The Twilight Zone (1985) : 1x6

In the far future, twelve-year-old Dickie must pass the government intelligence test. He is very nervous about the outcome of the test but eager to show how smart he is. At the end his parents get the news - Dickie "passed" the test...but the government kills anyone who is too intelligent. In 1985, a fever-stricken Peter Wood finds himself in telepathic contact with Charity Paine, a sick girl his age living in Puritan New England. The two rejoice in sharing their thoughts, and Peter gives Charity the chance to see things that she'd never experienced in her limit time and place. However, their new-found contact turns to horror when Peter's knowledge of the future endangers Charity's life. She inadvertently speaks of the future, causing the villagers to believe she is a witch.