Patrick Rall's Homepage

I am a PhD student at the University of Texas at Austin researching at the Quantum Information Center under Prof. Scott Aaronson.

I completed my undergraduate studies at the California Institute of Technology in June 2016. I have a Bachelor of Science in physics (major) and computer science (minor).

Curriculum Vitae List of courses at Caltech

Quantum Circuit Simulation

In Spring 2018 I developed an algorithm for simulating noisy quantum circuits. This randomized protocol can do additive-error probability estimation in polynomial time for stabilizer circuits.

2018: Simulating Quantum Circuits by Shuffling Paulis
quant-ph/1804.05404

Every state and gate has a cost, and the runtime is the product of all the costs. While this product is exponential in the circuit size, the cost of near-Clifford gates is close to 1, and the cost of depolarizing channels is less than 1.

The protocol can efficiently simulate many mixed states that previously did not admit fast simulation. Below are some cross-sections of two-qubit Bloch space, showing stabilizer mixtures in white and the new classically simulable states in gray.

I presented on this algorithm at APS March Meeting 2018. The slides are a bit out-of-date so I'll upload them later.

In early 2016 David Gosset and Sergei Bravyi developed a fast simulator for quantum circuits that extends the Gottesmann-Knill theorem to support T-gates:

Sergei Bravyi, David Gosset: Improved classical simulation of quantum circuits dominated by Clifford gates - quant-ph/1601.07601

Iskren Vankov and I maintain an implementation of this algorithm written in Python and C. We are hoping to test this out on a supercomputer and go for a record-number of T-gates.

CircuitSimulator on GitHub CircuitSimulator Slides

Magic State Distillation

When quantum computers begin to rely on quantum error correction they will face a serious problem: we only know how to implement Clifford operations fault-tolerantly. We can still make such a device universal by preparing certain 'magic' quantum states. Magic state distillation studies the preparation of these states.

In February 2017 I showed that any distillation procedure can be reduced to the signed quantum weight enumerators of a quantum stabilizer code:

2017: Signed quantum weight enumerators characterize qubit magic state distillation - quant-ph/1702.06990

In August 2017 I demonstrated that distillation exhibits fractal properties. Essentially, magic state distillation is about crafting fractals that suit our needs.

2017: Fractal Properties of Magic State Distillation
quant-ph/1708.09256

I won an honorable mention in the Visualising Science Compotition 2017 held annually by the College of Natural Sciences at UT Austin. The image is generated from the Five Qubit code.

UT Austin Visualizing Science 2017

Neutron Star Raytracing

In Spring 2018 I took a course on General Relativity by Dr. Richard Matzner at UT Austin. For our term project Devanshu Panchal and I wrote a raytracing application for visualising various black hole and neutron star metrics. Gravitational Raytracing Term Paper Raytracing Code on GitHub

Pre-graduate Research

At IQIM under Prof. John Preskill, I wrote a matrix product state simulator in Javascript and used it simulate quantum cellular automata.

2015: Quantum Block Cellular Automata Interactive Slideshow

In 2014 I worked in Prof. David Hsieh's laser lab, and assisted Hao Chu with his ultrafast pulsed laser pump-probe experiment.


At the German Aerospace Center, Laksh Bhasin and I analyzed sub-pixel detection algorithms for a robotics sensor.

2013: Sub-Pixel Detection Algorithms for Fiber-Bragg Gratings

I determined the orbit of an asteroid using telescope observations at the Summer Science Program 2011:

2011: Orbit Determination of 1951 Lick

My first research project was to analyze ATLAS detector data under Dr. Richard Nisius at the Max Plank Institute for Physics in Munich.

2011: ATLAS Top-Quark Jet Reconstruction Algorithms

Other code

PatVimLatex - A latex editor for Vim and llpp Three Sided Cards - A flashcard application for Chinese words

Last update: May 2018