This work introduces a new method for quantum random number generation (QRNG) based on a new model of n-dimensional quantum hyperchaotic systems ( \(\textrm{nD}-\textrm{QHCS}\) ) called nD Quantum Hyperchaotic Random Numbers Generation (nD-QHCRNG), which is derived from the classical n-dimensional hyperchaotic systems (nD-HCS) [1]. Our approach leveraging quantum measurement uncertainty via Von Neumann (VNman) projection to produce truly random bit sequences of nD-QHCS. The quantum system is described by the Hamiltonian \(\hat{H}=\sum _{i=1}^n \frac{\hat{p}_i^2}{2}+\sum _{i=1}^n\left(A \hat{q}_{i+1} \hat{q}_{i-1}-B \hat{q}_{i-2} \hat{q}_{i-1}\right) \) with \(\hat{p}_i=-i \hbar \frac{\partial}{\partial q_i}\) , where \(\hat{p}_i\) and \(q_i\) are the momentum and position of quantum system, respectively. The system exhibits complex quantum dynamics behavior with substantial entanglement between degrees of freedom. The proposed method harnesses quantum randomness through the measurement process, where the system evolves under the hyperchaotic Hamiltonian, quantum measurements induce wavefunction collapse according to the VNman projection axiom, and thus generate nondeterministic outcomes. Statistical analysis of bit sequences produced by the nD-QHCS generator demonstrates exceptional randomness quality, passing all NIST tests successfully. The nD-QHCS method combines the sensitivity to initial conditions characteristic of classical nD-HCS with the fundamental indeterminism of quantum measurement, resulting in a QRNG with entropy values approaching theoretical maximums. The performance analysis shows negligible autocorrelation and uniform distribution of bit patterns, making this method suitable for cryptographic applications requiring high-quality randomness.