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Error budget

As explained in Quantum Programming in Depth

An error budget is the maximum allowed probability that an algorithm fails during execution.

An error budget sets the maximum allowed probability that a quantum algorithm fails during execution. In resource estimation, it is a constraint alongside the program and the assumed fault-tolerant architecture. section 9.4

The budget shapes the estimated implementation by requiring the estimator to:

  • Search for error-correction and magic-state-distillation parameters that execute the program within the permitted failure probability. section 9.4
  • Translate logical resource demands—including qubits, gates, measurements, and circuit depth—into physical resource estimates. section 9.4

How Quantum Programming in Depth covers it

How deep it goes
Defines the failure-probability constraint and shows its effect on architecture search, but does not derive probability models or correction codes.
Examples
Uses Azure Quantum Resource Estimator outputs, including an example requiring about one hundred thousand physical qubits and roughly one second of execution.
What it assumes
Assumes a Qiskit or Q# program and familiarity with physical qubit parameters, error correction, and magic state distillation.
What you can do after
Evaluate/understand how an allowed failure probability influences estimated physical qubits, runtime, and fault-tolerant architecture parameters.
How it connects
Connects error budgets to resource estimation, fault-tolerant quantum computing, error correction, magic state distillation, and circuit depth.
Cover of Quantum Programming in Depth
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