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Quantum Similarity and Kernel Estimation

Question

Can swap-test and Hadamard-test overlap estimation reproduce classical cosine similarity and kernel computations on real quantum hardware, and where does the classical cost of state preparation eliminate any advantage?

Role

I chose the questions and experiments, reviewed the code and outputs, and am studying the repository in parallel with PhD applications.

Method

Implements swap-test and Hadamard-test overlap estimation for cosine similarity and quantum kernels over amplitude-encoded states, checked against classical ground truth on a noiseless simulator, with a small six-pair demonstration on IBM Quantum's ibm_fez processor.

Division of work

Human

Chose the research questions and experiment design, directed the benchmarking methodology, and reviewed the code and results.

AI

AI generated substantial implementation work: the estimator circuits, kernel assembly, and mitigation code.

Verification and limitations

Hardware observations (the ibm_fez demonstration) are kept explicitly separate from modeled-noise mitigation experiments in the repository. Independent reproduction is in progress.

Not peer-reviewed research and not evidence of quantum advantage. The repository states directly that arbitrary amplitude-state preparation costs up to O(2^n) gates, which removes any demonstrated end-to-end speedup for similarity search.

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