Selective and Efficient Quantum Process Tomography for Non-Trace-Preserving Maps: Implementation with a Superconducting Quantum Processor

PEARS STEFANO, Q.; PERITO, I.; REBÓN, L.

physical review applied

American Physical Society

Año: 2023

2331-7019

Alternatively to the full reconstruction of an unknown quantum process, the so-called selectiveand efficient quantum process tomography (SEQPT) allows estimating, individually and up to therequired accuracy, a given element of the matrix that describes such an operation with a polynomial amount of resources. The implementation of this protocol has been carried out with success to characterize the evolution of a quantum system that is well described by a trace preserving quantum map. Here, we deal with a more general type of quantum process that does not preserve the trace of the input quantum state, which naturally arises in the presence of imperfect devices and system-environment interactions, in the context of quantum information science or quantum dynamics control. In that case, we show that with the aid of a priori information on the losses structure of the quantum channel, the SEQPT reconstruction can be adapted to reconstruct the non-trace-preserving map. We explicitly describe how to implement the reconstruction in an arbitrary Hilbert space of finite dimension d. The method is experimentally verified on a superconducting quantum processor of the IBM Quantum services, by estimating several non trace-preserving quantum processes in dimensions up to d = 6. Our results show that it is possible to efficiently reconstruct non trace- preserving processes, with high precision, and with significantly higher fidelity than when the process is assumed to be trace-preserving.