Quantum computers as RNG: Quantum Supremacy (2019)
Quantum supremacy is the point at which quantum computers can solve problems that are practically unsolvable for “classical” (non-quantum) computers to complete in any reasonable timeframe. It is generally believed that at least 49 qubits are required to cross the quantum supremacy line.
Google’s ‘Sycamore’ quantum computer was able to achieve “quantum supremacy” — solving a complex problem that would otherwise be impossible for a classical computer to solve in its lifetime — in just three minutes and 20 seconds, compared to the estimated 10,000 years it would take the world’s most advanced classical computer, Summit.
To demonstrate quantum supremacy, we compare our quantum processor against state-of-the-art classical computers in the task of sampling the output of apseudorandom quantum circuit.Due to quantum interference, the probability distribution of the bitstrings resembles a speckled intensity pattern produced by light interference in laser scatter, such that some bitstrings are much more likely to occur than others. Classically computing this probability distribution becomes exponentially more difficult as the number of qubits (width) and number of gate cycles (depth) grows.
Related: DeepMind can predict rain (in Britain :-) from Doppler radar for the next hour: Ravuri, S., Lenc, K., Willson, M. et al. Skilful precipitation nowcasting using deep generative models of radar. Nature 597, 672–677 (2021). link
Can we improve simple algorithms like multiplication?
Derivation for the fourth order Runge-Kutta method which follows a similar logic as the one for rk2 in Landau’s book (in 9.5.2.) is not that simple. This is a “simplified” derivation: https://www.researchgate.net/publication/49587610_A_Simplified_Derivation_and_Analysis_of_Fourth_Order_Runge_Kutta_Method
Sedaghat, N., Romaniello, M., Carrick, J.E. and Pineau, F.X., 2021. Machines learn to infer stellar parameters just by looking at a large number of spectra. ]Monthly Notices of the Royal Astronomical Society, 501(4), pp.6026-6041.](https://arxiv.org/pdf/2009.12872.pdf) (using variational autoencoders)
Machine learning to analyse gravitational lensing observations
Machine learning in physics review: Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L. and Zdeborová, L., 2019. Machine learning and the physical sciences. Reviews of Modern Physics, 91(4), p.045002. arxiv
In 1975, Dr. Feigenbaum, using the small HP-65 calculator discovered that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4.6692.
Related question: Weather vs. climate. See 2021 Nobel prize in physics and also the ongoing COP26
Drótos, G., Bódai, T. and Tél, T., 2017. On the importance of the convergence to climate attractors. The European Physical Journal Special Topics, 226(9), pp.2031-2038. link
Sympletic integrators for nonlinear Hamiltonian systems: https://en.wikipedia.org/wiki/Symplectic_integrator
Corless, R.M., 1994. What good are numerical simulations of chaotic dynamical systems?. Computers & Mathematics with Applications, 28(10-12), pp.107-121. link
Li, X. and Liao, S., 2018. Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems. Applied Mathematics and Mechanics, 39(11), pp.1529-1546. link
Boekholt, T.C.N., Portegies Zwart, S.F. and Valtonen, M., 2020. Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length. Monthly Notices of the Royal Astronomical Society, 493(3), pp.3932-3937. link : “… using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic … three massive black holes with zero total angular momentum, we conclude that up to five percent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution”
