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## Quantum Information and Computing in Multilevel Systemsby
Ashok Muthukrishnan
The quantum equivalent of a classical bit is a qubit, a two-level system. Quantum computational logic involves conditional unitary transforms on two qubits, which are the quantum analogs of logic gates in classical computer science. The multilevel extension of a qubit is a qudit, a d-level quantum system. We present several programs for universal quantum logic involving qudits, and physically motivate the formalism with examples from quantum control. Wave packets arise from multilevel quantum interference, and they give an interesting new perspective on quantum information stored in a multilevel system. We show that an alternative realization of a qudit in a quantum system is a set of d wave-packet states that are physically separated in time. The wavepacket basis is connected to the energy-level basis by a Fourier transform, a key ingredient of quantum algorithms. We apply these ideas to Rydberg atoms, and show that an appropriate coupling between such atoms enables a conceptually simpler implementation of the quantum version of the Fast Fourier transform algorithm.
Lastly we explore atomic angular momentum as a computational observable.
Most of the states in the hydrogen atom are degenerate in energy but differ by discrete units of angular momentum. We show that using Laguerre-Gaussian laser modes, which possess orbital field angular momentum, these internal angular momentum states in the atom can be entangled with its quantized center-of-mass angular momentum. We propose this entanglement as the building block for multilevel quantum computing using angular-momentum states.
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