assignment3 - Physics 681-481 CS 483 Assignment#3(please...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
February 16, 2006 Physics 681-481; CS 483: Assignment #3 (please hand in after the lecture, Thursday, March 2nd) I. Other aspects of Deutsch’s problem Suppose one tried to solve Deutsch’s problem, not by the clever trick used in Chapter 2, Section B, but by doing the standard thing: Start with input and output registers in the state | 0 i| 0 i , apply a Hadamard to the input register, and then apply U f , thereby associating with the two Qbits the state | ψ i = 1 2 | 0 i| f (0) i + 1 2 | 1 i| f (1) i . (1) Given two Qbits in this state, a direct measurement only reveals the value of f at either 0 or 1 (randomly), but gives no information about whether f (0) = f (1). But is there anything more clever one can to two Qbits in the state (1) to learn whether or not f (0) = f (1), by applying a further unitary transformation before measuring? Deutsch noticed a way to do this successfully half the time: (a) Show that if you apply a Hadamard H to each Qbit prior to the measurement, then regardless of which of the four possible states (1) you have been given (corresponding to the four possible ways a function f can take one bit to one bit), there is a 50% chance that the measurement will enable you to conclude whether or not f (0) = f (1). But the other 50% of the time you learn nothing whatever from the measurement outcome, neither about whether f (0) = f
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern