Marek GluzaJul 22, 2023

Here's an #introduction of @frederikhahn as part of my agenda that #nice should be a characteristic demanded of academics.

In the past few years Freddy has been gently cracking his head on how to remove bottlenecks in a #quantumNetwork. He focused on relevant #quantum states and tweaked their parts like he tweaks parts in his bike to make it run seamlessly
https://arxiv.org/abs/1805.04559
(Local complementations interest me for #quantumCompiling: the unitary encoding the repetition code can be turned into a gate between any two qubits because one can distill Bell pairs out of #GHZ states.)

Rick came from Berlin to the #quantumInformation #workshop in #benasque by train. His tap water canister was half empty: he realized that meh whatev he can travel half Europe and not eat if the food is not what he wants provided he has water to last him even more than 24 hs.

Frederik is a scientist who leads by example, is sustainably concerned about the #climateCrisis but look at him shining. His #intermittentFasting skills allowed him to be chilled after a strainous long distance travel but I learn from him that being nice and chilled is a muscle we can all train.

His integrity at work reminds me that it's not impossible to keep our humanity first and also excell at research. I wish we had an equivalent of #citationMetrics for acts of kindness in academia.

These photos were taken on a Friday, on Monday that week he defended his thesis. In style, which is his style. For his #phd hat I'd add a phone charger, his daily cycling suffices to top up the battery. I don't know how to symbolize my thanks for having made my local science world wholesome, one #introvert thought at a time, but: thank you for caring, Dr Hahn!

Quantum network routing and local complementation

Quantum communication between distant parties is based on suitable instances of shared entanglement. For efficiency reasons, in an anticipated quantum network beyond point-to-point communication, it is preferable that many parties can communicate simultaneously over the underlying infrastructure; however, bottlenecks in the network may cause delays. Sharing of multi-partite entangled states between parties offers a solution, allowing for parallel quantum communication. Specifically for the two-pair problem, the butterfly network provides the first instance of such an advantage in a bottleneck scenario. The underlying method differs from standard repeater network approaches in that it uses a graph state instead of maximally entangled pairs to achieve long-distance simultaneous communication. We will demonstrate how graph theoretic tools, and specifically local complementation, help decrease the number of required measurements compared to usual methods applied in repeater schemes. We will examine other examples of network architectures, where deploying local complementation techniques provides an advantage. We will finally consider the problem of extracting graph states for quantum communication via local Clifford operations and Pauli measurements, and discuss that while the general problem is known to be NP-complete, interestingly, for specific classes of structured resources, polynomial time algorithms can be identified.

arXiv.org
Marek GluzaJul 13, 2023

Adrián Pérez-Salinas coordinated a #benasque session on variational #quantum algorithms. Here's the story what I think I learned :)

People now say various things about the state of the field.
It was clear to me from the very beginning that there will be trainability issues and you can verify it because I haven't written a single paper involving brute force training of circuits.

But.

While, I have been avoiding reading papers on VQAs (until I needed to cite variational diagonalization in context of my proposal to use double-bracket flows for diagonalization on quantum computers), now that the field has reached a milestone, here's a few insights I really like and claim will matter down the line:
- statements about #barrenPlateaus are quantitative
- appearance of barren plateaus is implied by presence of #t-design properties https://arxiv.org/abs/2101.02138
- plateaus result from high dimensionality of the training parameter set.

To paraphrase grandmaster Bronstein, it's not about what but how.
We now know very, very well how VQAs go wrong. Early on it was only clear what the problem will be.

Each of the points above can guide better #ansatzae:
- they need to operate on clumped circuits to reduce the dimensionality
- they shouldn't rotate back and forth but use physics equations to guide the #quantumCompiling
- a restricted ansatz with justified expressibility can be quantitatively tested using the average+variance criteria of regular barren plateaus.

What the field achieved is to inform a large group of people how to recognize what a good variational ansatz will be once we will encounter it.

And that it will not be naive? Come on, easy would have been boring.

Connecting ansatz expressibility to gradient magnitudes and barren plateaus

Parameterized quantum circuits serve as ansätze for solving variational problems and provide a flexible paradigm for programming near-term quantum computers. Ideally, such ansätze should be highly expressive so that a close approximation of the desired solution can be accessed. On the other hand, the ansatz must also have sufficiently large gradients to allow for training. Here, we derive a fundamental relationship between these two essential properties: expressibility and trainability. This is done by extending the well established barren plateau phenomenon, which holds for ansätze that form exact 2-designs, to arbitrary ansätze. Specifically, we calculate the variance in the cost gradient in terms of the expressibility of the ansatz, as measured by its distance from being a 2-design. Our resulting bounds indicate that highly expressive ansätze exhibit flatter cost landscapes and therefore will be harder to train. Furthermore, we provide numerics illustrating the effect of expressiblity on gradient scalings, and we discuss the implications for designing strategies to avoid barren plateaus.

arXiv.org