Quantum Advantage Crossover: Market Unlock Simulator (2D)

Scaling Regime

Model Parameters

Classical branching base a 2.00

Quantum polynomial degree k 3

Quantum logical-op overhead 1.0 ms/op

Target Market Distribution

Typical problem size (log10 N) 4.0

Size spread (σ, decades) 1.20

Live Readouts

Crossover N*

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Crossover runtime

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Classical @ N*

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Quantum @ N*

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Market value unlocked

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How it works

Two real runtime curves are evaluated directly from their scaling formulas, in log-space so they never overflow:

Exponential regime:
  T_classical(N) = t_c · a^N          (brute-force search / classical simulation)
  T_quantum(N)   = t_q · N^k          (polynomial quantum algorithm, e.g. Shor-class)

Grover regime:
  T_classical(N) = t_c · N            (linear classical scan)
  T_quantum(N)   = t_q · sqrt(N)      (Grover-class quadratic speedup)

t_c = 1 ns is a fixed classical clock-cycle time. t_q is the quantum logical-operation overhead slider — a real, larger constant factor from error correction and slower logical gate times (realistic surface-code logical ops run µs–s, not ns).

The crossover N* is found by real numerical root-finding on log T_classical(N) − log T_quantum(N) = 0: a coarse scan over log₁₀N brackets the sign change, then bisection refines it to convergence. Below N*, quantum's constant-factor overhead still dominates and classical wins; above N*, the better scaling exponent wins and quantum is faster — that is where real economic value unlocks.

Market value unlocked is the fraction of a log-normal distribution of real-world problem sizes (set by the typical-size and spread sliders) that falls above N*, computed from the normal CDF via a numerical error-function approximation.

Raising the overhead slider makes t_q bigger, which pushes N* to larger problem sizes — advantage arrives later.
Lowering it (better hardware/error correction) pulls N* down — advantage arrives sooner, unlocking more of the market distribution.

N* ≈ —
Unlocked —

Classical T(N) Quantum T(N) Crossover N* Target size density