Quantum computing with classical bits
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A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. We discuss static memory materials based on Ising spins that realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical spins can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or the brain. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.
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