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Extracts (9)

One question for computability: is the problem capable of producing a result

If a finite number of steps will produce an answer, it is a problem that can be solved by a Turing machine

Is the universe itself the equivalent of a Turing machine? This is not yet clear

Turing machines can’t always tell when the result has been obtained. No oracle machine is capable of solving its own halting problem

A Turing jump operator assigns to each problem X a successively harder problem, X prime. Setting a Turing machine the problem of making its own Turing jump creates a recursive effect called the Ouroboros

All problems solvable by quantum computers are also solvable by classical computers. Making use of quantum mechanical phenomena only increases speed of operation

two popular physical mechanisms, dots and liquids. Quantum dots are electrons trapped inside a cage of atoms, then excited by laser beams to superposed positions, then pushed to one state or the other. Quantum liquids (often caffeine molecules because of the many nuclei in them) are magnetically forced to spin all their nuclei in the same spin state; then NMR techniques detect and flip the spins

Decoherence happens at the loss of superposition and the resulting either/or. Before that a quantum calculation performs in parallel every possible value that the register can represent

Using superposition for computation requires avoiding decoherence for as long as possible. This has proved difficult and is still the limiting factor in the size and power of a quantum computer. Various physical and chemical means for building and connecting qubits have increased the number of qubits possible to connect before decoherence collapses the calculation, but

Quantum computers are restricted to calculations that can be performed faster than decoherence occurs in the superposed wave functions. For over a century this restricted time for a quantum computing operation to less than ten seconds

Qubes are room-temperature quantum computers with thirty qubits, the decoherence boundary limit for circuit-connected qubits, combined with a petaflop-speed classical computer to stabilize operations and provide a database. The most powerful qubes are theoretically capable of calculating the movements of all the atoms in the sun and its solar system out to the edge of the solar wind

Qubes are only faster than classical computers when they can exploit quantum parallelism. At multiplication they are no faster. But in factoring there is a difference: to factor a thousand-digit number would take a classical computer ten million billion billion years (lifetime of universe, 13.7 billion years); using Shor’s algorithm, a qube takes around twenty minutes

Grover’s algorithm means that a yearlong search using a classical computer in a random walk of a billion searches a second would take a qube in its quantum walk 185 searches

Shor’s algorithm, Grover’s algorithm, Perelman’s algorithm, Sikorski’s algorithm, Ngyuen’s algorithm, Wang’s algorithm, Wang’s other algorithm, the Cambridge algorithm, the Livermore algorithm,

entanglement is also susceptible to decoherence. Physical linkage of quantum circuits is necessary to forestall decoherence to useful time frames. Premature or undesired decoherence sets a limit on how powerful qubes can become, but the limit is high

it has proved easier to manipulate superposition than entanglement for computing purposes, and therein lies the explanation of many

The quantum database is effectively distributed over a multitude of universes

the two polarized particles decohere simultaneously no matter the physical distance between them, meaning the information jump can exceed the speed of light. The effect was confirmed by experiment in the late twentieth century. Any device that uses this phenomenon to communicate messages is called an ansible, and these devices have been constructed, but undesired decoherence has meant the maximum distance between ansibles has been nine centimeters, and this only when both were cooled to one millionth of a K above absolute zero. Physical limitations strongly suggest further progress will be asymptotic at best

powerful but isolated and discrete, somewhat like brains

questions of Penrose quantum effects in the brain have been effectively rendered moot, as these also occur in qubes by definition. If both structures are quantum computers, and one of them we are quite certain has consciousness, who is to say what’s going on in the other

human brain operations have a maximum theoretical speed of 10¹⁶ operations per second

computers have become billions to trillions times faster than human brains. So it comes down to programming; what are the operations actually doing

hierarchical levels of thought, generalization, mood, affect, will

super-recursive algorithms, hypercomputation, supertasks, trial-and-error predicates, inductive inference machines, evolutionary computers, fuzzy computation, transrecursive operators,

if you program a purpose into a computer program, does that constitute its will? Does it have free will, if a programmer programmed its purpose? Is that programming any different from the way we are programmed by our genes and brains? Is a programmed will a servile will? Is human will a servile will? And is not the servile will the home and source of all feelings of defilement, infection, transgression, and rage?

could a quantum computer program itself?