📊 Research lab

Run your own quantum search study

Choose a problem size, algorithm, target and noise level; run many experiments; graph the data; export CSV and a full report.

🔬 Research methodology — a worked example

Research question: How does Grover's query complexity scale with the number of candidates N?
Hypothesis: The number of Grover oracle iterations grows approximately as (π/4)√N, while classical sequential search needs about N/2 evaluations on average.
Variables: Independent: N (and, in a second study, noise p). Dependent: number of oracle iterations; classical evaluations; measured success rate. Controlled: one marked target, optimal iteration count, same noise model.
Experiment: Use the 'Sweep N' template (30 runs for each N = 4…1024), or define your own runs with the form.
Data collection: Each run records experiment ID, N, qubits, classical evaluations, Grover iterations, target probability, noise and the measured result. Export as CSV.
Graph: Plot N against classical evaluations and Grover iterations. Try the log₂N axis. For noise, plot p against success rate.
Observation: Describe the shapes of the curves. How does each change when N is multiplied by 4?
Conclusion: State whether the data support the hypothesis and quote numbers.
Limitations: Results come from classical simulation, so they show query counts, not physical run time. The oracle is assumed to cost one query. The noise model is a simplified global depolarizing channel. Simulations are limited to 10 qubits (N ≤ 1024). Random variation affects small samples.

Define the experiment

Problem size N (2–1024 candidates)Number of qubits (min 7; extra qubits add unused basis states)Number of experiments (1–500)

Algorithm

Target

Noise: depolarizing probability per Grover iteration0%

128 basis states · 28 unused · safe to simulate.

Research templates

Experiments run

Configurations

Mean classical evals

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Grover success

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Write up & export

ObservationConclusion

Noise model used here

After every Grover iteration the state is replaced, with probability p, by the maximally mixed state (global depolarizing channel). Because the Grover operator leaves the mixed state unchanged, P(target) = (1−p)ᵏ·P_ideal + (1−(1−p)ᵏ)/2ⁿ exactly. Real devices have gate-level, correlated noise — this is a simplified, clearly-stated model.