Carrier Pricing

Build a one-page web app called "Carrier Pricing" for painters, illustrators, generative artists, gallerists.

Headline: Encode print pricing as an amplitude vector and plot the embedding so artists navigate possibilities visually.

CONSTRAINTS (read first):
- I am on Lovable's FREE plan with ~5 credits. Build this in ONE message. Do NOT add features beyond what is listed.
- No accounts, no Lovable Cloud, no database, no auth. Static app only.
- One page: a workspace. Plus a small "About the quantum" strip at the bottom.

REAL QUANTUM (Quantinuum Guppy + Selene) — run AT BUILD TIME in the Lovable Linux sandbox, not at runtime:
1. In the sandbox, run:  pip install "guppylang>=1.0"
2. Create quantum/kernel.py containing an amplitude-encoding kernel that loads a normalized feature vector into log2(d) qubits and measures expectation values. It MUST be a real .py file on disk (Guppy reads source via inspect.getsource — REPL/exec strings fail).
3. Create quantum/run.py that imports the @guppy kernel, compiles it, and runs it on the Selene emulator (≤8 qubits, 256 shots) over 32 feature vectors, each loaded into 5 qubits = 32 expectation rows. Write the real results to src/data/quantum-results.json with shape: an array of { input, output } records where output contains expectation values per qubit.
4. Execute quantum/run.py ONCE during the build so src/data/quantum-results.json is committed real Selene output. Do not call Python at runtime — Cloudflare Workers cannot run Python.

FRONTEND (TanStack Start, single route /):
- Import src/data/quantum-results.json statically.
- Workspace UI: left = input picker tied to the precomputed grid (print pricing); center = live visual built from the selected record; right = a low-dimensional embedding scatter that updates as inputs change driven by the JSON.
- "Quantum trace" disclosure: show the raw expectation values per qubit for the active record and a "View Guppy source" toggle that prints the contents of quantum/kernel.py inline, so judges see this is genuine Amplitude encoding on Selene, not a fake.
- Design: dark workspace, ONE accent color matched to the Visual Art mood, ONE typeface family, tactile micro-interaction when the user picks a new record.

Deliverable: a single deploy where every number on screen traces back to a real Selene shot from quantum/kernel.py. Ship in one message.

--- QUANTINUUM APPENDIX (self-contained reference — paste verbatim) ---
[1] INSTALL (Lovable Linux sandbox, Python >= 3.12):
  python -m pip install --no-cache-dir "guppylang>=1.0" numpy
  # Guppy v1 is a BREAKING release: the Selene emulator now ships INSIDE guppylang.
  # Do NOT pip-install the old standalone emulator package, and do NOT use pre-v1 syntax.

[2] IMPORTS (Guppy v1 — use exactly these, no other quantum libs):
  # quantum/kernel.py and quantum/run.py top
  from guppylang import guppy, OptimizationLevel
  from guppylang.std.builtins import array, output          # `output`, NOT `result`
  from guppylang.std.quantum import qubit, h, cx, rx, ry, rz, measure, measure_array, discard, t as tgate, tdg
  from guppylang.std.angles import angle, pi
  from selene_sim import Quest                              # error models still live here
  from selene_sim.error_models import (
      IdealErrorModel, DepolarizingErrorModel, SimpleLeakageErrorModel,
  )
  import math, json, sys, tempfile, importlib.util, uuid
  from pathlib import Path

[3] HARD RULES (violating any breaks the build):
  - GUPPY v1: use output("tag", v) — `result()` no longer exists. measure(q) returns a
    Measurement object; call .read() before using it in output(...) or an `if`.
    Run via my_kernel.emulator(...).with_shots(S).run() — the pre-v1 build() helper is gone.
  - @guppy reads source via inspect.getsource → kernels MUST live in a real .py file on disk. No exec(), no REPL strings, no inline templates.
  - Allowed gate set ONLY: h, rx, ry, rz, cx, tgate, tdg. There is NO native ccx/toffoli, cswap, cphase, or crz — decompose using the snippets in [7].
  - Qubit ownership: a qubit passed to a function is moved. You MUST measure() or discard() every qubit exactly once; never reuse after measure.
  - Angle hygiene before baking a float into generated source:
        theta = ((theta + math.pi) % (2.0 * math.pi)) - math.pi
    and write it with repr: f"... {theta!r} ..."  (str(float) can truncate).

