Jordan
Taylor
Academic Bio
Tensor networks, wavefunction branches, AI safety.
I'm a PhD candidate at the University of Queensland, Australia, under Ian McCulloch. I've been working on new "tensor network" algorithms, which can be used to simulate entangled quantum materials, quantum computers, or to perform machine learning.
I'm also interested in AI safety: working on interpretability, evaluation, and (mis)generalization properties of machine learning systems. I wrote a guide to graphical tensor notation for mechanistic interpretability, did a machine learning/ neuroscience internship in 2020/2021, and attended the Machine Learning for Alignment Bootcamp in Berkeley, 2022. I also wrote a post exploring the potential counterfactual impact of AI safety work.
I've just finished a paper using quantum circuit complexity to define wavefunction branches. The idea is that you can treat terms in a superposition as effectively decohered "branches" if getting relative-phase information between them is much harder than distinguishing them.
Contact me: jordantensor [at] gmail [dot] com Also see my CV, LinkedIn, or Twitter.
Defining wavefunction branches
Wavefunction branching: when you can't tell pure states from mixed states
Jordan K. Taylor and Ian P. McCulloch (2023)
Jordan K. Taylor and Ian P. McCulloch (2023)
Ian McCulloch and I recently proposed a criterion for finding effectively decohered wavefunction "branches" in arbitrary quantum states, without the need for a system / environment split. We say that branches are defined if you can write your quantum state as a superposition of terms which are easy to distinguish, but hard to interfere (as measured by the number of local operations required).
We argue that these branches
Allow the full state to be replaced with a probability distribution over the branches
Only grow "further apart" for exponentially long times under natural time evolution
Tend to absorb spatial entanglement
Are strengthened by the presence of conserved quantities
Are effectively the opposite of good error correcting codes
We conjecture that branch formation is a ubiquitous process in nature, occurring generically in the time evolution of many-body quantum systems (even when there is no clear "environment"). We're currently looking for branches in various numerical time evolution simulations, by developing an algorithm to find them tensor-network states.
Check out the paper or the poster! We give many examples of states with good branch decompositions.
Good branches are effectively the opposite of good error-correcting codes.
The complexity of distinguishing two states |a⟩ and |b⟩ is ~ the size of the smallest circuit satisfying this (~ swapping |a⟩+|b⟩ with |a⟩-|b⟩ ).
The complexity of interfering two states |a⟩ and |b⟩ is ~ the size of the smallest circuit satisfying this (~ swapping |a⟩ with |b⟩ ).
Graphical tensor notation for interpretability
A tutorial applying Penrose graphical notation to mechanistic interpretability: understanding how Transformer AI systems like GPT work, and the most basic kinds of algorithms they can learn internally. As well as AI systems, I also apply the notation to the singular value decomposition and its higher-order extensions, and introduce tensor-network decompositions.
Detecting beeps from brains
The result of a two month internship at Max Kelsen, applying machine learning to neuroscience research. I used data from a few neurons in the brains of rats to predict the timing of audio beeps they were hearing. I applied unsupervised clustering techniques, as well as supervised neural networks and gradient-boosting. I found interpretability tools to be vital for increasing generalization robustness to new neurons, new sessions, new audio tones, and new rats.
Solving PDEs in parallel
Iterative implicit parallelisation of the Crank-Nicolson method
J. K. Taylor, M. W. J. Bromley, L. Rabenhorst, M Richards (2020)
J. K. Taylor, M. W. J. Bromley, L. Rabenhorst, M Richards (2020)
A pretty simple new method to run the Crank-Nicolson method in parallel. This is a method for implicitly solving partial differential equations (PDEs) like the time-dependent Schrodinger equation. Our parallel modification provides a speedup even though it increass compute usage, and extends the Crank-Nicolson method to allow it to hande PDEs with non-linear terms. C++ code is available at https://github.com/jordansauce/iterative_parallel_CN
Simulating atomic clocks
Hyperpolarisability calculations for optical lattice atomic clocks (Honours thesis)
Jordan K. Taylor, supervised by Michael W. J. Bromley (2019)
Jordan K. Taylor, supervised by Michael W. J. Bromley (2019)
I ran numerical calculations to characterize errors in the world's most accurate atomic clocks. Specifically, AC-stark frequency shifts induced by the trapping laser in strontium optical lattice clocks. The effects of these frequency shifts can be partially cancelled by operating the trapping laser at a "magic wavelength", so the characterizing the dominant further errors required going to 4th order perturbation theory, calculating the "hyperpolarisability" of strontium using C++ code.
Talks
My PhD confirmation talk on isometric tensor networks and gauge fixing (July 2021)
Connections between tensor networks and machine learning (May 2021)
Other slides
