True experimental reconstruction of quantum states and processes via convex optimization
Akshay Gaikwad, Arvind, Kavita Dorai
TL;DR
This work tackles the problem of unphysical reconstructions in quantum state and process tomography that arise from standard linear inversion. It introduces a constrained convex optimization (CCO) framework solved by semi-definite programming (SDP) to enforce physical constraints, yielding valid density matrices $\rho$ and process matrices $\chi$ without ancillary qubits. Applied to a two-qubit NMR processor, CCO QST produces $\rho$ with high fidelity and CCO QPT yields a positive semidefinite $\chi$ with fidelities $>0.98$, enabling extraction of Kraus operators $\{E_i\}$ for real gates. The method is further extended to Markovian decoherence via a Lindblad master equation, providing good short-time agreement and offering a robust tool for noise characterization and mitigation in quantum devices.
Abstract
We use a constrained convex optimization (CCO) method to experimentally characterize arbitrary quantum states and unknown quantum processes on a two-qubit NMR quantum information processor. Standard protocols for quantum state and quantum process tomography are based on linear inversion, which often result in an unphysical density matrix and hence an invalid process matrix. The CCO method on the other hand, produces physically valid density matrices and process matrices, with significantly improved fidelity as compared to the standard methods. The constrainedoptimization problem is solved with the help of a semi-definite programming (SDP) protocol. We use the CCO method to estimate the Kraus operators and characterize gates in the presence of errors due to decoherence. We then assume Markovian system dynamics and use a Lindblad master equation in conjunction with the CCO method to completely characterize the noise processes present in the NMR qubits.