Quantum Cloud Shot Budget: Measurement Statistics

Qubit Preparation

State-prep angle θ 90°

Readout error rate 2%

Shots per run 50

Cloud Job Control

outcome |0⟩ outcome |1⟩ estimate p̂(1)

Live Readout

Total shots N

Job cost

$0.0000

Estimate p̂(1)

—

Std. error

—

Ideal Born-rule P(1) = sin²(θ/2)

0.500

How it works

P(1) = sin²(θ/2)
P(0) = cos²(θ/2)

A single measurement gives one random bit — it never reveals P(1) directly. A quantum-cloud provider (QaaS) bills per repeated circuit execution ("shot"). Averaging N independent shots gives the maximum-likelihood estimator and its standard error:

p̂(1) = (# outcomes "1") / N
SE = sqrt( p̂(1)·(1 − p̂(1)) / N )   ← shrinks as 1/√N

A noisy readout stage flips the true outcome with probability ε before it is reported, so the data actually converges on the shifted value:

P_observed(1) = P(1)·(1 − ε) + P(0)·ε

θ slider — sets the true superposition and therefore the ideal probability the histogram should converge to.
Readout error ε — models real hardware measurement infidelity; watch the yellow estimate line settle on the shifted (not the ideal) value once ε > 0.
Shots per run — batch size submitted to the simulated queue each time you click Submit; more shots buys a tighter SE at proportional cost, exactly as a real QaaS shot bill scales.

This is the same statistics every gate-based cloud backend (IBM Quantum, Amazon Braket, Azure Quantum) exposes to users: a circuit's expectation value is never read directly, only estimated from a finite, paid-for number of repeated shots.

chip: simulated 1-qubit QPU billing: $0.00003 / shot

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