Von Neumann entropy
A measure in quantum mechanics of the degree of mixing of a density matrix, defined as S = -Tr(ρ·ln ρ). In the VPU it is used as a convergence metric, corresponding to temperature in simulated annealing.
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Entanglement entropy is a tool for quantifying the degree of entanglement between two quantum systems, defined as the von Neumann entropy of the remaining subsystem after taking the partial trace over the composite system.
VPU's solution is to run quantum-inspired state evolution on a low-rank approximation of the Hermitian Hamiltonian matrix: represent the problem space as a high-dimensional state vector σ∈[0,1]^dim, evolve the effective Hamiltonian H_eff using RK4 numerical integration, keep computation feasible through low-rank approximation, and finally measure convergence using von Neumann entropy.
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Entanglement entropy is a tool for quantifying the degree of entanglement between two quantum systems, defined as the von Neumann entropy of the remaining subsystem after taking the partial trace over the composite system.
50%UnverifiedVPU's solution is to run quantum-inspired state evolution on a low-rank approximation of the Hermitian Hamiltonian matrix: represent the problem space as a high-dimensional state vector σ∈[0,1]^dim, evolve the effective Hamiltonian H_eff using RK4 numerical integration, keep computation feasible through low-rank approximation, and finally measure convergence using von Neumann entropy.
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