Natalie Parham

quantum computing, cs theory phd student @columbia

[Isaac Kim @Isaac__kim]

I've been sitting on this result for some time because it seemed too crazy to be true. I really hope I didn't make any stupid mistakes! https://t.co/OwlAAlCwKA A 🧵 on why I think this is a rather strange result.

[Natalie Parham @nat_parham]

In particular, KGP also used that stabilizer states have discrete mutual information, and WL also identified the infectiousness property, proving an exact version. (9/9)

[Natalie Parham @nat_parham]

I have a new paper out: "Quantum Circuit Lower Bounds in the Magic Hierarchy".🔮🪜
https://t.co/jhWR5WBq4g
a thread:

[Natalie Parham @nat_parham]

I'd also like to highlight great recent work by Korbany–Gullans–Piroli (https://t.co/a2qctSdTZk) and Wei–Liu (https://t.co/UcGcvGHp3Q), who independently proved lower bounds for these circuits from a condensed matter perspective. (8/9)

[Harvard University @Harvard]

“No government—regardless of which party is in power—should dictate what private universities can teach, whom they can admit and hire, and which areas of study and inquiry they can pursue.” - President Alan Garber https://t.co/6cQQpcJVTd

[Natalie Parham @nat_parham]

@traditionalboi @henryquantum @GoogleQuantumAI Thanks Adam!

[Natalie Parham @nat_parham]

Aw thanks @henryquantum! And huge thanks to @GoogleQuantumAI, I’m so very grateful for the support.

[Henry Yuen @henryquantum]

Natalie Parham (@nat_parham), a PhD student who I am proud to call myself an advisor to, is one of the recipients of the Google PhD Fellowships in Quantum Computing. Congrats Natalie! Here's a nice Q&A with her: https://t.co/De4Usg1ClV. Be on the lookout for what she does next.

[Natalie Parham @nat_parham]

Beautiful! It's cool to see this problem resolved!

[Henry Yuen @henryquantum]

Parity is not computable by subexponential-size QAC0 circuits -- new paper by @quantumashley, Shao and Verdon. I'm happy to see this question resolved! I look forward to reading their paper more closely... https://t.co/gZwist9ZAn

[Steve McCormick @Quasilocal]

Sneak peek into how math research is done

[Natalie Parham @nat_parham]

@ang3linawang @CornellInfoSci @cornell_tech @StanfordHAI @sanmikoyejo Huge congrats Angelina!!! I’m so grateful for u for inspiring me to consider research way back when :) Cornell is so lucky to have you!

[Natalie Parham @nat_parham]

hwqd to those that celebrate

[Columbia Quantum Initiative @ColumbiaQuantum]

Happy World Quantum Day from some quantum Columbians!

[Natalie Parham @nat_parham]

We conjecture that our spectral concentration bound holds without this dependence on aux. qubits.

This would immediately imply that polynomial-size QAC0 circuits cannot compute the parity function -- resolving a > 20-year-old open question!

[Natalie Parham @nat_parham]

New paper out with @ShivNadimpalli, Francisca Vasconcelos, and @henryquantum!

Linal Mansour and Nisan (LMN) showed that AC0 circuits ≈ low-degree polynomials

We ask: Are QAC0 circuits ≈ low-degree Pauli-nomials?

https://t.co/F1Z0DSvkND

[Natalie Parham @nat_parham]

Our results nearly match those of LMN!

...with the exception of a pesky dependence on the number of auxiliary qubits :(