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

TL;DR

This paper extends selective and efficient quantum process tomography to non-trace-preserving maps, enabling accurate characterization of quantum processes with losses, demonstrated on a superconducting quantum processor with high fidelity.

Contribution

It introduces a method to adapt SEQPT for non-trace-preserving quantum processes using prior information, validated experimentally on IBM quantum hardware.

Findings

Successfully reconstructed non trace-preserving processes up to dimension 6

Achieved higher fidelity than assuming trace preservation

Demonstrated efficiency and high precision in experimental implementation

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.