Abstract
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
Highlights
The hypothesis pursued in this paper is that the power of quantum computation solely resides in a proper “translation” of “holistic” properties of functions—manifesting themselves in the relational values for different elements of their domain, or of their entire image—into orthogonal subspaces and their associated perpendicular projections
In what follows we shall attempt to enumerate conditions under which a given algorithmic task can be quantum mechanically encoded into orthogonal subspaces, thereby identifying criteria for potential quantum speedups
Most notably Schrödinger struggled with quantum coherence, today known as quantum parallelism, throughout his entire life, bringing forward seemingly absurd consequences of the formalism, such as the cat paradox, or quantum jellification [2]
Summary
The hypothesis pursued in this paper is that the power of quantum computation solely resides in a proper “translation” of “holistic” properties of functions—manifesting themselves in the relational values for different elements of their domain, or of their entire image—into orthogonal subspaces and their associated perpendicular projections. This is usually facilitated by quantum parallelism—the possibility to co-represent and co-encode classically distinct and mutually exclusive clauses into simultaneous coherent superpositions thereof. This involves the possibility to orthogonalise non-orthogonal vectors of some initial Hilbert space by interpreting them as orthogonal projections of mutually orthogonal vectors in a Hilbert space of greater dimension
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