits which is increasing the time cost again. Therefore, cutting quantum circuits for classical simulation is not always useful; instead, there is a tradeoff between reducing runtime by reducing RAM and the exponential overhead - thus, such techniques are usually only useful for quantum circuits with limited connectivity such that only a manageable number of cuts must be performed. In the literature this cutting is usually denoted as Hybrid Schrödinger Feynman Technique (HSF) [4, 5, 6] - still, the underlying ideas are quite similar to quantum circuit cutting. Let's look at the core idea of cutting circuits for classical simulation and where this aforementioned exponential overhead comes from.

How to Cut Circuits for Simulation

Conceptually, classical cutting of quantum gates (contrasting quantum circuit cutting, one is usually not considering wire cuts for HSF simulation) merely requires performing a Schmidt-Decomposition on the gate(s) to be cut. Considering the CNOT gate, this can be done quite easily by just factoring out properly as follows

where we just wrote down the CNOT gate in Dirac notation and factored out the projector P_0 and P_1 respectively. This can be represented graphically in a circuit diagram as

With this illustration it becomes more apparent what is meant by cutting. We decomposed the CNOT gate, which originally acts on two qubits jointly, into a representation with two contributions (terms) in which each one is bipartite: The first term is just the projector onto the zero state on the first qubit and nothing on the other. The second term is the projector onto the other computational basis state as well as a separate Pauli X gate on the other qubit. You can see that the qubit wires are not connected anymore in the separate contributions that constitute the cut.

If you have a larger circuit that you want to partition into two smaller parts which should be simulated separately and they are connected by a single CNOT gate, cutting would give you two pairs of bipartite circuits. Each of them is smaller than before, thus, faster to simulate. This toy example has a pretty small overhead in the number of simulations, often also denoted as "paths", namely only two. If more gates are cut, this grows exponentially as the number of paths per gate has to be multiplied. Mathematically speaking, this number of paths is determined by the Schmidt-rank of each cut gate. As mentioned before, the Schmidt Decomposition is the core tool to perform cutting and thus, we briefly look into how this Schmidt Decomposition is done in general.

Classical Cutting in General by Schmidt-Decompositions

In order to spare you tedious notation with a lot of confusing indices, let's consider the general case in graphical notation only. Any quantum circuit can be represented as a tensor network [7]. Each quantum wire can be interpreted as leg of a tensor with physical dimension 2 (since qubits have a basis with 2 vectors). Consider some operator A with n=6 qubits (the logic applies for arbitrarily many qubits) as shown in the figure below. Assume that we want to cut this operator in the middle. Originally, operator A has 2n legs , but we can reshape those legs/wires according to the desired cut location as shown on the right-hand side - resulting in two "big" legs with higher dimensions than before. The dimension of the upper and lower big leg is determined by the number of qubits n_a in the upper partition and n_b in the lower partition respectively, in our example n_a=n_b=3. The upper big leg has dimension 2^(2n_a) and the lower 2^(2n_b).

Doing this not only fixes the cut position but is a way of matricizing the previously higher rank object - allowing to perform a Singular Value Decomposition (SVD), which can be applied on matrices (having 2 legs) only. An SVD decomposes a matrix into three parts, two isometries, U and V as well as the diagonal matrix σ containing the singular values (shown diagramatically below). The number of singular values fixes the aforementioned Schmidt-rank [8] of the original operator/gate A which, in turn, determines the aforementioned overhead, the number of paths in the simulation. The isometries can be absorbed into the top and bottom and the remaining sum can be made explicit such that we end up with a bipartite representation, similar to the one shown for the CNOT gate. This allows to decompose the gate into two parts, at the cost of a higher number of paths for the simulation.

Conclusion

Now you know how circuit cutting can be applied for classical simulations as well - it merely requires performing a Schmidt Decomposition in order to find bipartite representations of gates to be cut. Interestingly, performing cuts for classical simulation induces an exponential overhead - similar to quantum circuit cutting for real quantum devices. Even though conceptual differences are present between both approaches, this parallel neatly shows that one can never avoid the exponential complexity of quantum systems: We can merely shift the complexity (e.g. memory complexity into time complexity as for HSF simulation), to hope for nice tradeoffs and computing advantages - but no method can get rid of the inherent exponential complexity of quantum systems.

References

[1] Blog Post "Cutting Quantum Circuits into Pieces - Why and How?"

[2] Blog Post "Quantum Circuit Cutting - with Randomly Applied Channels"

[3] Bechtold, M., Barzen, J., Leymann, F., Mandl, A., Obst, J., Truger, F., & Weder, B. (2023). Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices. In Quantum Science and Technology (Vol. 8, Issue 4, p. 045022). IOP Publishing. https://doi.org/10.1088/2058-9565/acf59c

[4] Aaronson, S., & Chen, L. (2016). Complexity-Theoretic Foundations of Quantum Supremacy Experiments (Version 2). arXiv. https://doi.org/10.48550/ARXIV.1612.05903

[5] Markov, I. L., Fatima, A., Isakov, S. V., & Boixo, S. (2018). Quantum Supremacy Is Both Closer and Farther than It Appears. arXiv. https://doi.org/10.48550/ARXIV.1807.10749

[6] Burgholzer, L., Bauer, H., & Wille, R. (2021). Hybrid Schrödinger-Feynman Simulation of Quantum Circuits With Decision Diagrams. In 2021 IEEE International Conference on Quantum Computing and Engineering (QCE). 2021 IEEE International Conference on Quantum Computing and Engineering (QCE). IEEE. https://doi.org/10.1109/qce52317.2021.00037

[7] Blog Entry Pennylane, "Tensor Network Quantum Circuits"

[8] Nielsen, M. A., Dawson, C. M., Dodd, J. L., Gilchrist, A., Mortimer, D., Osborne, T. J., Bremner, M. J., Harrow, A. W., & Hines, A. (2003). Quantum dynamics as a physical resource. In Physical Review A (Vol. 67, Issue 5). American Physical Society (APS). https://doi.org/10.1103/physreva.67.052301

[prairiefalcons]

shit changes for the worse sometimes

rodent by the menzingers / dorothy at forty by cursive / boy staring at an apparition by goya / the rat by the walkmen / millstone by brand new / i've got it all (most) by modest mouse / down in it by nine inch nails / how to disappear completely by radiohead / lives by modest mouse / cowboy dan by modest mouse / between aging and old by jack gilbert / beware of dog by john brosio / wasted days by cloud nothings / development by john brosio