[4] SELENE SHOT LOOP (Guppy v1 emulator builder — the ONLY correct form):
  res = (
      my_kernel                       # the @guppy program itself, NOT .compile()
        .emulator(n_qubits=N)
        .with_shots(S)
        .with_seed(7)
        .with_simulator(Quest())
        .with_error_model(IdealErrorModel())
        .run()
  )
  shots = []
  for shot in res:                    # EmulatorResult is iterable
      shots.append({str(tag): int(v) for tag, v in shot.entries})
  # N = MAX number of qubits simultaneously LIVE in the kernel.
  # measure(q) releases the slot, so one ancilla reused across k windows still counts as 1.
  # The pre-v1 build(prog.compile()) + shot-loop helper NO LONGER EXISTS.
  # Other builder methods: with_n_processes, with_timeout, with_verbose, with_progress_bar.
  # ALWAYS pin .with_seed(<int>) — an unseeded run is not reproducible evidence.
  # If you report GATE COUNTS, also pin program.with_opt_level(OptimizationLevel.Classical);
  # v1 optimises on compile and will otherwise flatter your numbers.

[5] DRIVER PATTERN — sweep a kernel over many inputs (closures do NOT work):
  ROOT = Path(__file__).resolve().parent.parent
  if str(ROOT) not in sys.path: sys.path.insert(0, str(ROOT))

  def run_one(params: dict, shots: int = 256):
      # Bake params as literals into a fresh .py file that imports your kernel helpers.
      src = (
          "from quantum.kernel import guppy, my_helper\n"
          "@guppy\n"
          "def program() -> None:\n"
          f"    my_helper({params['a']!r}, {params['b']!r})\n"
      )
      tmp = Path(tempfile.gettempdir()) / "qprogs"; tmp.mkdir(exist_ok=True)
      name = f"prog_{uuid.uuid4().hex[:8]}"
      path = tmp / f"{name}.py"; path.write_text(src)
      spec = importlib.util.spec_from_file_location(name, path)
      mod  = importlib.util.module_from_spec(spec)
      sys.modules[name] = mod                       # register BEFORE exec_module
      spec.loader.exec_module(mod)
      res = (
          mod.program
            .emulator(n_qubits=5)
            .with_shots(shots)
            .with_simulator(Quest())
            .run()
      )
      out = []
      for shot in res:
          out.append({str(l): int(v) for l, v in shot.entries})
      return out

[6] PER-QUBIT INTEGER DECODE (host-side):
  # kernel emits: for j in range(n): output(f"x{j}", measure(q[j]).read())
  # measure() returns a Measurement in v1 — .read() gives the bool/bit.
  # Compiler error if you forget: "Values of type 'Measurement' cannot be passed to 'output' directly".
  def decode(rec, n):
      x = 0
      for j in range(n): x |= (rec.get(f"x{j}", 0) & 1) << j
      return x

[7] DECOMPOSITION LIBRARY (copy verbatim into quantum/kernel.py):

  # ---- Toffoli (CCX) from H, CX, T, Tdg — 6-T standard decomposition ----
  @guppy
  def toffoli(c1: qubit, c2: qubit, tgt: qubit) -> None:
      h(tgt)
      cx(c2, tgt); tdg(tgt)
      cx(c1, tgt); tgate(tgt)
      cx(c2, tgt); tdg(tgt)
      cx(c1, tgt); tgate(c2); tgate(tgt)
      h(tgt)
      cx(c1, c2); tgate(c1); tdg(c2)
      cx(c1, c2)

  # ---- CSWAP (Fredkin) from CX + Toffoli ----
  @guppy
  def cswap(c: qubit, a: qubit, b: qubit) -> None:
      cx(b, a)
      toffoli(c, a, b)
      cx(b, a)

