Quantum Computing and the Quest for Quantum Computational Supremacy Scott Aaronson (University of Texas at Austin) SparkCognition, January 22, 2019
The field of quantum computing and information arguably started here in Austin in the early 1980s—with David Deutsch and other students, faculty, and postdocs in physics In this talk, I want to convince you that the impossibility of ubercomputers is also something physicists should think about, and also something that may have implications for physics. Together with colleagues, we’re now seeking to build up a new quantum computing and information presence at UT Austin
Quantum Mechanics “Probability theory with minus signs”
THE RULES: If a system can be in two distinguishable states, labeled |0 and |1, it can also be in a superposition, written |0 + |1 Here and are complex numbers called amplitudes, which satisfy ||2+||2=1. A 2-state superposition is called a qubit. If we observe, we see |0 with probability ||2 and |1 with probability ||2. But if the qubit is isolated, it evolves by rules different from those of classical probability. In the 1980s, Feynman, Deutsch, and others noticed that a system of n qubits seems to take ~2n steps to simulate on a classical computer, because of the phenomenon of entanglement between the qubits. They had the amazing idea of building a quantum computer to overcome that problem
Popularizers Beware: A quantum computer is NOT like a massively-parallel classical computer! Exponentially many possible answers, but you only get to observe one of them Any hope for a speedup rides on choreographing an interference pattern that boosts the amplitude of the right answer
Bounded-Error Quantum Polynomial-Time NP-complete Bounded-Error Quantum Polynomial-Time NP Factoring BQP P
Wait, building a full scalable fault-tolerant QC is how hard? “Quantum Supremacy” For me, the #1 application of quantum computing: disprove the people who say it’s not possible! Interesting Shor 1994: Fully scalable, universal fault-tolerant quantum computers will be able to factor an n-digit integer in only ~n2 steps Wait, building a full scalable fault-tolerant QC is how hard? More immediate way to prove quantum supremacy: sampling tasks. In the near future, could we get a quantum device to sample a probability distribution over n-bit strings (say, n70), such that any classical algorithm would need ~2n steps to sample the same distribution? (But how would we know?)
Random Circuit Sampling What Google is hoping to do in “O(1) years” with its 72-qubit superconducting chip Bristlecone A.-Chen 2017: Proposed a test to apply to the outputs of a random quantum circuit, called “HOG” (Heavy Output Generation). Showed that, under a plausible-looking complexity assumption, there’s no fast classical algorithm to pass the HOG test
Certified Randomness from Quantum Supremacy (A., in preparation) SEED CHALLENGES If a quantum computer repeatedly and quickly solves “HOG” challenges, then under a suitable complexity assumption, we show that its responses must contain lots of entropy; they can’t be deterministic Leads to a scheme to produce public verifiably-random bits for cryptocurrencies, etc.—perhaps with a near-term QC with 50-70 qubits! (1st feasible application of QC??)
Ewin Tang’s Breakthrough (2018) Ewin was a junior in my Intro to Quantum Information Science undergrad course at UT For her senior thesis, she “de-quantized” the main example we’d had of a quantum algorithm thought to get exponential speedup for a real-world machine learning problem: the Kerenidis-Prakash algorithm for recommending products in Netflix-like systems I.e., gave a classical randomized algorithm that was only polynomially slower This was the opposite of what we and others expected, and underscores the need for careful theoretical study of quantum speedups
Summary This is a particularly exciting time for QC. After decades of theory and experiment, we finally look close to getting clear speedups over classical computers for specialized problems, with ~50-70 qubit devices Achieving full scalability and fault-tolerance, and threatening public-key crypto, will take longer Quantum speedups are subtle and depend on structure Not just free exponential parallelism—”weirder than a sci-fi writer would have had the imagination to invent!” At UT, we’re trying to build a QC presence (undergrad courses, students, postdocs, additional faculty…)