Adaptive Tomography of Pure States and Unitary Gates
The successful implementation of complex quantum algorithms depend crucially on our ability to determine unknown quantum states and operations. In this work, we present adaptive and non-adaptive methods to determine a 1-qubit unitary gate with 5 and 6 Pauli measurements. We demonstrate the method on the Bloch sphere to show that studying higher dimensional real space may help in finding tomography methods of multiple qubit unitary gates. Next, we show an adaptive method to uniquely determine a general d-dimensional pure state among all quantum states with at most 2d - 1 measurements. This method is then applied to determine a general d-dimensional unitary gate with at most d^2 + d - 1 measurements. These methods are applied in tomographing a 2-qubit universal gate set with five unitary gates. On the NMR experimental system, the lowest fidelity achieved was above 97% with 42 Pauli measurements, comparing to 99% using traditional method that requires 240 Pauli measurements.