Using Nuclear Magnetic Resonance to Assess and Optimize the Precision of Methods for Controlling Quantum Dynamics

摘要

The most significant achievements of this project were: (1) Development and validation of the hardware and software needed to implement 'strongly modulating pulses', by which high precision quantum gates can be obtain in realistic systems of up to 12 qubits; (2) A detailed analysis and evaluation of a 3-qubit quantum Fourier transform via full quantum process tomography; (3) An extensive set of mathematical and computational techniques to accomplish these goals, including Hadamard products, the real density matrix, and methods of fitting superoperators to experimental data; (4) Creation of a 3- qubit 'noiseless subsystem', of a Bell state on two 2-qubit decoherence-free subspaces (DFS), and the invention of 'partial' pseudopure states which will enable us to demonstrate robust methods for controlling multi-DFS-qubit systems by NMR; (5) Implementation of several quantum chaotic maps, and the discovery that these provide a scalable approach to determining the magnitude and kind of errors present in complex quantum computations; (6) The invention of a 'spin amplifier', by which entanglement can be used to enable single spin measurement, and a small-scale demonstration by NMR; (7) Experiments demonstrating that the foregoing advances enable implementation of complex entangling unitary and decoherent operations, culminating in creation of a 12-qubit CAT state.