Research directions

Fast circuits for quantum multiplication

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 has a sub-quadratic gate count but uses as few as one or two total ancilla qubits. Furthermore it moves a large part of the algorithmic complexity into classical pre-computation, reducing the circuit sizes in practice. (Manuscript in preparation; see Talks section for a talk I recently gave on these results.)

Classically-verifiable quantum computational advantage

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."

Massively parallel numerical quantum dynamics

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.

Talks and presentations

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

About me

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.