Quantum Computer Studio

01 / Prepare & control

Build a quantum circuit

Append gates, step through the circuit, then sample measurement outcomes. Click any gate in the list to remove it. Qubit q0 is the leftmost bit.

Noise and reproducibility

These are editable teaching parameters, not measured specifications or a ranking of platforms. Noise acts on the gate's participating qubits. M is an ideal, nonselective measurement and has no added gate noise.

Enable density-matrix noise

T2 must be ≤ 2T1. Readout error changes reported bits only. Reset state rewinds the random seed. Turning noise off gives exact ideal unitary evolution up to floating-point precision.

02 / State inspection

What is the register doing?

Applied gates

Purity Tr(ρ²)

Global l1 coherence

Inspect reduced qubit state

Complex amplitudes

Available for the pure ideal reference before any M gate. Phase is in degrees; global phase is unobservable.

Basis	Amplitude	Phase

The Bloch vector belongs to one qubit's reduced density matrix. A zero-length vector can result from entanglement or noise. Reduced mixedness alone does not prove entanglement in a noisy global state.

03 / Measure

Outcome probabilities

Blue: current exact Z-basis probabilities. Teal underline: sampled frequencies, including enabled readout error. Outcomes are displayed as |q0 q1 …〉.

Sampling re-prepares the current density matrix for each shot and leaves it unchanged. “Measure once” projects the current register; a second ideal measurement repeats the result. Run circuit starts again at |00…0〉.

Gate operation

Try this first

Keep the Bell pair example.
Click Step gate twice.
Compare the joint probabilities with each qubit's Bloch vector.
Sample 1,000 shots. Why are 01 and 10 absent?

References & further study

External readings require internet access. All computations, diagrams, lessons, and experiments in this file work offline.

What this simulator computes

Gate laboratory: 1–6 qubits, a complex state vector for pure ideal amplitudes, and full complex density matrices for ideal and noisy evolution. Gates update ρ → UρU†. Memory grows as 4ⁿ; the six-qubit limit keeps browser work manageable.
Noise: independent local Pauli errors E(ρ) = (1−p)ρ + p(XρX + YρY + ZρZ)/3; amplitude damping γ = 1−exp(−t/T1); and pure dephasing with off-diagonal factor exp[−t(1/T2−1/(2T1))]. This convention's p is total nonidentity Pauli probability, not the alternative maximally-mixed replacement parameter.
Timing: serial logical gates. Two-qubit gates use the chosen duration multiplier. Only participating qubits receive these channels. Idle decoherence, scheduling, connectivity, crosstalk, leakage, and compiler overhead are omitted.
Measurement: M removes target-qubit off-diagonal blocks without selecting an outcome. The final collapse button instead samples and projects the whole register. Readout errors flip the reported classical bits; they do not change the physical projected state.
Driven two-level system: exact closed-system solution under a constant rotating-frame Hamiltonian. The displayed response is valid for the two-level and rotating-wave approximations.
Photonics: exact single-photon, dual-rail Mach–Zehnder amplitudes with symmetric survival loss. General multi-photon Fock dynamics, squeezing, continuous variables, and probabilistic entangling resources are not modeled.
BEC: finite fixed-N, two-mode Bose–Hubbard Hamiltonian. Complex Schrödinger evolution uses RK4 with an adaptive-to-Hamiltonian fixed step bound. The display reports norm drift before normalization. It omits higher spatial modes, heating, atom loss, and finite-temperature effects.

This is an educational classical simulation of specified small quantum models, not a full digital twin of a quantum computer. Platform selections do not turn an abstract logical CNOT into a calibrated native pulse sequence. No real quantum hardware is contacted. No performance or quantum-advantage claims follow from these examples.

Content and reference links assembled September 2026. Noise defaults are synthetic teaching values and deliberately identical across gate platforms.

Quantum Computer Studio

A condensate needs a many-body model

Build a quantum circuit

What is the register doing?

Complex amplitudes

Outcome probabilities

Gate operation

Try this first

Compare the physical approaches

From probability amplitudes to a computation

Check your understanding

Eight experiments with predictions and checks

References & further study

What this simulator computes