A comparison between the Google estimator U for the fidelity and two improved estimators that we studied MLE (maximum likelihood estimator) and V (a variant of U). (More figures at the end of the post.)
Here are some links on quantum matters. I hope to return to them in more detail in some future posts.
1. A paper with Yosi Rinott and Tomer Shoham on the Statistics of Google’s experiment
Yosef Rinott, Tomer Shoham and Gil Kalai: Statistical aspects of the quantum supremacy demonstration, (arXive)
The notable claim of quantum supremacy presented by Google’s team in 2019 consists of demonstrating the ability of a quantum circuit to generate, albeit with considerable noise, bitstrings from a distribution that is considered hard to simulate on classical computers. Verifying that the generated data is indeed from the claimed distribution and assessing the circuit’s noise level and its fidelity is a purely statistical undertaking.
The objective of this paper is to explain the relations between quantum computing and some of the statistical aspects involved in demonstrating quantum supremacy in terms that are accessible to statisticians, computer scientists, and mathematicians.
Starting with the statistical analysis in Google’s demonstration, which we explain, we study various estimators of the fidelity, and different approaches to testing the distributions generated by the quantum computer. We propose different noise models, and discuss their implications. A preliminary study of the Google data, focusing mostly on circuits of 12 and 14 qubits is discussed throughout the paper.
I am greatly enjoying working with Yosi and Tomer, and I hope to devote a special post to the very interesting statistics of the Google supremacy experiment.
2. My paper The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims
Here is how the paper concludes
Over the past four decades, the very idea of quantum computation has led to many advances in several areas of physics, engineering, computer science, and mathematics. I expect that the most important application will eventually be the understanding of the impossibility of quantum error-correction and quantum computation. Overall, the debate over quantum computing is a fascinating one, and I can see a clear silver lining: major advances in human ability to simulate quantum physics and quantum chemistry are expected to emerge if quantum computational supremacy can be demonstrated and quantum computers can be built, but also if quantum computational supremacy cannot be demonstrated and quantum computers cannot be built.
Some of the insights and methods characteristic of the area of quantum computation might be useful for classical computation of realistic quantum systems – which is, apparently, what nature does.
3. My Dec 2019 surprise lecture and the panel discussion
My Dec 19 2019 (B.C.) surprise lecture at the mathematics of quantum computing school and the afternoon panel on the same day. It turned out that the lecture was videotaped. The slides can be seen in this post. Remarkably, social distancing was pioneered by the session chair toward the end of the lecture (while not justified in that case).
Here once again again is the link for the panel discussion on quantum supremacy of the same day (reviewed here) . Here is a quote of mine from the panel.
Of course, it is important to think what are the implications of quantum supremacy, is it useful? what does it say on the extended Church-Turing thesis? on prospects for quantum error-correction and universal quantum computers? etc. but I think that in the next few years one thing that we need to also concentrate on is the following question: Is the Google experiment correct? Is this a correct scientific verification of quantum supremacy?
4. My July 15 USTLC lecture
Four slides from my USTLC zoom lecture. (Click to enlarge.)
5. A small taste of quantum poetry for the skeptics. (A full post is coming.)
Poems by Peter Shor and Renan Gross (click to enlarge)
Peter Shor pioneered quantum poetry for the skeptics over Twitter. There were many very nice contributions all over social media by Renan Gross, John Dowling, Vidit Nanda, ⟨dl|yonge|mallo⟩, Alfred Marcel Bruckstein, Kenneth Regan, and others. Keep the quantum poems coming! Of course, the poems should be taken with humor. Here is a small taste.
My short response to Peter’s poem
Understanding nature and ourselves is a worthy dream
Requiring no interaction with the supreme
A quantum computer from Google,
Turned the Church-Turing thesis to strudel.
And yet there remain,
Many doubting this claim,
And we lash all of them with wet noodles.
“There once was a quantum computer
Whose pet was a five-legged hamster …”
So Peter and Gil
Their grandchildren will
Tell “…happy they lived ever after”
Avi suggests a kids’ chorus saying “yeah, right” or “sure, sure”, after each line
For sale: quantum computer. Never used.
Another 6-word story (mine) with a rhyme (of some sort)
Michelson and Morley weren’t Google employees.
6. More figures from my paper with Yosi and Tomer.
Various estimators for the fidelity for the Google data compared to simulations.
The model expected values compared to the empirical distribution. On the left for the real data and on the right for simulated data. As it turned out the Google noise model does not fit for the sample data. (Our readout model provides only a small improvement.)
The size biased distribution fits the model very well.