Programming Abstractions for Quantum Linear Algebra
summary
Cobble is a domain language that compiles algebraic matrix expressions into circuits operating on block encodings, tracking both query count and the crucial subnormalization (α) that multiplies runtime. It implements rewrites like sum fusion and polynomial fusion and offloads polynomial evaluation to the quantum singular value transformation to reduce α and query complexity; a worked example drops expected repetitions from 20.8 to 8 and benchmarks show 2.6×–25.4× speedups over existing circuit optimizers.
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chapters (10)
- 0:00Quantum linear algebra intro
- 2:50Quantum speedup models
- 4:34Math to quantum circuits
- 6:43Storing vectors/matrices
- 9:10Circuit synthesis automation
- 12:24Optimizing with sum fusion
- 14:33Limitations of naive rewriting
- 15:54Polynomial fusion & QSVT
- 17:59Performance evaluation
- 19:00Future of quantum linear algebra
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