  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).
