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The concept of Shannon's informational entropy is introduced through a series of exercise problems. The problem was designed by the author as a part of assignment of Brown PHYS 1530.
For looking up various definitions and propositions in abstract algebra. Notes taken from Brown MATH 1530 course.
This section introduces the mathematical foundations of quantum gates and qubit transformations. It covers Pauli operators, phase and basis changes, gate composition, tensor-product operations, and CNOT, culminating in the construction of a Bell state and the transition to entanglement.
From Hilbert spaces and operators to projective state spaces, the Bloch sphere, and SU(2).
Persistent homology can read structural change in a financial time series that a price chart alone does not show. We embed market data into point clouds, estimate Betti numbers with classical solvers and with quantum phase estimation, and show that spikes in β₀ line up with crash regimes — then train a simple LSTM on those topological features.
The quantum Fourier transform is the same classical Fourier transform, applied to amplitudes. On a periodic amplitude comb it piles constructive interference at multiples of N/r and cancels everywhere else — which is why period finding, and therefore Shor, can read a hidden period from a single measurement.