Quantum computing with classical bits

TL;DR

This paper explores how classical Ising spin systems can emulate quantum computing processes, including entanglement and unitary operations, potentially enabling new computational architectures without quantum hardware.

Contribution

It introduces a formalism linking classical probabilistic systems with quantum computation, demonstrating how static memory materials can realize quantum gates and entanglement.

Findings

Classical Ising spins can represent quantum states and operations.

Static memory materials can transport boundary information through the bulk.

Probabilistic systems can emulate quantum entanglement and unitary evolution.

Abstract

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. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems 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 which may, in turn, correspond to continuous variables or fields. 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 perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.