  # ---- Controlled phase exp(i*theta) on |11> from rz + cx ----
  @guppy
  def cphase(c: qubit, d: qubit, theta: float) -> None:
      rz(d, angle(theta / 2.0))
      cx(c, d)
      rz(d, angle(-theta / 2.0))
      cx(c, d)

  # ---- Amplitude-encoded feature state (3 floats in [0,1] → 2-qubit state) ----
  @guppy
  def prep_features(q0: qubit, q1: qubit, a: float, b: float, c: float) -> None:
      ry(q0, angle(a))
      ry(q1, angle(b))
      cx(q0, q1)
      rz(q1, angle(c))

  # ---- SWAP test kernel; HOST inverts:  F = clamp(2*P(anc=0) - 1, 0, 1) ----
  @guppy
  def swap_test(ai: float, bi: float, ci: float,
                aj: float, bj: float, cj: float) -> None:
      anc = qubit()
      pi0 = qubit(); pi1 = qubit()
      pj0 = qubit(); pj1 = qubit()
      prep_features(pi0, pi1, ai, bi, ci)
      prep_features(pj0, pj1, aj, bj, cj)
      h(anc)
      cswap(anc, pi0, pj0)
      cswap(anc, pi1, pj1)
      h(anc)
      output("anc", measure(anc).read())
      discard(pi0); discard(pi1); discard(pj0); discard(pj1)
  # n_qubits = 5 for swap_test above.

[8] CLASSICAL CROSS-CHECK (NumPy reference — commit alongside quantum result):
  import numpy as np
  I = np.eye(2); X = np.array([[0,1],[1,0]])
  def RY(t): c,s = math.cos(t/2), math.sin(t/2); return np.array([[c,-s],[s,c]])
  def RZ(t): return np.array([[np.exp(-1j*t/2),0],[0,np.exp(1j*t/2)]])
  CX = np.array([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]])
  def prep_psi(a,b,c):
      s = np.kron(RY(a)@np.array([1,0]), RY(b)@np.array([1,0]))
      s = CX @ s
      s = np.kron(I, RZ(c)) @ s
      return s
  def classical_fidelity(p, q):
      return float(abs(np.vdot(prep_psi(*p), prep_psi(*q)))**2)
  # Commit BOTH quantum and classical values per record:
  #   {"input": [...], "quantum": 0.873, "classical": 0.881, "shots": 256}

[9] FRONTEND HANDOFF (TanStack Start):
  # quantum/run.py last step:
  Path("src/data/quantum-results.json").write_text(json.dumps({
      "records": records,                          # list of {input, quantum, classical, ...}
      "circuit": {"n_qubits": 5, "shots": 256},
      "kernel_source": Path("quantum/kernel.py").read_text(),  # show on /code tab
  }, indent=2))
  # In React:  import data from "@/data/quantum-results.json"  (resolveJsonModule:true).
  # Render data.records; render data.kernel_source in a <pre> inside the Quantum trace tab.

[10] BUILD ORDER (do not deviate — keeps you under 5 credits):
  1. Write quantum/kernel.py with the helpers from [7] you actually need.
  2. Write quantum/run.py: driver pattern from [5], Selene loop from [4], cross-check from [8], JSON write from [9].
  3. Execute once:  python quantum/run.py   (commit src/data/quantum-results.json).
  4. Build the React route: static JSON import, shadcn Card + Tabs + Slider + Badge wiring.
  5. Deploy. No Python at runtime; every on-screen number traces to committed Selene output.

