Assignment 9, due Dec. 7, 2005

Read as much as you can:

R. Weiss et al., "Genetic Circuit Building Blocks for Cellular Computation, Communications, and Signal Processing", Natural Computing, vol. 2, pp. 47-84, 2003. (Weiss et al. 03 in the usual place).

Prof. Weiss will be visiting us next week starting at about half-time. This is a long review paper, so you will probably want to read only the first few sections carefully, and then skim the remainder. Note especially the main ideas behind the implementation of the standard classical gates. Come with good questions.

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Problems:

Reference all sources accurately and completely.

Among the many thousands of web pages that discuss entangled states, their meaning, and their uses, you find a spectrum ranging from complete dribble to high-quality exposition. Learn to be fussy! Here's a random hit I liked and which you might find useful: Tony Hey lecture, part of a series of lectures at the Quantum Technology Collaborative Group, based at the University of Southampton, UK: QTC which reviews what we've discussing and goes further. An informed and economic introduction.

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1. The two-qubit state (1/sqrt(2))(|00> + |11>) is the input to a quantum CNOT gate. What is the (two-qubit) output?

2. The input in Problem 1 is "(maximally) entangled"; it's sometimes called an "EPR" or "Bell" state. Explain what this means.

3. Is the output in Problem 1 entangled?

4. The three-qubit state (1/sqrt(2))(|111>+|010>) is the input to a Fredkin gate. What is the (three-qubit) output? Is it as entangled as possible?

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