Stage 4 · Lesson 12 of 17

How circuits are fitted to quantum chips

40 minutesNo coding required10-question quiz

1 · Big question

How is a logical circuit adapted so a particular physical chip can run it?

  • Distinguish logical and physical qubits.
  • Explain transpilation in plain language.
  • Map logical qubits to a generic connectivity graph.
  • Identify when routing may insert SWAP operations.

2 · Before we begin

Ideas to bring with you

  • A circuit diagram states intended operations.
  • Physical hardware may differ from an ideal simulator.

3 · New words

Meet the words before we use them

logical qubit
A qubit role in the intended circuit, which software later assigns to a physical qubit learned about in Lesson 11.
transpilation
Adapting and rearranging a circuit so a selected machine can execute it.
SWAP
An operation sequence used to exchange two qubit states for routing.

4 · Simple explanation

Build one idea at a time

A logical circuit describes what the computation should do. A selected chip has physical qubits, supported native instructions and a connectivity map showing which pairs can directly interact.

Before execution, software adapts the logical circuit to those constraints. This process is called transpilation after its plain-language purpose is understood.

If two required qubits are not directly connected, routing can insert SWAP operations or choose a different mapping. Fewer added operations are often helpful on noisy hardware, but the shortest circuit is not automatically best in every setting.

Watch it happen

Map a logical circuit to a teaching chip

Calculated teaching model

Place two logical qubits on a generic connectivity map and insert a simplified SWAP route when required.

Ready. Use Step or Play to begin.
Text description of the animation

A generic four-node teaching map shows allowed links. A logical two-qubit gate between non-adjacent mapped nodes requires a highlighted route and added SWAP operations. Original and adapted operation counts are listed.

  1. Map two logical qubits to the generic physical nodes.
  2. Check whether their required two-qubit interaction follows a direct link.
  3. Insert the simplified SWAP route when needed and compare operation counts.

Evidence to calculate or record: The adapted circuit obeys the teaching map’s connectivity and reports every added operation.

Predict

Commit to an idea before the reveal

If logical qubits A and B are mapped to physical nodes with no direct link, can their two-qubit gate run unchanged?

Choose a prediction to enable the experiment.

Try it

Choose a mapping and route

Teaching model

Map two logical qubits to the generic physical nodes.

Make and lock a prediction first.

Detailed activity results will appear here.

8 · Observe

What did the result actually show?

Look at the displayed values before reading the explanation. Record a pattern, an exception or something that changed.

Mappings that place interacting logical qubits beside each other need fewer routing operations in this teaching example.

9 · Explain the result

Connect the evidence to the idea

A processor executes only operations compatible with its target instructions and connections. Transpilation preserves the intended computation while changing its physical implementation.

10 · Model and limitation

Useful model, honest boundary

What this model shows

The graph makes connectivity constraints and routing overhead concrete.

What this model does not show

It is a generic teaching model, not a current IBM processor topology. Real transpilers consider more constraints and calibration information.

11 · Common mix-ups

Careful wording prevents big mistakes

Logical and physical qubits are always the same numbered object.

Software maps logical roles to selected physical locations.

Transpilation changes the intended answer on purpose.

It should preserve the computation while adapting its implementation.

The fewest gates is automatically the best circuit.

Noise, duration, connectivity and calibration can create trade-offs.

12 · Real quantum-computing connection

Where this appears in circuit work

Qiskit transpilation maps logical qubits, routes interactions and translates instructions to the selected backend’s supported instruction set.

13 · Show me moreOptional deeper explanation

Show me more

Modern transpilers use staged passes for layout, routing, translation, optimisation and scheduling. The selected backend’s target records constraints such as instructions and connectivity.

Try this

Explain the deeper idea in your own words, including one limitation.

14 · Quick summary

Keep these ideas

  • Logical circuits describe intent.
  • Physical chips impose instruction and connectivity constraints.
  • Transpilation adapts the circuit.
  • Routing may add SWAP operations.

Ten-question quiz

Check the ideas—not decorative details

Feedback appears after submission. Retry whenever you like; 8/10 or above means “Topic understood”.

1What is a logical qubit?

Concept · Easy

2What is the main purpose of transpilation?

Concept · Medium

3Why might routing add operations?

Concept · Medium

4Software maps logical qubit A to physical qubit 2. What does that mean?

Vocabulary · Easy

5What does a SWAP operation do in the routing model?

Vocabulary · Easy

6Logical A and B need CX and are mapped to directly linked nodes. What simplified routing is needed?

Prediction · Medium

7On links 0–1–2–3, A maps to 0 and B to 2. What does the teaching model show before their direct two-qubit interaction?

Prediction · Medium

8Which claim about a valid logical circuit needs correction?

Misconception · Medium

9Which evidence helps compare two teaching-model mappings?

Evidence · Medium

10Three logical qubits interact mostly as A–B and B–C. Which line-map placement is a sensible first choice?

Application · Hard

Sources and accuracy notes3 checked references · reviewed 2026-08-15

These records identify the claim each source supports. External documentation can change; dated platform claims were checked on the shown access date.

  1. Introduction to transpilationIBM Quantum · Instruction set architecture and transpiler stages · accessed 2026-08-15

    Supports quiz questions ql-12-q-01, ql-12-q-02, ql-12-q-03, ql-12-q-04, ql-12-q-05, ql-12-q-06, ql-12-q-07, ql-12-q-08, ql-12-q-10 and their related lesson explanations about logical-to-physical qubit mapping; native-instruction translation and device connectivity; routing operations including inserted SWAP gates.

  2. CircuitsIBM Quantum Learning · Quantum circuits — Circuits · accessed 2026-08-15

    Supports the simple explanation, activity and model boundaries about classical and quantum circuit models; gates and wires; standard-basis measurement.

  3. Quantum Computing: An Applied ApproachSpringer · 2021 · Second edition, Parts I–II · accessed 2026-08-15

    Supports quiz questions ql-12-q-09 and their related lesson explanations about applied circuit workflows; hardware noise and practical limitations; quantum and classical workflow comparisons.

Lesson accuracy notes
  • This model is deliberately limited: It is a generic teaching model, not a current IBM processor topology. Real transpilers consider more constraints and calibration information.
  • Predictions, simulations and physical-hardware evidence are labelled separately.