[11] OUTPUT CONTRACT — selene_run v1 (write this exact shape to src/data/quantum-results.json):
  {
    "schemaVersion": 1,
    "experiment": "<idea-slug>",
    "title": "<idea title>",
    "description": "<one plain-English sentence — what a non-quantum dev sees>",
    "kernel": { "snippet": "<first 40 lines of quantum/kernel.py>", "qubits": <int>, "shotsPerRow": <int> },
    "verdict": { "text": "<one-sentence headline of the result>", "good": true },
    "metrics": [ { "name": "<label>", "value": <number>, "unit": "<%|bits|Hz|...>", "good": true } ],
    "series":  [ { "id": "<id>", "kind": "histogram"|"bar"|"line", "title": "...",
                   "xLabel": "...", "yLabel": "...", "yKeys": ["count"],
                   "points": [ { "label": "<x>", "values": { "count": <num> } } ] } ]
  }
  Also include provenance so the result is checkable:
    "extras": { "shots": <int>, "seed": <int>, "nQubits": <int>,
                "errorModel": "IdealErrorModel"|"DepolarizingErrorModel(...)",
                "guppy": ">=1.0", "generatedAt": "<ISO date>" }
  NO ESCAPE HATCH: extras is for non-rendered metadata ONLY. Anything the user is
  meant to SEE belongs in metrics[] or series[] — if you need extras to render, the
  mapping is wrong. Render the provenance line as plain text under the chart.
  Reason: one schema = one renderer = a polished demo without bespoke React per idea.
  All metric / series VALUES must come from real Selene shot data committed in step 3 — no mocks.

[12] RENDERER — create src/components/SeleneRunView.tsx with EXACTLY this body (no deps beyond react + tailwind):

  import * as React from "react";
  type Point  = { label: string; values: Record<string, number> };
  type Series = { id: string; kind: "histogram"|"bar"|"line"; title: string;
                  xLabel?: string; yLabel?: string; yKeys: string[]; points: Point[] };
  type Metric = { name: string; value: number; unit?: string; good?: boolean };
  export type SeleneRun = {
    schemaVersion: 1; experiment: string; title: string; description: string;
    kernel: { snippet: string; qubits: number; shotsPerRow: number };
    verdict: { text: string; good: boolean };
    metrics: Metric[]; series: Series[]; notes?: string;
  };
  const fmt = (n: number) => Math.abs(n) >= 100 ? n.toFixed(0) : Math.abs(n) >= 1 ? n.toFixed(2) : n.toFixed(3);
  function Bars({ s }: { s: Series }) {
    const max = Math.max(1, ...s.points.flatMap(p => s.yKeys.map(k => p.values[k] ?? 0)));
    return (
      <div className="space-y-1">
        {s.points.map((p, i) => (
          <div key={i} className="flex items-center gap-2 text-xs">
            <div className="w-20 truncate text-muted-foreground">{p.label}</div>
            <div className="flex-1 h-3 bg-muted rounded-sm overflow-hidden">
              <div className="h-full bg-primary" style={{ width: `${(100*(p.values[s.yKeys[0]]??0))/max}%` }} />
            </div>
            <div className="w-12 text-right tabular-nums">{fmt(p.values[s.yKeys[0]]??0)}</div>
          </div>
        ))}
      </div>
    );
  }
  function Line({ s }: { s: Series }) {
    const W=320, H=120, P=20;
    const ys = s.points.map(p => p.values[s.yKeys[0]] ?? 0);
    const min = Math.min(...ys), max = Math.max(...ys), span = max - min || 1;
    const pts = ys.map((y, i) => {
      const x = P + (i*(W-2*P))/Math.max(1, ys.length-1);
      const yy = H - P - ((y - min)/span)*(H - 2*P);
      return `${x},${yy}`;
    }).join(" ");
    return (
      <svg viewBox={`0 0 ${W} ${H}`} className="w-full h-32">
        <polyline fill="none" stroke="currentColor" strokeWidth="2" points={pts} className="text-primary" />
      </svg>
    );
  }
  export function SeleneRunView({ run }: { run: SeleneRun }) {
    return (
      <div className="space-y-6">
        <header>
          <div className="text-xs uppercase tracking-wider text-muted-foreground">{run.experiment}</div>
          <h2 className="text-2xl font-semibold">{run.title}</h2>
          <p className="text-sm text-muted-foreground">{run.description}</p>
          <div className={`mt-2 inline-block px-3 py-1 rounded-full text-xs ${run.verdict.good?"bg-emerald-500/15 text-emerald-400":"bg-amber-500/15 text-amber-400"}`}>
            {run.verdict.text}
          </div>
        </header>
        <section className="grid grid-cols-2 md:grid-cols-4 gap-3">
          {run.metrics.map((m, i) => (
            <div key={i} className="rounded-lg border border-border p-3">
              <div className="text-[10px] uppercase tracking-wider text-muted-foreground">{m.name}</div>
              <div className="text-xl font-semibold tabular-nums">{fmt(m.value)}<span className="text-xs text-muted-foreground ml-1">{m.unit}</span></div>
            </div>
          ))}
        </section>
        <section className="space-y-6">
          {run.series.map(s => (
            <div key={s.id} className="rounded-lg border border-border p-4">
              <div className="flex items-baseline justify-between mb-3">
                <div className="text-sm font-medium">{s.title}</div>
                <div className="text-[10px] text-muted-foreground">{s.xLabel} / {s.yLabel}</div>
              </div>
              {s.kind === "line" ? <Line s={s} /> : <Bars s={s} />}
            </div>
          ))}
        </section>
        <footer className="text-[11px] text-muted-foreground">
          kernel: {run.kernel.qubits} qubits · {run.kernel.shotsPerRow} shots/row
        </footer>
      </div>
    );
  }

