#quantum computing

[quasi-normalcy]

Hey, so--we cooled your boyfriend down to a hundredth of a kelvin above absolute zero. Yeah, it was so cold that all of the chemical reactions in his body ceased. Sorry. We, uh, yeah, we used him as a dielectric material in a tiny qubit. And then we quantum-entangled him with another qubit, just to see if we could. Sorry. Yeah, anyway, we thawed him out after two weeks and apparently he's doing fine now. Didn't really teach us anything about how quantum processes work in biological systems, but it sure was, uh, cool. If you'll pardon the pun.

[asomaton]

I looove that quantum computers look, you know, LIKE THAT ™

Like a clockwork waiting to chime in a new age (or a bell who may toll for all of us).

Next step is pentagrams and runes instead of circuits.

How many angels can dance on top of a qubit chip? Immeasurable

[stormy-skyzzzzzz]

“If the Universe was designed, it seems, the designer is a programmer.”

Black Holes: The Key To Understanding The Universe, Brian Cox and Jeff Foreshaw

[wikipediapictures]

Quantum computing

[mindblowingscience]

The potential of quantum computing is immense, but the distances over which entangled particles can reliably carry information remains a massive hurdle. The tiniest of disturbances can make a scrambled mess of their relationship. To circumvent the problem, quantum computing researchers have found ways to stabilize long lengths of optical fibers or used satellites to preserve signals through the near-vacuum of space.

Continue Reading.

[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

[cslearninghub]

Quantum Computing 101: What are Qubits?

Curious about quantum computing? Let's break it down!

🔍 What’s a Qubit? A qubit is the basic unit of quantum information. Unlike classical bits (0 or 1), qubits can be 0, 1, or both at the same time thanks to a phenomenon called superposition.

✨ Why Is This Cool?

Superposition: Allows qubits to explore many possibilities simultaneously.

Entanglement: Qubits can be linked, so the state of one affects the state of another, no matter the distance.

⚙️ In Action: This means quantum computers can tackle complex problems faster by processing a huge number of possibilities at once!

Follow for more insights on the future of tech! 🚀✨

Instagram: cs_learninghub YT: CS Learning Hub

[materialsscienceandengineering]

Unique magnetic properties of 2D triangular lattice materials have potential applications for quantum computing

Researchers from a large international team, including ANSTO, have investigated the magnetic properties of two unique 2D triangular lattice antiferromagnetic materials (2D-TLHAF) using various neutron scattering techniques. Multiferroic materials are being explored for use in advanced computers. Their quantum properties make them suitable for future computing applications, as they can manage and process the significantly larger volume of information more efficiently. Additionally, the unique properties of 2D magnets, such as flexibility and stackability, which is an ability to control layers of quantum devices or materials to create more efficient systems, have applications in magnetism and spintronics. The materials, hexagonal h-Lu0.3Y0.7MnO3 and h-Lu0.47Sc0.53FeO3, are a type of frustrated antiferromagnet, which means that the spins of the atoms in the material cannot all align in a way that minimizes their energy due to the triangular arrangement of the lattice.

Read more.

[frenzyarts]

Just learned about superdense coding and that shit is SO COOL. Two for the price of one… quantum style 😎

[uncontrolledfission]

Why should you care about quantum computers?

Post #5 on Physics and Astronomy, 23/09/23

Welcome back. It’s been a while. 

First, let’s backtrack. What even are quantum computers?

Today’s computers are run on bits. These are the smallest increment of data on a computer, and are run in binary–they can be in the state of either 0 or 1. This essentially corresponds to two values: off and on. 

This, therefore, means that information can only remain in one, definite state. 

So, what makes quantum computers so different?

A quantum computer is run on qubits (short for quantum bits). Qubits, instead of a single state, can remain in an arbitrary superposition of states (meaning it’s not in any specific state until it’s measured). Qubits, on their own, aren’t particularly useful. But it performs one, very useful, function: it can store a combination of all possible states of the qubit into one area. This means that complex problems can be represented differently in qubits compared to bits. 

Quantum computers aren’t fully developed and at their full capacity quite yet. So far, there’s nothing a quantum computer can do that a regular supercomputer cannot. However, this opens an opportunity for some wonderful new things to happen. 

