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By Darwin C. G.

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Extra resources for A Quantum Theory of Optical Dispersion

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This statement may be interpreted as saying that a digital computer with a random number generator (and unlimited memory) can execute any known algo- Principles of quantum computation rithm with overhead which is at most polynomial in the size of the problem, compared with the resources required for another computer. The importance of quantum computation is that it violates this thesis! Quantum computers can solve certain mathematical problems faster than is possible using classical resources alone, and moreover, classical computers cannot efficiently simulate quantum computations!

The Deutsch-Jozsa algorithm 4. 1. 2. 1. 2. 3. 4. Fungibility 5. 1. 2. 3. 4. 5. Noisy coding theorem 6. 1. 2. 3. 4. 5. Examples 7. 1. 2. 3. 4. 5. Fault-tolerance and scalability References 5 5 5 7 7 12 12 13 14 15 18 19 22 22 23 23 26 28 30 32 ~2 ~4 ~5 ~7 t7 40 41 42 43 44 45 47 48 50 51 51 53 54 This Page Intentionally Left Blank 1. Introduction This chapter summarizes lectures I gave at the Les Houches school on quantum information, from June 30, 2003 through July 10, 2003. Much of the material is based on the book Quantum Computation and Quantum Information [1] ("QCQI"), co-authored with Michael Nielsen, but aside from a quick introduction to the subject, in this write-up the focus is on new topics and approaches, including quantum circuit analysis methods, a survey of entanglement as a physical resource, a review of information theory, examples of open quantum system dynamics, and a summary of ideas from quantum error correction.

4) 10000) + 10011) + II100) + Ii111). 8) x=0 where x is a two-bit number, conveniently written in decimal form. 9) x--0 when appropriately relabeled. Example 3: 100) + 101) + I10) is entangled. 1111) is entangled, but we'd like to think it is somehow less entangled than 100) + I11); this is indeed the case, as we will see. Example 4: 1000) + l111) is a three-qubit entangled state known as the GHZ state. In fact, most multi-qubit states are entangled. 2. Applications of entanglement We illustrate the usefulness of entangled states with two applications: precision measurement and teleportation.

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