  Then in the route: import data from "@/data/quantum-results.json"; <SeleneRunView run={data as any} />.
  Quantum trace tab: <pre>{data.kernel.snippet}</pre>.

[13] SKILL v2 GOTCHAS (must-follow)
- angle(x) is HALFTURNS, not radians. angle(0.5) == π/2 (S gate).
  For a radian θ, write angle(θ / math.pi). Never pass raw radians.
- If a source formula contains an explicit π (e.g. t = π/(16·h)),
  divide the π out BEFORE angle(): angle(1/16), NOT angle(math.pi/16).
- Only three Selene noise models exist:
    from selene_sim.error_models import (
      IdealErrorModel, DepolarizingErrorModel, SimpleLeakageErrorModel,
    )
  There is NO coherent / T1-T2 model — do not import one.
- Optional "noisy vs ideal" second pass (adds one extra series):
  run the same kernel twice, once with IdealErrorModel() and once with
  DepolarizingErrorModel(p_1q=1e-4, p_2q=1.29e-3, p_meas=0.9e-3),
  emit both under series[].points so the chart shows the gap.
- Run the CLASSICAL baseline BEFORE writing any quantum code and keep its number.
  An encoding bug that scores a perfect 1.000 on every input is caught by the
  baseline, never by the circuit.
- Shot-noise pass bar is 4*sqrt(0.5/shots) — see [16]. Do NOT use 3*sqrt(p(1-p)/n);
  it produces false FAILs whenever a probability sits near 0 or 1.
- Hardware footer line (render below the chart, one <div> only):
  "Runs today on Helios (98 qubits). Roadmap: Sol → Apollo → Lumos."

[14] BUILD SAFETY (Lovable sandbox + production runtime)
- Results ship as a COMMITTED JSON file only. Do NOT create a
  createServerFn, API route, or handler that shells out to Python or
  reads a cache directory: production stubs child_process and blocks
  arbitrary filesystem reads, so it builds and then fails live.
- If you install deps with `pip install --target .pydeps ...`, add
  `.pydeps/` to .gitignore FIRST. An unignored vendored dep tree makes
  the build time out and roll back, wasting credits.
- Make the sweep resumable: before moving to the next row, write it to
  _cache_run/<row-tag>.json and skip rows whose cache file exists.
  Assemble src/data/quantum-results.json from the cache at the end.
  Keep the grid small (<= 100 rows, <= 256 shots/row) so one pass fits.

[15] IF THE TURN ROLLS BACK (Lovable orchestration)
- A big Guppy/Selene turn can fail with "An internal error occurred". That is
  a task-transaction rollback: every file write from that turn is discarded.
  Do not debug the app — nothing broke. Re-do the work in smaller gates.
- Author in ATOMIC GATES, one per message, each ending in a saved artifact:
    (a) quantum/kernel.py + a smoke run of a handful of shots
    (b) quantum/run.py resumable driver (per-row cache)
    (c) the cached sweep -> src/data/quantum-results.json
    (d) the React route reading the committed JSON
  A rollback then costs one gate, not the whole build.
- Persistence canary: on a fresh session, make one trivial edit and end the
  turn. If it persists, larger gates are safe.


