It occurred to me that the Quine statement is one which in a quantum
computer would duplicate a state. A quantum state ψ that is a set of qubits
and a set of operations {O} will as a Quine Q = {O, ψ} result in producing
itself with ψ → ψψ and Q^2 = {O×O,.ψψ}. This is not something permissible
in QM, so there must be a Hadamard gate operation that demolishes quantum
phase.
The reason why this duplication of quantum states is not quantum mechanical
is that for ψ = a|+> + b|-> then a duplication ψψ is
ψψ = a^2|++> + b^2|--> + ab(|+-> + |-+>).
However, if this duplication is unitary I can transform to a basis so the
duplicated state is a^2|++> + b^2|-->, bu just duplicating on these basis
elements. But no such unitary transformation exists.
LC
On Wednesday, June 5, 2019 at 5:21:24 AM UTC-5, Philip Thrift wrote:
>
>
> *Computational self-reference and the universal algorithm*
> Queen Mary University of London, June 2019
>
> via @JDHamkins
>
> *This was a talk for the Theory Seminar for the theory research group in
> Theoretical Computer Science at Queen Mary University of London. The talk
> was held 4 June 2019 1:00 pm.*
>
>
> Abstract. Curious, often paradoxical instances of self-reference inhabit
> deep parts of computability theory, from the intriguing Quine programs and
> Ouroboros programs to more profound features of the Gödel phenomenon. In
> this talk, I shall give an elementary account of the universal algorithm,
> showing how the capacity for self-reference in arithmetic gives rise to a
> Turing machine program e, which provably enumerates a finite set of
> numbers, but which can in principle enumerate any finite set of numbers,
> when it is run in a suitable model of arithmetic. In this sense, every
> function becomes computable, computed all by the same universal program, if
> only it is run in the right world. Furthermore, the universal algorithm can
> successively enumerate any desired extension of the sequence, when run in a
> suitable top-extension of the universe. An analogous result holds in set
> theory, where Woodin and I have provided a universal locally definable
> finite set, which can in principle be any finite set, in the right
> universe, and which can furthermore be successively extended to become any
> desired finite superset of that set in a suitable top-extension of that
> universe.
>
>
> http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/
> slides:
>
> http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf
>
>
> @philipthrift
>
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