laura cui

according to other sources commercial panels were only at around 15% a decade ago (when I was learning about energy science in high school the quoted number was around 10%)

also according to wikipedia the record for solar cell efficiency performance in r&d testing is close to 48% which is crazy when you compare to photosynthesis (~5%) and ecological trophic levels (~10%)

video & comments make some very sharp points ("quantum computers are to classical computers what planes are to cars" @ f5673-t1h)

... but I'm actually more amazed by what she said about modern solar panels 🤯 25% efficiency for commercially available panels in 2025 is crazy

One more day, one more chance to pretend that I understand the word "topological"

Adding one more note which I missed from the magic-augmented Cliffords paper

tough crowd

YouTube video by rosc2112 log song

p.s. if our paper had a catchy jingle it would be youtu.be/8-9scNP5KWk?...

"it's log log it's better than bad it's good!"

@dulwichquantum.bsky.social does this count as a meme?

Designs from magic-augmented Clifford circuits We introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-eff...

Finally, highlighting recent concurrent work (arxiv.org/abs/2507.02828) which achieves ~exp k + log log n designs w/ magic-enhanced Clifford circuits, separating n and k 🙌 (but w/ much larger cost in k)

8/8

Our work ties up several loose ends in the random circuit literature 🎀 but there are a few caveats & remaining questions!

One is decoupling k and n dependence: we can only show the lower bound log k + log log n, but our construction has multiplicative dependence log k log log n

7/8

With all the recent progress on designs and random unitaries, you might wonder if it's possible to do even better than log k and log log n

We show that the answer is no, by proving a new lower bound for the circuit depth needed for additive error designs w/ any # of ancillas

6/8

We also introduce a new framework for analyzing experiments on k copies of a unitary w/ processing steps in b/w 🖥️

We call distinguishability in this model "measurable error"

As a bonus we give a short alternate proof of the existence of pseudorandom unitaries w/ our framework!

5/8

A key fact we use is that random unitary statistics look the same (w/ 1/exp error) if we restrict to input spaces w/ k distinct basis states

We project onto alternating local distinct subspaces on which the moments of our circuit are equal to those of fully random unitaries

4/8

Putting these functions on blocks of log n qubits and "gluing" them gets us unitaries that look random on k copies in depth

❇️ log k log log nk w/ ~nk ancillas or

❇️ k log log nk w/ ~n ancillas

in "quasilocal" 1D circuits w/ connections b/w qubits O(log n) distance apart!

3/8

Our work combines efficient classical functions which appear random for any k different inputs (inspired by the PFC ensemble) w/ ideas from gluing

We also swap permutations for *shuffling operators* based on the "nearly random" functions to bring our depth down to log k 🤠

2/8

Title: Unitary designs in nearly optimal depth, Abstract: We construct ε-approximate unitary k-designs on n qubits in circuit depth O(log k log log nk/ε). The depth is exponentially improved over all known results in all three parameters n, k, ε. We further show that each dependence is optimal up to exponentially smaller factors. Our construction uses Õ(nk) ancilla qubits and O(nk) bits of randomness, which are also optimal up to log(nk) factors. An alternative construction achieves a smaller ancilla count Õ(n) with circuit depth O(k log log nk/ε). To achieve these efficient unitary designs, we introduce a highly-structured random unitary ensemble that leverages long-range two-qubit gates and low-depth implementations of random classical hash functions. We also develop a new analytical framework for bounding errors in quantum experiments involving many queries to random unitaries. As an illustration of this framework's versatility, we provide a succinct alternative proof of the existence of pseudorandom unitaries.

What is the min depth you need for a random unitary?

In this work w/ Tommy Schuster, @RobertHuangHY, Fernando Brandão (arxiv.org/abs/2507.06216) we glue random unitary blocks w/ only random phases on log n qubits (fns on log n bits) to get designs in d = log k log log n 🧩

1/8

Digital painting of a sunrise sky, cornflower blue, filled with wispy clouds of bright, fluorescent orange and yellow, and peach and muted purple higher in the frame.

We report that there is something corrosive about this sunrise; acidic orange clouds, biting winds, the light eating houses one after the other. The back wall of our kitchen is about to be swallowed too, all bright and golden. We have to admit that we are not much for mornings.

Not Bullshit