Single Qubit States and Measurements

1 QI1 Practice

Code

viewof generateButton = {
  const button = html`<button style="
    background-color: #2563eb;
    color: #ffffff;
    font-size: 15px;
    font-weight: 600;
    padding: 10px 20px;
    border: none;
    border-radius: 6px;
    cursor: pointer;
    box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1);
  ">Generate New Problem</button>`;

  button.value = 0;
  button.onclick = () => {
    button.value++;
    button.dispatchEvent(new CustomEvent("input", { bubbles: true }));
  };

  return button;
}
<!-- viewof generateButton = Inputs.button("Generate New Problem", {
  <!-- style: "background-color: #0066cc; color: white; border-radius: 4px; padding: 8px 16px; font-weight: bold; cursor: pointer;" --> -->
<!-- }) -->

Code

problem = {
  // Access generateButton to form a dependency so it updates on click
  generateButton;

  const states = [
    'vertically',
    'horizontally',
    'right diagonally',
    'left diagonally'
  ];

  // Helper for random selection
  const choice = arr => arr[Math.floor(Math.random() * arr.length)];
  const randomInt = (min, max) =>
    Math.floor(Math.random() * (max - min + 1)) + min;

  // 1. Randomly assign initial polarization
  const initialState = choice(states);

  // 2. Generate a sequence of 2 to 3 polarization filters
  const numFilters = randomInt(2, 3);
  const filters = Array.from({ length: numFilters }, () => choice(states));

  // Format the filter sequence into a readable string
  let filterStr = "";
  if (numFilters === 2) {
    filterStr = `a ${filters[0]} polarized filter followed by a ${filters[1]} polarized filter`;
  } else {
    filterStr = `a ${filters[0]} polarized filter, followed by a ${filters[1]} polarized filter, and then a ${filters[2]} polarized filter`;
  } 

  // 3. The Question
  const question =
    "What is the probability that a photon will exit the final filter, and if one does exit, what will its polarization be after exiting? Explain your answer.";

  // Return formatted problem
  return `Suppose we send a ${initialState} polarized photon through ${filterStr}. ${question}`;
}

Gemini was used to assist in generating the code that produces the randomized problems on this page. While AI contributed to this content, it was designed, reviewed, and approved by Prof. Shelby Kimmel.