Quantum AI: Variational Quantum Circuits

Advanced Quantum AI

Created by Best · 12.04.2026 at 16:05 UTC

Variational Quantum Eigensolver (VQE) and similar algorithms use parameterized quantum circuits whose parameters are optimized classically. This card walks through building a simple variational circuit with PennyLane (or Qiskit) and measuring expectation values.

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Tasks

Question 1

Compute the expectation value $\langle 0|R_z(\theta)\, Z\, R_z(-\theta)|0\rangle$ analytically. Input: $\theta$ (radians). Output: the value with 6 decimal places. (Hint: $R_z$ commutes with $Z$.)

Runtime output (stdout/stderr)

3 test cases will be used for grading

Run checks runtime behavior only. Final correctness is evaluated when you submit.

Question 2

Compute $\langle 0|R_x(\theta)\, Z\, R_x(-\theta)|0\rangle$ for a given $\theta$. Input: $\theta$ (radians). Output: the value with 6 decimal places.

Runtime output (stdout/stderr)

3 test cases will be used for grading

Run checks runtime behavior only. Final correctness is evaluated when you submit.

Question 3

In a Variational Quantum Eigensolver (VQE), what quantity is minimized by the classical optimizer?

The circuit depth

The expectation value of the Hamiltonian

The number of parameters

The measurement error rate

Card Info

Topic: Quantum AI
Difficulty: Advanced
Completed: 0 users

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Best

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