Supersymmetry-Driven Quantum Gate Design Based on Feynman Path Integral and TPCP Map Optimization

We use supersymmetry to enlarge the dimension of the Hilbert space on which the unitary evolution of the state of the quantum fields acts. We discuss how to control the unitary evolution or TPCP maps generated by the quantum evolution of the fields by controlling the vacuum expectations of other fields in the theory. This amounts to breaking supersymmetry using control vacuum expectation values of the other fields. The evolution of the wave functional or TPCP maps obtained by tracing out over other fields is based on the Feynman path integral formula for the fields. By using the methods of quantum stochastic filtering, we estimate the evolving state of the fields from non-demolition noise measurements and then design a family of TPCP maps evolving in time whose outputs match the estimated evolving state. In this way, we are able to simulate the evolution of the state of the quantum noisy fields. Direct matching of the designed TPCP map to output the evolving system state is not possible since there is no way by which we can determine the exact evolving state, we can only estimate it using non-demolition measurements. The family of designed TPCP maps can be based on using a simulated master equation with unknown parameters incorporated into the Hamiltonian and the other Lindblad operators, chosen so as to match the state outputted by the quantum filter.