Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation
Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation
We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schr\"odinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized …