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Cove: A Practical Quantum Computer Programming Framework Matt Purkeypile Fall 2008

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Quantum Computing All existing computers operate on bits and are referred to as classical computers. –They keep getting smaller and faster, but operate on the same principles Turing laid out in the 1930s. Quantum computers operate on quantum bits (qubits). The project is to provide a framework to program quantum computers. –This framework will also contain a prototype of a quantum computer simulator that allows for working code to be executed. –All simulations experience exponential slow down.

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Qubits A qubit is the quantum unit of information. –Can be 0, 1, or a probabilistic combination (superposition) of the two. When observed, qubits collapse to 0 or 1. –Thus the output is classical information. The probability amplitudes of states are expressed by complex numbers that can be less than zero. –Probabilistic bits must be greater than or equal to 0. –Think of n qubits being able to express all possible 2 n possibilities at once. –State of a two qubit register:

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What have I done the past 3 months? Completed a major revision of the dissertation. –There is much rework still needed about the properties the project will satisfy. –Many implementation details still absent. Made significant progress on the quantum computer simulation, which allows for working code to be tested. Latest developments available on the blog: https://cove.purkeypile.com/trac/blog https://cove.purkeypile.com/trac/blog –Note: https

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An example: tossing quantum coins A classical coin will always be heads or tails with equal probability after every toss. A quantum coin will also be heads or tails with equal probability, if observed after one toss. However, if the quantum coin is tossed twice (without observation) it will always be in the same state as before tossing. –Coin is heads, toss twice, observe, it will always be heads.

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How does this happen? Recall that the probabilities of every state are expressed by complex numbers, which are potentially less than zero. Certain states can be reinforced, while others can cancel out. –This is called constructive and destructive interference. –This interference plays a key part in quantum computation.

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Mathematically

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Physically When encountering a beam splitter the photon is rotated left 90 degrees if direction is altered (else no change). Mirrors rotate the photon 180 degrees.

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How this is accomplished in Cove Output: , all coins are the same as before the toss.

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Second Example: Entanglement Two qubits are put in superposition, where their states are related. When one qubit is observed as 0, the other will also be observed as 0. –This happens instantly –Regardless of the distance between them. Theoretically, even light years apart. –No information is sent, so no violations of laws of nature. (Information cannot be sent faster than light.) Einstein called this “spooky action at a distance”.

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Entanglement in Cove Output: “00” or “11” This is a common two qubit state, known as an EPR pair. –Cove will allow for common states to be obtained via static “generator” methods.

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Goals to accomplish through New Years October: Expand the implementation of the local simulation. Targets include: –Application of multiple qubit operations on slices. –Finishing “slices” (subsets) of quantum registers. November: Shift focus to major rework of the dissertation. –At this point the priority is the dissertation. The framework should be relatively stable and fairly usable at this point. Ultimate goal: Defend in June 2009.

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Questions? https://cove.purkeypile.com/

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