011 Quantum Search

Simulate Grover's quantum search on 4 cards: spread, mark, boost and look, and see the amplitude bars grow so the marked card shows up in one look. Honest about the square root speedup. Simulator only.

You will learn: Amplitude amplification and the square root speedup of Grover search.

The circuit

Two coins give four states, one per card. Spin both coins so all four cards have equal amplitude, then ask the check: it flips the sign of the marked card only. Then apply inversion about the mean (Spin both coins, flip the sign of the all Heads state, Spin both coins again). The circuit is H, H, oracle, H, H, flip |00>, H, H, measure.

What the bars show

Each bar is the amplitude of a card. Up is positive and down is negative; the chance is the amplitude squared. After step 1 all four are at 0.5, which is 25% each. After step 2 the marked bar points down but its chance is still 25%. Step 3 reflects every bar around their average: the three unmarked bars shrink to zero and the marked bar grows to 1. This growth is the reason it is called amplitude amplification.

Honest notes

• Square root, not magic. For N cards you need about the square root of N rounds. With 4 cards that is 1 versus 2.25 checks on average (3 at worst) by hand. For 1,000,000 cards it is about 800 versus about 500,000.
• Four cards is a lucky case. One round is exact only for N = 4. For 8 cards, one round gives about 78% and two give about 95%. Too many rounds make the chance fall again.
• The check must be a quantum circuit. It is not a search through a plain list stored in memory.
• It does not break wallets or 256-bit keys. It roughly halves the effective key length, which is why longer keys are the standard answer. See Can a quantum computer break my wallet? and Grover's Algorithm Explained Step by Step.

Run on real hardware: coming soon. The planned provider is IBM Quantum. It is not connected yet. Every result on this page comes from a simulator running in your browser, not from a quantum computer.

How it works: the simulator keeps the exact quantum state of the qubits as a list of complex numbers, applies each gate to it, and draws random samples from the resulting probabilities. The random numbers are ordinary pseudo random numbers from your browser, and a real device would add noise. No QNT, wallet or account is needed.

Sources

• Grover (1996): A fast quantum mechanical algorithm for database search (arXiv:quant-ph/9605043)
• Wikipedia: Grover's algorithm

This is an educational simulator, not financial advice. QUANTUM (QNT) is an independent community token on Solana and does not perform quantum computation.

Updated 2026-10-12 | Free, no account, no token needed