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02 · Noise models and fake backends0%

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Learn/QC 301Noise and Errors·Lesson 2 of 4

Noise models and fake backends

How a simulator imitates a device: depolarising, thermal relaxation and readout channels built from calibration data.

Advanced12 min read4 sections · 2 questions+45
By the end you will be able to
  1. 01Name the three channels in a fake backend's noise model.
  2. 02Explain what a density matrix adds over a statevector.
  3. 03Choose between fake backends for a given circuit.

A fake backend is a snapshot of a real machine: its coupling map, basis gates and a day's calibration. Qiskit Aer turns the calibration into a noise model with three channels: depolarising error after each gate (scaled to the measured gate error), thermal relaxation during each gate's duration (from T1, T2) and a readout confusion matrix. Simulating with it predicts hardware histograms surprisingly well.

ρ↦(1−p)ρ+3p​(XρX+YρY+ZρZ)
The single-qubit depolarising channel. Noise maps pure states to mixed ones, so the simulator must track a density matrix ρ (2ⁿ × 2ⁿ) instead of a statevector (2ⁿ). That is why noisy simulation stops around 12–14 qubits.
Hands-on

Three chips, one circuit

Preset '3 noisy chips' runs the same Bell pair on three fake backends. Compare the total variation distances in Metrics; then open Hardware → calibration for each to see which number explains the ranking.

OpenQASM 3
OPENQASM 3.0;
include "stdgates.inc";
qubit[2] q;
bit[2] c;
h q[0];
cx q[0], q[1];
c = measure q;
Sign in to run (nothing is saved)
Open in the IDE Open in the Playground
Knowledge check

2 questions · one try each counts

Question 1

Why does a noisy simulation need a density matrix?

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Question 2

Which calibration number most affects a deep circuit with few two-qubit gates?

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Key takeaway

Fake backends turn a device's calibration into depolarising, relaxation and readout channels. They need density matrices, cost more to simulate, and are the honest reference before spending hardware minutes.

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Up next
Lesson 3 · 10 min
Error mitigation
Cheaper than correction: readout calibration, zero-noise extrapolation, and what mitigation cannot do.
Further reading
  • Docs: noisy targets
More in Noise and Errors
  • NISQ reality
  • Error correction in one lesson
NISQ realityError mitigation
In this lesson0%
  1. Introduction
  2. Try it: Three chips, one circuit
  3. Knowledge check
  4. Key takeaway
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