How to “Multiply” Quantum States
summary
Presents an explicit quantum procedure that produces a normalized pointwise product state from two constructible inputs by applying the quantum Fourier transform, forming the convolution, adding registers in superposition, then decoding. Decoding succeeds when the Fourier-domain supports overlap so x+y uniquely determines x and y — concretely when the dual code is list-decodable beyond 1/2 error and the coordinate filter is a random hash. Yields a sampler for the product distribution and a contrived code+hash problem with conjectured superpolynomial quantum advantage (no period finding, no public‑key assumptions).
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chapters (13)
- 0:00Introduction
- 0:41Classical World
- 5:38Fourier Domains
- 6:27Convolution Theorem
- 7:27Multiplying Quantum States
- 8:59Decoding Procedure
- 10:35Convolution
- 12:46Regev
- 18:44Input States
- 19:56Decoding Problem
- 20:07Input State
- 20:24Valid Coordinate State
- 24:13Why Care
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