Stochastic emulation of quantum algorithms

Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and fact that unitary transformations on can be broken down to universal gates act only one or two qubits at same time. The former aspect renders direct classical simulation difficult. Here we introduce higher-order partial derivatives a probability distribution particle positions as new object shares these basic properties mechanical needed for algorithm. Discretization allows represent state $n_\text{bit}$ by $2(n_\text{bit}+1)$ stochastic bits. Based this, demonstrate many-particle representation pure entangled via distributions find set maps correspond gate set. We prove propagation map built those reproduces up prefactor exactly evolution with corresponding algorithm, leading automated translation algorithm implement several well-known algorithms, analyse scaling number realizations qubits, highlight role destructive cost emulation. Foundational questions raised are discussed.