One of these things can include the cracking of passwords. 

Today’s encryption works by using “trapdoor” functions, which means that data is easy to compute in the forward direction, but extremely difficult to crack in the reverse without special keys. Keywords, ‘extremely difficult’; it is not impossible. However, this is not a massive concern: encryption works on the basis that it would simply take too long to crack.

To give you a tangible example, 100,003 and 131,071 are relatively easy to multiply together, giving you the answer 13,107,493,213. How easy, however, would it be to determine a prime factor pair of this number? It would take a computer a long time to figure this out, since it runs on bits, which can only show one definite state of data.

With quantum computers, it’s different. As aforementioned, qubits can remain in a superposition of states; somewhere in there, the desired answer lies. It’s just a matter of obtaining the resources to make this happen. 

Don’t worry, though. Ordinary people aren’t at any risk quite yet.

[nerdymemes]

[diablo1776]

Fucking Skynet once they load AI on it if they haven't already.

[galaxymagitech]

Spent quantum computing lecture doodling Batman characters in pure confusion.

Behold, the fruits of my labors!

Here we have Oracle, Robin V, Red Hood, Nightwing, Robin IV, and a sleeping Robin III, accompanied by something about representing complex numbers with e, phase shifts, and single-qubit gates.

Now we’re onto two-qubit gates, something about superposition, and now we have a universal gate set (which the instructor was literally grinning and laughing about). Plus Tim waking up “early” (11:46 am) and a tiny Robin hiding in Batman’s cape.

Notes about measurement collapsing the quantum state. A coin flip was mentioned, so there’s an obligatory Two-Face doodle and metaphor.

[youare-number6]

How to Make - Operate -- Quantum Computers Pt 1

Futuristic Quantum Computing with instructions!

[mindblowingscience]

For most of us, the passage of time flies in just one inexorable direction. But for theoretical quantum physicists, time's direction isn't quite so inflexible. It's possible to theoretically model, simulate, and observe the backwards flow of time in ways that are impossible to achieve in the real world. And now, scientists have shown that simulations of backwards time travel can help solve physics problems that cannot be resolved with normal physics. Led by physicist David Arvidsson-Shukur of Cambridge University, a team of physicists conducted an experiment in which the input state can be altered by simulating a backwards loop of time that allows them to alter the parameters after they have already been set. These loops are purely hypothetical, of course – but they can be simulated using quantum teleportation circuits created with entangled particles, in order to mathematically solve problems. "Imagine that you want to send a gift to someone: you need to send it on day one to make sure it arrives on day three," Arvidsson-Shukur explains. "However, you only receive that person's wish list on day two. So, in this chronology-respecting scenario, it's impossible for you to know in advance what they will want as a gift and to make sure you send the right one. "Now imagine you can change what you send on day one with the information from the wish list received on day two. Our simulation uses quantum entanglement manipulation to show how you could retroactively change your previous actions to ensure the final outcome is the one you want."

Continue Reading.

[mysteriousquantumphysics]

Updates from my Quantum Journey

It's been silent on my blog for a while now - the past year has been a busy time for me since I was working on my Master's thesis as well as working as a research assistant at Fraunhofer in parallel. Both were great experiences but it became so time-consuming that I totally lost track of posting any content on this blog!

In April 24 I finished my Master's Thesis in Physics in which I was mainly working on tensor networks. We tried to make DMRG (Density Matrix Renormalization Group) for Quantum Chemistry-like setups more efficient by lifting degeneracies in the symmetry sectors of the tensor network structure. Besides from what I learned on the physics-side of this project, it helped me to foster my fascination for method-development.

My work at Fraunhofer was very rewarding as well - I did not only learn a lot, I also had the chance to contribute in two publications in the area of quantum circuit cutting. In case you are interested, I could write a blog entry for one or both of the papers(:

During all this hard work and (to be honest) frustration and exhaustion in the past year I had this optimistic hope of doing a PhD after finishing my Master's degree. Now, this dream has become a reality and I started my PhD at the Technical University of Munich this month. I am really grateful for this oppurtunity in which I can work full-depth in the field of quantum computing - with a strong focus on software/method development. I am excited about what this journey has to offer and I am very much looking forward to it!