Stage 4 · Lesson 12 of 17
How circuits are fitted to quantum chips
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
Place two logical qubits on a generic connectivity map and insert a simplified SWAP route when required.
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.
- Map two logical qubits to the generic physical nodes.
- Check whether their required two-qubit interaction follows a direct link.
- 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
Map two logical qubits to the generic physical nodes.
Make and lock a prediction first.
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
The graph makes connectivity constraints and routing overhead concrete.
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”.
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.
- 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.
- 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.
- 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.
- 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.