Accurate and robust unitary transformation of a high-dimensional quantum system

Understand

Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing.

• For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge becomes how to implement these with high fidelity in the presence of experimental imperfections and decoherence.
• For two-level systems (qubits) most aspects of unitary control are well understood, but for systems with Hilbert space dimension d>2 (qudits), many questions remain regarding the optimal design of control Hamiltonians and the feasibility of robust implementation.
• Here we show that arbitrary, randomly chosen unitary transformations can be efficiently designed and implemented in a large dimensional Hilbert space (d=16) associated with the electronic ground state of atomic 133Cs, achieving fidelities above 0.98 as measured by randomized benchmarking.