Nasir Siddiqui | Office of Undergraduate Research

Comparing classical and quantum algorithms to solve systems of linear equations

We present the results of a method we have devised to empirically measure the time complexity of the conjugate gradient algorithm for solving systems of linear equations as a function of matrix system sizes ranging from n=1 to n=9. Our experimental results demonstrate that the actual number of iterations required to solve the system are consistent with the theoretical numbers. We also demonstrate the implementation of a quantum algorithm to solve a system of equations by obtaining a solution state vector proportional to the actual solution for a 2x2 system.

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