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What are the consequences of quantum pollution?

The best introductory reference to quantum computing is “Quantum Computing for Computer Scientists” by Noson S. Yanofsky and Mirco A. Mannucci.

Some major low level quantum programming langauges are QCL (see tph.tuwien.ac.at/~oemer/qcl.html), Q Language, qGCL, QFC, QPL, QML, and Quantum Lambda Calculus. QCL is the major quantum programming languuage.

The Quipper Language (see www.mscs.dal.ca/~selinger/quipper/) is a high level quantum programming language developed with funding from the U.S. government.

It is most likely that quantum computing will be used along side classical computing in a hybrid system.

Three state logic (using trits) was the basis of Konrad Zuse’s computers (Zuse I, II, and III), the second one being the first electronic computer. Tri-state logic includes all of binary logic and other options (such as a “don’t care” state, which is common in designing logic circuits). The first volume of Donald Knuth’s “Art of Computer Programming” discusses many number base systems and points out that the trinary number system actually has significant mathematical advantages over the binary and decimal systems, including that there is only one unique trinary representation for any real number (while in binary and decimal there are two representations).

The first volume of Donald Knuth’s “Art of Computer Programming” also discusses the quater-imaginary number system, which produces all real and all complex numbers.

You could potentially use any of binary, trinary or quater-imaginary digits in quantum computers, but all current approaches use bianry in a system of qubits.

Qubits (quantum bits) are measured at the end of the quantum computation and then fall into either the ground or excited state — giving us the same two values as classical bits. The big advantage of qubits is that while they are in the quantum state, they have superposition, meaning that they hold all possible values. This gives us the ability to perform operations that are exponential in classical physics (and therefore take more resources than the entire universe for fairly small problems) and turn them into quantum operations that take quadratic time (which makes solving them practical).

The Toffoli gate is in fact classical complete all by itself.

You can apply multiple steps to a quantum computer, although each step introduces a probability of error. That’s not a serious problem, because the probabilistic nature of quantum computing requires using multiple runs and taking the most common answer.

Also, each step is a tensor product across the entire quantum register, so each step involves many operations (even if some of them are identity operations).

Each step must be reversible (a requirement of quantum mechanics), so different methods are used in quantum computing than in classical computing.

The biggest problem with multiple steps is that each step increases the chance of decoherence, losing everything.

From a practical point of view there are many operations where the quantum computer is capable of performing the calculations but it is impractical.

Most of the recent papers on quantum computing have looked at hybrid systems where the classical computer component performs all of the calculations where a classical computer is efficient.

Several of the recently published algorithms have used an approach of using the quantum computer to get near an answer (concentrating on steps that would require exponential time on a classical computer) and having a classical computer finish the evaluation (when only polynomial steps remain).

A quantum computer gains two things from a classical-quantum hybrid: lower cost and more time before decoherence. The bigger a quantum computer and the more steps in the process, the greater the chance of a random interaction causing decoherence, destroying all of the computations in process. WIth improvements in technology, decoherence may become less of a problem, but right now, minimizing quantum steps is more than just a cost savings measure. Anything that can be done efficiently with classical computers should be done in either pre- or post- quantum processing.

A related topic is the matter of quantum pollution [external link]

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Last Updated: July 21, 2013

Created: July 21, 2013

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