maiden name: Greg Meyer

Some of the most important quantum algorithms, including Shor's algorithms for factoring and discrete logarithms, require performing multiplication on superpositions of integers.
The standard algorithm for multiplication, known as the "Schoolbook algorithm," requires a number of operations that is quadratic in the length of the inputs.
In the classical setting, faster algorithms have been known for decades, but building quantum circuits that implement them has been challenging---especially because the structure of the fast algorithms tends to require a large number of ancillas.
I designed a **new algorithm for quantum multiplication which simultaneously achieves a gate count nearly linear in the input size, yet requires zero ancilla qubits.**
Furthermore it moves a large part of the algorithmic complexity into classical pre-computation, reducing the circuit sizes in practice.
See paper here.

Recent experiments have performed quantum computations that seem to be infeasible to reproduce with even the world's most powerful supercomputers.
However, a subtlety of those experiments is that the output of the computations is also computationally hard to verify---for the largest computations, it is not possible to directly show that the results are actually correct.
Much of my PhD work focused on **tests of quantum computational advantage that are efficiently verifiable by classical computers, while still remaining hard to spoof.**

Some of my results include:

- I broke a cryptographic proof of quantumness protocol that had stood for over a decade, by discovering a classical algorithm to extract its secret key.
- I then published a new proof of quantumness protocol for which spoofing the results is provably as hard as integer factorization, but which is more feasible than Shor's algorithm to implement in the near-term.
- I worked with experimentalists to perform a first small-scale demonstration of that protocol, using mid-circuit measurements to implement a quantum interactive proof in practice.
- I also worked with theory colleagues to improve the protocol further and extend its applicability, showing that it can also be used to constrain the behavior of an untrusted quantum device via cryptographically "certified qubits."

Numerical study has proven to be one of the core tools for exploring the emergent properties of many-body quantum systems.
I am the main author of the dynamite library, which provides **extremely fast time evolution and eigensolving for numerical quantum many-body spin chain physics, parallelized using MPI and GPU acceleration**.
The backend is written in C and CUDA C++; the library exposes a Python frontend with an intuitive interface for building and analyzing spin chain Hamiltonians.
The library is already being used by a number of labs; a list of publications using it can be found on the project's homepage.
I have published works that use dynamite to explore Floquet prethermalization, time crystals in such a prethermal phase, and many-body chaos in the Sachdev-Ye-Kitaev model.
(The manuscript officially releasing dynamite is in preparation).
I also have published works using the LOBPCG algorithm to drastically reduce memory usage for mid-spectrum eigensolving of large many-body quantum Hamiltonians, in particular to explore the phenomenon of many-body localization.

I was involved with the following organizations during graduate school; feel free to contact me or follow the links below if you're interested in getting involved!

Student group for the LGBTQ+ community in Berkeley Physics. I served as an officer.

Annual workshop aimed at improving department climate and preventing sexual violence and sexual harassment. I served each year as a facilitator, and helping to organize the workshop.

Teaching science lessons to elementary school students around the Bay Area. I participated as a teacher, and a member of the Steering Committee.

If you would like me to speak, feel free to contact me!

**2024-05-16**, Google Quantum AI.

*Qualtran group meeting*.

"Fast integer multiplication without ancillas." (1 hr) [slides]

**2023-11-02**, University of Hawaiʻi at Mānoa, Department of Physics and Astronomy.

*Department colloquium*.

"How to prove you have built a quantum computer." (1 hr) [slides]

**2023-10-26**, Google Quantum AI.

*Seminar*.

"Fast integer multiplication with very few ancillas." (1 hr) [slides]

**2023-10-25**, Caltech Institute for Quantum Information and Matter.

*IQIM seminar*.

"Fast integer multiplication with very few ancillas." (1 hr.) [slides]

**2023-10-20**, MIT Quantum Information Science group.

*Quantum Information Processing Seminar*.

"Fast quantum integer multiplication with very few ancillas." (1 hr) [slides]

**2023-10-19**, Harvard University.

*Quantum information seminar*.

"Fast quantum integer multiplication with very few ancillas." (1 hr) [slides]

**2023-07-14**, Simons Institute Summer Cluster Workshop.

*Lightning talk*.

"Fast integer multiplication with almost no ancillas." (20 min) [slides] [video]

**2023-03-01**, IBM Quantum.

*Guest seminar*.

"Cryptographic protocols for classically-verifiable quantum advantage and more." (1 hr) [slides]

**2022-08-04**, CLEAR Project.

*PubScience*.

"Quantum computing: how to do math with atoms, and how to trust the answers" (1 hr) [slides]

**2022-05-03**, UC Berkeley.

*Guest lecture, CHEM 195/295: Special topics in Quantum Computing*.

"Classical verification of quantum computation." (1.5 hr) [slides]

**2022-03-15**, APS March Meeting.

*Quantum Digital and Analog Algorithms [Focus] (invited)*.

"Classical verification of quantum computational advantage." (30 min) [slides]

**2022-02-22**, Harvard University.

*CMT Kid's Seminar*.

"Classical verification of quantum computational advantage." (1 hr) [slides]

**2022-02-09**, Quantum Systems Accelerator (QSA).

*Science session*.

"Classical verification of quantum computational advantage." (15 min) [slides]

**2021-11-10**, IBM Quantum.

*Quantum computing seminar*.

