Quantum diagonalization of hermitean matrices

To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource: Hermitean (N × N) matrices can be diagonalized, in principle, by performing appropriate quantum mechanical measurements. To do so, one considers the given matrix as an observable of a single spin with appropriate length s which can be measured using a generalized Stern–Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As the underlying working principle is the ‘collapse of the wavefunction ’ associated with a measurement, the procedure is neither a digital nor an analogue calculation—it defines thus a new example of a quantum mechanical method of computation. PACS numbers: 0367, 0365 Non-classical features of quantum mechanics such as Heisenberg’s uncertainty relation and entanglement have intrigued physicists for several decades. From a classical point of view