Realization of quantum process tomography in NMR

Abstract

Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.

Quantum-process tomography: Resource analysis of different strategies

“…Equation (24) means that for any unbiased estimator the error is lower-bounded by the inverse of the Fisher information. The Fisher information matrix is indeed a measure of information about χ that exists in the data D X .…”

“…SQPT has been experimentally demonstrated in liquid-state NMR [24,25,26], optical [27,28], atomic [29] and solid-state systems [30]. Since the map E is linear, it can in principle be reconstructed from the measured data by a proper inversion.…”

NMR Quantum Information Processing

“…It allows for a comparison between different devices, and indicates the prospects of these devices with respect to the fault-tolerant quantum computing [20]. The traditional approach for characterizing any quantum process is known as quantum process tomography (QPT) [21,22], which has been realized in up to 3-qubit systems in experiment [23][24][25][26][27][28]. However an arbitrary process on a n-qubit system has (2 ) free parameters.…”

NMR Quantum Information Processing

“…This equation yields a nonunitary evolution of the density matrix so that pure states can evolve into mixed states. To understand and test models of decoherence, methods based on quantum process tomography (QPT) were developed to measure Γ [52,53], so that the dynamics of the system could be simulated more accurately. The full model of the system including coherent, incoherent and decoherent dynamics, has been tested extensively with a three qubit QPT of the Quantum Fourier Transform superoperator [54].…”