A research paper has been published in *Nature* detailing Google’s quantum supremacy experiment. Link

The idea of quantum supremacy is to find a testbed where quantum computers outperform classical computers. In the specific case, the calculation was very much related to the theory of quantum computing itself: not only the calculation is performed with a quantum computer, but it calculates quantities that refer to a quantum computation. Yes, it’s a bit “meta”.

The calculation is that of sampling a probability distribution. If you ask some acquaintances how tall they are, you are sampling from the probability distribution of heights in humans. More precisely, there may well be some hidden correlations that actually mean that your sampling is biased: it is not just that of the heights of living humans, but very likely of those living near to you (if you live in Sweden, the emerging distribution may differ considerably from Italy).

Similarly, it is possible to construct quantum experiments such that the outcomes of each experimental measurement belongs to a probability distribution which is hard to compute. If one were to randomly initialize N qubits, the outcomes would span the exponentially large configuration space, 2^N. If the qubits where completely “randomly initialized”, each possible outcome would take the same probability. Instead, what was done in the quantum supremacy experiment, was much more convoluted — in order to obtain a probability distribution that is hard to guess or simulate without a quantum computer. What that may be? Well, the outcome of measuring a many-qubit quantum state after several gates are applied to it in a run, and then feeding the measured state at the end of the run again to the same set of gate operations, which is called a quantum circuit.

Researchers at Google first performed the trials on a small number of qubits, which could be easily simulated on a normal computer. Then they scaled up the number of qubits, and of multiple runs, testing the performance of the quantum computer. They were able to test quantum circuits involving a number of qubits that in general would make the calculation unfeasible to test, but they exploited the inner structure of such quantum circuits to find patterns that could be easily simulated on a non-quantum computer.

Then they cranked up also the “difficulty” knob, and performed some measurements that could not be tested on any other non-quantum computer. Their estimate in this hard cases would require thousands of years to check.

Shortly before the publication of the paper in Nature, and shortly after its leak on a NASA server (NASA Quail collaborates with Google on a long-standing basis and also did for this paper, among with researchers from other institutions), IBM Research scientists uploaded to the arXiv, the physics online archive, a paper that confuted that estimate. It was shown how a mix of modern techniques in tensor network description and high performance computing protocols could be adopted to cut down the simulation time on even the world fastest supercomputer to days (“Summit” is made by IBM and operated at on of US national labs, Oak Ridge).

IBM’s paper claims even more generally that any such algorithm run on the Sycamore chip designed by Google, even for much deeper quantum circuits, the scaling of the resources would be linear in the classical simulation. Link

The reported errors on the single-qubit operations were around 0.1%, which means that one can manipulate a qubit around 1000 times before it looses coherence. You can learn more from John Martinis talk on the experiment. Link

Interestingly, the kind of gates that are used to control the qubits, iSWAP-like, are also very natural choice for quantum simulation, since they implement interactions typical of spins or particles. This may be one of the most interesting realistic applications for quantum devices in the short term, as also pointed out by David DiVincenzo. Link

If you are into coding, here is a sneak-peak tutorial into looking for yourself what the theory behind the experiment can look like. Link

This experiment generated a huge quantity of articles. Alphabet CEO Sundar Pichai wrote a blog post. Link

Ivanka Trump tweeted about the quantum supremacy experiment. While she has been scathed for underscoring the administration involvement in the result, I would still agree on the fact that this was a concerted effort (involving researchers from all over the world), but fueled by sustained US federal funding over many years (including before Martinis lab became Google’s). Link

For the future, Google aims to upgrade its chips to one million qubits, exploiting one of the crucial advancements implemented in Sycamore, the adjustable couplers for each qubit in the chip, and for two-qubit gates, a technology pioneered at MIT’s Lincoln Lab in Will Oliver group, who as one of the referees for *Nature* also wrote a comprehensive and clear commentary. Link

*Nature* also interviewed some of the other players in this space to ask what is beyond quantum supremacy. Link

This is a collection of my articles on quantum technology, part of my Quantum Tech Newsletter. You can read the original posts also on Medium:

- Quantum Supremacy
- Analog Computing
- Quantum Internet
- Quantum Games
- Open-Source Quantum Tech
- Quantum Machine Learning
- Space Quantum Communication

© Nathan Shammah — 2017 and beyond.