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Has quantum advantage been achieved?

Dominik Hangleiter

Abstract

Quantum computational advantage was claimed for the first time in 2019 and several experiments since then have reinforced the claim. And yet, there is no consensus whether or not quantum advantage has actually been achieved. In this article, I address this question and argue that, in fact, it has. I also outline next steps for theory and experiments in quantum advantage.

Has quantum advantage been achieved?

Abstract

Quantum computational advantage was claimed for the first time in 2019 and several experiments since then have reinforced the claim. And yet, there is no consensus whether or not quantum advantage has actually been achieved. In this article, I address this question and argue that, in fact, it has. I also outline next steps for theory and experiments in quantum advantage.
Paper Structure (24 sections, 3 equations, 7 figures)

This paper contains 24 sections, 3 equations, 7 figures.

Table of Contents

  1. What is quantum advantage and what has been done?
  2. What is quantum advantage?
  3. Random circuits are really hard to simulate!
  4. The breakthrough: classically hard programmable quantum computations in the real world
  5. Proxy of a proxy of a benchmark
  6. A few notes
  7. Considering the evidence for quantum advantage
  8. What is the issue?
  9. Quantum advantage of finite-fidelity RCS
  10. Getting the scaling right: weak noise and low depth
  11. Where are the experiments?
  12. The phase transition matters!
  13. But we cannot compute the XEB!
  14. That is exactly how experiments work!
  15. The theoretical computer scientist
  16. ...and 9 more sections

Figures (7)

  • Figure 1: XEB/fidelities achieved by the random circuit sampling experiments since 2019.
  • Figure 2: From ware_sharp_2023. The $y$-axis label $\Delta( \ln \chi )$ is the decay rate of the XEB $\chi$, $N=n$ the number of qubits and $\varepsilon$ is the local noise rate.
  • Figure 3: Fidelities of the experiments as a function of qubit number $n$ relative to the near-ideal score $F \ge 90$% and the uniformly random score $F = 2^{-n}$.
  • Figure 4: The theoretical computer scientist's cartoon of verifying a quantum computer from classical samples.
  • Figure 5: To achieve verifiable advantage in the 100-logical-qubit regime we need to close the gap between random circuit sampling and proofs of quantumness.
  • ...and 2 more figures