Deriving a Kronecker-Free Functional Quantum Simulator
summary
Derives a compositional, Kronecker-free interpreter that applies circuits directly to 2^n state vectors using the vectorization trick (vec/unvec, transposition and matrix-multiplication identities) instead of forming 2^n×2^n unitaries. Implements a functional-DSL prototype (Haskell/OCaml style) and microbenchmarks showing usable simulations up to ~15 qubits versus ~7 when materializing unitaries, and better than naive matrix construction though still behind hand-tuned imperative simulators; supports measurements and can emit imperative/gate-backend code.
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chapters (13)
- 0:00Introduction
- 0:22Circuit specs to simulators
- 1:03Declarative vs imperative
- 2:30Eliminating matrices
- 4:34Functional circuit DSL
- 6:47Compositional semantics
- 7:50Deriving interpreter
- 10:43Tensor product handling
- 11:46Interpreter implementation
- 12:50Benchmarking performance
- 13:57Related work
- 15:00Future research
- 16:27Q&A
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