Selective and efficient quantum process tomography for non-trace preserving maps: a superconducting quantum processor implementation

• URL: http://arxiv.org/abs/2205.10453v3
• Date: Thu, 26 Jan 2023 17:04:23 GMT
• Title: Selective and efficient quantum process tomography for non-trace preserving maps: a superconducting quantum processor implementation
• Authors: Quimey Pears Stefano, Ignacio Perito and Lorena Reb\'on
• Abstract summary: We describe a general type of quantum process that does not preserve the trace of the input quantum state. We show that with the aid of it a priori information on the losses structure of the quantum channel, the reconstruction can be adapted to reconstruct the non-trace-preserving map. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Alternatively to the full reconstruction of an unknown quantum process, the so-called selective and efficient quantum process tomography (SEQPT) allows estimating, individually and up to the required 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 {\it 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.

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