QTM104 · Quantum Gates and Circuits

Categories: Emerging Technology
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About Course

Learn the standard quantum gate set, how multi-qubit gates create entanglement and logic, and how circuits are compiled to the native gates and connectivity of real hardware.

Build · 6 hours · 4 lessons, a lab, an assessed assignment and a portfolio piece

Who it is for

Learners who understand qubits and measurement and want to design, read and optimize quantum circuits.

Prerequisites

QTM103; comfort with matrix multiplication from QTM102.

What you will be able to do

  • Apply the Pauli, Hadamard, phase (S, T) and rotation gates and predict their effect on a state
  • Use CNOT, CZ, SWAP and Toffoli gates to build reversible logic, including a quantum half adder
  • Explain phase kickback and use circuit identities to simplify circuits
  • Transpile a circuit for a real device and compare depth and two-qubit gate counts across optimization levels

Lessons

  • Lesson 1 · Single-qubit gates
  • Lesson 2 · Multi-qubit gates and reversible logic
  • Lesson 3 · Circuits on real hardware: compilation
  • Lesson 4 · Lab and assignment

Lab: Build, simplify and transpile circuits

You design a quantum half adder and a teleportation circuit visually in IBM Quantum Composer and inspect their statevectors. You then rebuild them in Qiskit, transpile them for a simulated IBM device at optimization levels 0 to 3 and compare the resulting depth and two-qubit gate counts. No paid hardware time is needed.

Free tools: IBM Quantum Composer (free account) and Google Colab with Qiskit and a fake backend from qiskit-ibm-runtime

Assessed assignment

Design a quantum circuit that implements a three-input "majority" function: the output qubit should be 1 when at least two of three input qubits are 1. Verify it on all eight inputs with a simulator and present a truth table. Then transpile it for a fake IBM backend at optimization levels 0 and 3 and report depth, total gates and two-qubit gates. Explain in one page which circuit identities or layout choices reduced the cost and propose one further manual simplification.

Criterion Weight What excellent work looks like
Correct reversible logic 35% Circuit returns the correct majority output for all eight inputs, with inputs preserved.
Verification evidence 20% Truth table and simulator outputs are complete and clearly presented.
Transpilation analysis 30% Metrics are reported accurately for both levels and the reasons for differences are explained correctly.
Optimization insight 15% Proposes a valid further simplification using circuit identities or qubit layout.

Portfolio piece

A documented set of quantum circuits (half adder, teleportation, majority function) with transpilation metrics.

Self-paced, 12-month access. Questions are answered in writing through the student panel. A completion record is issued when you finish the course.

Next step

Continue with QTM105 · Programming Quantum Circuits with Qiskit · 8 hours · $56.00

Continue to the next course

Prefer the whole program? Program in Quantum Computing Foundations · $277.00 (10% less than buying the courses separately)

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What Will You Learn?

  • Apply the Pauli, Hadamard, phase (S, T) and rotation gates and predict their effect on a state
  • Use CNOT, CZ, SWAP and Toffoli gates to build reversible logic, including a quantum half adder
  • Explain phase kickback and use circuit identities to simplify circuits
  • Transpile a circuit for a real device and compare depth and two-qubit gate counts across optimization levels

Course Content

QTM104 · Quantum Gates and Circuits (6 h)
Learn the standard quantum gate set, how multi-qubit gates create entanglement and logic, and how circuits are compiled to the native gates and connectivity of real hardware.

  • Lesson 1 · Single-qubit gates
  • Lesson 2 · Multi-qubit gates and reversible logic
  • Lesson 3 · Circuits on real hardware: compilation
  • Lesson 4 · Lab and assignment
  • QTM104 Assessment · Quantum Gates and Circuits
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