In 2019, Google claimed that they have achieved quantum supremacy/advantage with their 53 qubit quantum processor Sycamore. The paper is here. But I have not even been able to find what their algorithm is called. I know that is just a sampling problem. How would I go to create a similar sampling for a smaller circuit (say 5 qubits) using Qiskit?

I have checked this good 3-part series of questions Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 1): choice of gate set. Yet I am still unable to understand from where to start. Does Qiskit have predetermined functions for this purpose? Especially on how would I go to confirm it out later? My key issue here is that I do not know the name of the algorithm so I only have Google experiment related sources.

I am not concerned with the issue that they may have achieved quantum supremacy or not.


1 Answer 1


the benchmarking method used in this paper is called cross entropy benchmarking (XEB). An example circuit implementation for a 5 qubit XEB sequence is shown in fig. 3 of the paper.

For further info, I recommend looking at the supplementary information (SI) of this paper, particularly fig. S15. Another source of info for 2 qubit XEB and the cross entropy calculation for a small number of qubits can be found in section D of the SI here: https://arxiv.org/pdf/2001.08343.pdf

hope this helps.

  • $\begingroup$ Thanks! What’s SI? $\endgroup$
    – Mauricio
    Aug 9, 2021 at 8:24
  • $\begingroup$ SI = supplementary info $\endgroup$
    – Lior
    Aug 9, 2021 at 9:19
  • 1
    $\begingroup$ There's also a few implementations of XEB as Cirq tutorials, see here for example: quantumai.google/cirq/qcvv/isolated_xeb $\endgroup$
    – forky40
    Aug 9, 2021 at 17:39
  • $\begingroup$ @forky40 yeah I noticed that once I knew it is called XEB, but I was looking for Qiskit resource. $\endgroup$
    – Mauricio
    Aug 9, 2021 at 19:08

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