3 ms·

Why use the subtext? In the peer review (pp30-31), the authors >acknowledge [that] Hamiltonian learning of an actual physical system has not been performed [an

Why use the subtext? In the peer review (pp30-31), the authors >acknowledge [that] Hamiltonian learning of an actual physical system has not been performed [and] have therefore further de-emphasized the quantum advantage claim in the revised manuscript https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-025-09526-6/MediaObjects/41586_2025_9526_MOESM2_ESM.pdf https://static-content.springer.com/esm/art%3A10.1038%2Fs415...

qnleigh 1y ago
This excerpt misses the wider point of the paper. The paragraph immediately following the one you quote still does make claims of quantum advantage: "Our second order OTOC circuits introduce a minimal structure while remaining sufficiently generic that circumvents this challenge by exploiting the exponential advantage provided by including time inversion in the measurement protocol, see arXiv:2407.07754." The advantage claimed by the paper isn't about Hamiltonian learning (i.e extracting model parameters from observational data), but instead about computing the expectation value of a particular observable. They acknowledge that the advantage isn't provable (even the advantage of Shor's algorithm isn't provable), but they argue that there likely is an advantage.
- johncolanduoni 1y ago
  Shor’s algorithm’s advantage isn’t proven, but a proof that integer factorization doesn’t admit a classical algorithm faster than O((log N)^3) could be found. The same applies for Google’s artificial problem.
  - gsf_emergency_4 1y ago
    An analogy which is closer to Google's experiment: measuring versus calculating the energy gaps in benzene to an arbitrary accuracy. It is "verifiably" faster to measure those with state of the art "quantum tools" but that does not improve our understanding of other aromatic molecules. (we may still get some insights about anthracene however) The googles' advantage can be satisfactorily summarised as "not having to write the problem (ie off-diagonal terms) in terms of a classical basis" -- there is a severe overhead of having to represent qubits as bits. Still, I suspect that that 13000x came from not putting in effort to implement the aforementioned "minimal structure" in their classical counterparts. They emphasized "echoes" and "ergodicity" & I think the "quantum" can further be dropped :) In general, I do believe that whatever "informational advantage" we can get from these experiments should likewise be used to improve classical calculations. As another eg: In the arxiv paper linked by GP they talk about provably-efficient shallow classical shadows

qnleigh 1y ago

This excerpt misses the wider point of the paper. The paragraph immediately following the one you quote still does make claims of quantum advantage: "Our second order OTOC circuits introduce a minimal structure while remaining sufficiently generic that circumvents this challenge by exploiting the exponential advantage provided by including time inversion in the measurement protocol, see arXiv:2407.07754." The advantage claimed by the paper isn't about Hamiltonian learning (i.e extracting model parameters from observational data), but instead about computing the expectation value of a particular observable. They acknowledge that the advantage isn't provable (even the advantage of Shor's algorithm isn't provable), but they argue that there likely is an advantage.

johncolanduoni 1y ago
Shor’s algorithm’s advantage isn’t proven, but a proof that integer factorization doesn’t admit a classical algorithm faster than O((log N)^3) could be found. The same applies for Google’s artificial problem.
- gsf_emergency_4 1y ago
  An analogy which is closer to Google's experiment: measuring versus calculating the energy gaps in benzene to an arbitrary accuracy. It is "verifiably" faster to measure those with state of the art "quantum tools" but that does not improve our understanding of other aromatic molecules. (we may still get some insights about anthracene however) The googles' advantage can be satisfactorily summarised as "not having to write the problem (ie off-diagonal terms) in terms of a classical basis" -- there is a severe overhead of having to represent qubits as bits. Still, I suspect that that 13000x came from not putting in effort to implement the aforementioned "minimal structure" in their classical counterparts. They emphasized "echoes" and "ergodicity" & I think the "quantum" can further be dropped :) In general, I do believe that whatever "informational advantage" we can get from these experiments should likewise be used to improve classical calculations. As another eg: In the arxiv paper linked by GP they talk about provably-efficient shallow classical shadows