Deriving a Kronecker-Free Functional Quantum Simulator
summary
Derives a Kronecker-free interpreter that evaluates an n‑qubit circuit on a 2^n state vector without first building the 2^n×2^n unitary by using the vectorization trick and inductive algebraic reasoning; implements a functional interpreter (Standard ML–style) that replaces global tensor/matrix construction with recursive, local operations. Benchmarks on Grover circuits show the unitary approach times out around 9 qubits while the naive functional version reaches 14–15 qubits; base gates use direct matrices, no heavy gate‑fusion or sparsity optimizations yet.
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chapters (12)
- 0:00Kronecker-free quantum simulator intro
- 12:22Circuit semantics without Kronecker
- 14:54Evaluating circuits via matrix-vector
- 16:01Vectorization and interpreter derivation
- 19:33Base cases in interpreter
- 21:17Tensor product case in interpreter
- 23:01Implementation insights
- 24:26Grover's algorithm evaluation
- 26:34Performance comparison
- 28:00Comparison with simulators
- 28:21Related work and future
- 29:25Q&A
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