"Classical verification of quantum computational advantage." (1 hr) [slides]

**2021-10-08**, MIT cryptography and information security.

*CIS seminar*.

"Classical verification of quantum computational advantage." (1.5 hr) [slides]

**2021-09-29**, NSF Challenge Institute for Quantum Computation (CIQC).

*Colloquium introduction*.

"Computability and complexity (introducing Jarrod McClean)." (20 min) [video]

**2021-09-28**, Physics of Information and Quantum Technologies, IT Lisbon.

*Group meeting*.

"Classical verification of quantum computational advantage." (45 min)

**2021-07-14**, Simons Institute for the Theory of Computing.

*Quantum Wave in Computing Reunion*.

"Classical verification of quantum computational advantage." (45 min) [video]

**2021-05-21**, MIT Quantum Information Science group.

*Quantum Information Processing Seminar*.

"Classical verification of quantum computational advantage." (45 min)

**2021-04-26**, UT Austin quantum information center.

*Group meeting*.

"Classical verification of quantum computational advantage." (45 min)

**2021-04-23**, AIDE-QC.

*All hands meeting*.

"Classical verification of quantum computational advantage." (20 min)

**2021-04-21**, Quantum Systems Accelerator (QSA).

*Science session*.

"Classical verification of quantum computational advantage." (15 min)

**2021-02-01**, Quantum Information Processing (QIP 2021).

"An efficiently-verifiable test of quantum advantage." (poster)

**2020-08-26**, AIDE-QC.

*Verification and debugging thrust meeting*.

"Efficiently-verifiable quantum advantage."

**2020-06-02**, APS DAMOP 2020.

"An efficiently-verifiable test of quantum advantage." (poster)

**2019-05-30**, APS DAMOP 2019.

"A numerical study of many-body localization using LOBPCG." (poster)

**2018-03-08**, APS March Meeting 2018.

"A long range, pre-thermal time crystal in one dimension." (15 min)

**2017-06-07**, APS DAMOP 2017.

"Simulation of quantum many-body dynamics for generic strongly-interacting systems." (poster)

See my page at Google Scholar

(GDKM = Gregory D. Kahanamoku-Meyer)

GDKM. **Exploring the Limits of Classical Simulation: From Computational Many-Body Dynamics to Quantum Advantage.** Ph.D. dissertation, University of California at Berkeley, 2023 [link]

GDKM, N. Yao. **Fast quantum integer multiplication with zero ancillas.** arXiv:2403.18006 [arxiv]

GDKM. **Forging quantum data: classically defeating an IQP-based quantum test.** Quantum 7, 1107 (2023) [arxiv + journal]

Z. Brakerski, A. Gheorghiu, GDKM, E. Porat, T. Vidick. **Simple Tests of Quantumness Also Certify Qubits.** CRYPTO 2023 [arxiv] [conf. proceedings]

GDKM^{*}, D. Zhu^{*}, L. Lewis, C. Noel, O. Katz, B. Harraz, Q. Wang, A. Risinger, L. Feng, D. Biswas, L. Egan, A. Gheorghiu, Y. Nam, T. Vidick, U. Vazirani, N. Yao, M. Cetina, C. Monroe. **Interactive cryptographic proofs of quantumness using mid-circuit measurements.** Nat. Phys. 19, 1725–1731 (2023) [arxiv] [journal]

^{*} Co-first-authored paper

GDKM, S. Choi, U. Vazirani, N. Yao. **Classically-verifiable quantum advantage from a computational Bell test.** Nat. Phys. 18, 918–924 (2022) [arxiv] [journal]

R. Van Beeumen, K. Ibrahim, GDKM, N. Yao, C. Yang. **Enhancing scalability of a matrix-free eigensolver for studying many-body localization.** The International Journal of High Performance Computing Applications, 36(3), 307–319 (2022) [arxiv] [journal]

B. Kobrin, Z. Yang, GDKM, C. Olund, J. Moore, D. Stanford, N. Yao. **Many-Body Chaos in the Sachdev-Ye-Kitaev Model.** Phys. Rev. Lett. 126, 030602 (2021) [arxiv] [journal]

F. Machado, D. Else, GDKM, C. Nayak, N. Yao. **Long-Range Prethermal Phases of Nonequilibrium Matter.** Phys. Rev. X 10, 011043 (2020) [arxiv] [journal]

R. Van Beeumen, GDKM, N. Yao, C. Yang. **A scalable matrix-free iterative eigensolver for studying many-body localization.** HPCAsia2020: Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region (2020) [conf. proceedings]

F. Machado, GDKM, D. Else, C. Nayak, N. Yao. **Exponentially Slow Heating in Short and Long-range Interacting Floquet Systems.** Phys. Rev. Research 1, 033202 (2019) [arxiv] [journal]

Publications and conferences for which I have reviewed papers include npj Quantum Information, QIP 2022, QCE 2023, QIP 2023, QIP 2024, and TQC 2024.

I grew up in Vermont, and enjoy archery, bouldering, Ultimate, and generally being outdoors.

My family is German and Czech, the name "Kahanamoku" comes from my spouse, who is Hawaiian.

I speak English natively, French conversationally, Spanish shabbily, and Hawaiian enough to say I'll do the dishes.

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