> For the complete documentation index, see [llms.txt](https://docs.sirraya.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.sirraya.org/examples/fidelity_scaling.md). # fidelity\_scaling It's gate count, not qubit count, that drives your fidelity budget down. This example makes that concrete. ```bash cargo run --example fidelity_scaling ``` ## What it does Builds GHZ-state-preparation circuits (`H` on qubit 0, then a `Cx` ladder out to every other qubit) at widths `[2, 4, 8, 16, 32, 64, 98]`, compiles each to the native gate set, and prints source gate count, native `(1q, 2q)` counts, optimized gate count, and estimated fidelity on Quantinuum Helios. ```rust for num_qubits in [2usize, 4, 8, 16, 32, 64, 98] { let circuit = ghz_circuit(num_qubits); let native = optimize(&decompose(&circuit)); let fidelity = estimate_circuit_fidelity(&native, &cal); // ... } ``` ## Why 98 qubits specifically 98 matches Quantinuum Helios's own qubit count. A full-width GHZ state at that size is close to a worst case for the device: *n*−1 sequential two-qubit gates sit on the critical path, so the fidelity estimate at the top of the table is a genuine "how bad can it get on this exact hardware" number, not an arbitrary large-*n* extrapolation. ## Why it matters The pattern across the table is the point: fidelity doesn't degrade because qubit *count* went up — it degrades because *gate* count went up, and those two only track each other because this particular circuit's gate count happens to scale linearly with width. A compiler that avoids unnecessary gates (the peephole `optimize` pass, run here on every row) matters more, not less, as circuits grow, because every gate it removes is one less multiplicative factor in the fidelity estimate. ## Related * [`gate_cheatsheet`](/examples/gate_cheatsheet.md) — the per-gate cost accounting this example's fidelity numbers are built from * [`backend_cost_comparison`](/examples/backend_cost_comparison.md) — the same fidelity-estimation machinery, comparing backends instead of scaling one circuit --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://docs.sirraya.org/examples/fidelity_scaling.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.