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Quantum vs. Symplectic Computers
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In this paper, we propose the concept of symplectic computers, which have the potential to be more powerful than quantum computers. Unlike quantum computing, which consists of a sequence of unitary transformations (gates) and projectors (measurements), symplectic computation involves a sequence of symplectic transformations and measurements. The proposal to explore symplectic computers is based on the following quantum-symplectic duality. The Schr\"odinger equation in its standard complex form describes the unitary evolution of a quantum system, while its real form describes the symplectic evolution of a classical mechanical system. This quantum-symplectic duality can be leveraged to enhance the capabilities of quantum and symplectic computers. In this symplectic approach, the role of a quantum bit (qubit) is taken by a symplectic bit (symbit).
Forward citations
Cited by 3 Pith papers
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Real Quantum Field Theory, J-Quantization, and Standard Model
Quantum field theory can be reformulated entirely in real numbers by substituting the matrix J for i, with all physical predictions unchanged.
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Notes on Real Quantum Mechanics in a Kahler Space
A real-number Kähler-space reformulation of quantum mechanics is claimed to be equivalent to the complex one, but the stated measurement postulate is inconsistent.
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Classical and quantum complex dynamics
A proposed complex phase-space formalism and quantization rule for non-conservative systems, but the energy formulas are dimensionally inconsistent and the key derived relations fail direct checks.
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