[16] EVIDENCE & VERIFICATION (do this, it is what makes the demo credible)
- STEP 0, before any quantum code: compute the CLASSICAL baseline for your task
  (cosine similarity, brute-force search, direct FFT — whatever the honest
  non-quantum answer is). Print it, keep it, and show it next to the quantum
  number in the UI. If the quantum result is identical to a trivial baseline on
  every input, your encoding is degenerate — fix the encoding, not the chart.
- PASS BAR for any probability comparison (quantum shots vs NumPy reference):
      import math
      tol = 4.0 * math.sqrt(0.5 / shots)     # shots = shots PER CELL
      ok  = abs(p_measured - p_expected) <= tol
  At 256 shots tol ~= 0.088. Use this exact form. The textbook
  3*sqrt(p(1-p)/n) form collapses to ~0 near p=0 or p=1 and reports false FAILs.
- The verdict.good flag in [11] MUST be computed from that comparison
  (e.g. good = all(cells_ok)), never hand-written as true.
- ANGLE SANITY CELL (30 seconds, saves the whole sweep): before the full run,
  do one 256-shot single-qubit check — prepare h(q); rz(q, angle(0.5)); h(q),
  measure, and assert P(1) ~= 0.5 within tol. If it comes out 0 or 1 you passed
  radians into angle() somewhere. Halfturns, always (see [13]).
- Report shots + seed + tolerance in the UI next to the verdict. A number
  without its shot count and seed is a rumour, not a result.

[17] OPTIONAL — LIVE SHOT STREAM (stretch goal, ONLY if you still have credits)
Skip this unless the committed JSON demo from [1]-[12] is already working. It is
polish, not proof.
- Selene/Python cannot run in production. For a live "watch the shots land" panel,
  port ONE small kernel (<= 4 qubits, gates H / RX / RZ / CX / measure) to a pure
  TypeScript statevector mini-sim in src/lib/mini-sim.ts: complex amplitudes as two
  Float64Array's, one closed-form unitary per gate, projective measure with collapse
  (compute P(0), draw vs rng(), zero the dead branch, renormalise).
- Mirror the Guppy gate ORDER exactly and return the same labelled keys your
  Python driver passes to output(...). Same kernel, two runtimes.
- Stream it from src/routes/api/public/shots.ts as Server-Sent Events
  (`data: ${JSON.stringify(shot)}\n\n`), seeded from a URL param so a session is
  reproducible. The client shows a "Live-verified" badge once >= 500 streamed shots
  land within the [16] tolerance of the analytic probability, "Drift" otherwise.
- HARD LIMIT: <= 4 qubits and no noise model. Anything bigger, anything needing real
  compilation or a noise model, and anything that IS the claim stays in the committed
  Selene JSON. The stream is a UX layer on top of an already-verified experiment.

[HOOK] AMPLITUDE ENCODING — feature vector → state, read Z-expectations.
  Kernel: ry(qj, angle(fj))  # halfturns: fj∈[0,1] gives π·fj rad rotation per feature; cx ladder q0→q1→…; rz on tail for non-trivial phase.
  output("z{j}", measure(q[j]).read()) for each j.
  Host: per-qubit expectation  E_j = (#0 - #1) / S  ∈ [-1, +1].
  Cross-check with the prep_psi() NumPy snippet in [8] and  E_j = <ψ|Z_j|ψ>.
  selene_run mapping:
    metrics: [ {"name":"embedding norm","value":norm,"unit":""},
               {"name":"qubits","value":n,"unit":""} ]
    series:  [ {"id":"expectations","kind":"bar","title":"⟨Z_j⟩ per qubit",
                "xLabel":"qubit","yLabel":"⟨Z⟩","yKeys":["count"],
                "points":[{"label":f"q{j}","values":{"count":Ej}} for j,Ej in enumerate(expectations)]} ]