Manipulating matter at the quantum level is an exciting but challenging scientific endeavor. Quantum systems always interact with their environment, and the resulting many-body correlations destroy the quantum properties of the system. Achieving accurate control over solid-state systems involves deep understanding of the quantum many-body dynamics far from equilibrium. Besides fundamental interest, this research is important for applications ranging from quantum magnetism and nanosciences to quantum information processing.
I will present our recent work devoted to the quantum control of electronic and nuclear spins in diamond. I will describe the computational tools we have developed to treat the quantum dynamics of many spins , and reliably assess performance of different control approaches. These simulations guided our joint theory/experiment work towards achieving control of a single quantum spin in solid state  and protecting it from the environment. As a next step, the environment-protected manipulation of a two-spin system has been implemented, and first quantum computation on two individual diamond spin qubits  has been performed. Extending this approach to many spins in diamond, we have demonstrated nanoscale tomography with single-spin resolution , and a quantum operation on six coupled spins in diamond. I will discuss the possible applications of our work for nanoscale magnetic analysis, and for studying the quantum dynamics in the frustrated systems with long-range dipolar coupling.
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