Feynman [19] pointed out that simulating quantum physics on a classical computer will eventually need unmanageable resources. To simulate a typical quantum scenario, a classical computer must handle matrices of exponentially large size. Recall that to simulate n qubits a Hilbert space of dimension is needed. Running the QTS will inevitably meet these basic constraints. To provide some guidelines for expected runtimes when operating a QTM with the QTS package, we have compiled some timing results. For the step operator, as defined in package QTMC, we define the Feynman Hamiltonian as and the unitary time translation operator .

Let be the Nth order approximation of , that is, .

Let

q:= InitQTM[2,b,Interval[{0,4}],{{1,b[1]},{3,b[1]}},9,h,-3];

We measure the CPU time needed to compute .

All measurements are taken on a standalone PC with no other application running. The technical details of the PC configuration are as follows:

Intel Pentium II, MMX, 128 MB RAM, 450 MHz, Windows 98, Mathematica 4

The timings provided by Mathematica are shown in Figure 4 below.

Figure 4.