Can we conclude that errors on Sycamore are Poisson-distributed Pauli errors?

Question

In Martinis' recent Caltech lecture on the Sycamore paper, he appears to make much of the fact that FIG. 4 of the paper show straight-line fidelity - that is, the fidelity decreases log-linearly with an increase in the number of qubits, and an increase in the depth (number of gates) of the circuit.

I believe a position of Martinis is that the scientific value of Sycamore, which is independent of the claims of supremacy, is that errors can be modeled collectively as digital Pauli errors, and further these errors are independently distributed and don't cluster. This seems to conflict with, for example, Kalai's objection to quantum computing that errors collude and coordinate with increasing qubit count/depth.

Martinis notes that "high school probability" can be used to model the decrease in fidelity with an increase in qubit count/gate count.

But what is this "high school probability" that Martinis refers to?

If I were to model insertion of errors into a large-depth circuit, I might decide, with probability $p$, to insert a randomly selected Pauli error (bit-flip and/or phase shift) between any two gates. The probability would be independent of the depth/qubit count of the circuit.

Is this "Poisson-process" of error-insertion similar to the high school probability to which Martinis refers?

Answer 1

The model's accuracy is purely empirical observation. The error trend (Fig 4, or 41:50 in the video) demonstrates that the error of the system (cross entropy fidelity with respect to simulated results) is tracked closely by the "high school probability" model he mentions.

The way this basic model would work is to assume 1- and 2-qubit gate errors are Markovian (time-independent) and also occur independently of other qubits' behavior and then take the product of all the fidelities of gates acting on a single qubit as its total error at measurement time. So if I have the circuit $X(q_0) CNOT(q_0, q_1) X(q_0)$ with an X-gate fidelity of 95% and a CNOT fidelity of 90%, I might say the total error (before applying measurement error) on $q_0$ is $.95 \times .90 \times .95 = 82\%$ and the error on $q_1$ is $90\%$. This probably isn't the exact way they implemented this but it captures how you can might predict the fidelity of the full circuit assuming that qubit errors occur independently.

This seems to conflict with, for example, Kalai's objection to quantum computing that errors collude and coordinate with increasing qubit count/depth.

That objection is probably still valid in general. Since this model's performance was an empirical observation using the results of a specific family of circuits, the validity of such a model won't necessarily generalize to more complicated circuits. Its likely that there will be types of circuits for which correlated errors contribute significantly to the output accuracy.