Quantum vs. Symplectic Computers

TL;DR

This paper introduces symplectic computers, a new computational paradigm potentially more powerful than quantum computers, based on symplectic transformations and a duality with quantum systems.

Contribution

It proposes the concept of symplectic computers and explores their theoretical foundation through quantum-symplectic duality, offering a novel approach to computation.

Findings

Symplectic computers utilize symplectic transformations and measurements.

Quantum-symplectic duality links quantum and classical mechanical evolutions.

Symplectic bits (symbits) replace qubits in this framework.

Abstract

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).