Quantum computing with classical bits
Quantum computing is based on a sequence of unitary operations acting on the wave function. Classical computing uses bits or Ising spins that can only take two values. A computation is again a series of operations on the bits. These are generally viewed as deterministic operations. Quantum operations or gates can be performed by Ising spins or classical bits, within a classical statistical setting. It is argued that classical systems realizing quantum computing have to be truly probabilistic. It is shown that there is no sharp boundary between probabilistic computation with classical bits and quantum computation with isolated qubits. Classical bit operations can do whatever quantum operations can do however without any speed up that could be achieved by a quantum computer. It is proposed that quantum operations can directly be performed by neural networks. Since neural networks operate classically, this amounts to realizing quantum statistics by classical statistical systems. Finally a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases is proposed.
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