Circuits, Gates, and Measurements in Code

Overview

This page introduces the programming concept that a circuit is an ordered list of operations with explicit wiring:

• which qubit an operation acts on
• where measurement results are stored

It answers: How do circuit diagrams translate into code objects precisely?

Conceptual Mapping

A circuit diagram has three kinds of “wires”:

• qubit wires (quantum information)
• classical wires (measurement outcomes)
• time flowing left to right (operation order)

In code:

• qubits are indexed: 0, 1, 2, ...
• classical bits are indexed: 0, 1, 2, ...
• order is the order you call methods like h, cx, measure

Two key mappings:

• Gate application order matters (non-commuting operations).
• Measurement mapping matters (which classical bit gets which qubit’s measurement).

Code Walkthrough

A minimal two-qubit example to show ordering and measurement mapping:

from qiskit import QuantumCircuit
 
qc = QuantumCircuit(2, 2)
 
qc.h(0)
qc.cx(0, 1)
 
qc.measure(0, 1)
qc.measure(1, 0)
 
print(qc)

Line by line:

• QuantumCircuit(2, 2) creates 2 qubits and 2 classical bits.
• h(0) acts only on qubit 0.
• cx(0, 1) uses qubit 0 as control and qubit 1 as target.
• measure(0, 1) stores the measurement of qubit 0 into classical bit 1.
• measure(1, 0) stores the measurement of qubit 1 into classical bit 0.

The last two lines intentionally “swap” the mapping. This is a reminder that classical bits are separate storage.

What Happens Under the Hood

Conceptually, Qiskit keeps a data structure for the circuit:

• a list of operations
• each operation has a type (gate/measurement) and targets (qubits/bits)

When you run the circuit on a backend:

• the backend reads this list
• it executes operations in order
• measurement operations write classical bits
• the final classical bitstring is what you see in results

So results like "01" are not “qubits.” They are classical bits after measurement, arranged in a specific order.

Turtle Tip

Common Pitfalls

Quick Check

What’s Next

Next we’ll compare simulators and real hardware. You’ll learn which parts of this workflow are idealized in simulation, and why hardware adds extra constraints and noise.