Bosonic modes (quantum harmonic oscillators) provide vast hardware-efficient quantum resources because even a single bosonic mode can be used as a multi-level quantum system. We are interested to design quantum control protocols to harnessing these continuous-variable bosonic systems for quantum computation, by constructing finite dimensional qudits from an oscillator using simple Jaynes-Cummings interactions, which is readily implementable on trapped ion quantum computers.
Hybrid CV-DV Quantum Signal Processing
Quantum signal processing (QSP) relies on two components: i) a block-encoding of the operator; and ii) the ability to impart an arbitrary phase shift to the encoded operator. Block-encoding in simply means embedding the target operator inside a unitary matrix. Methods for block-encoding on qubit devices are mostly limited and block-encoding of a general Hamiltonian is difficult. It might thus seem that such block-encoding will be especially challenging for infinite dimensional bosonic oscillators. Surprisingly, some physical interactions between qubits and oscillators can provide natural block-encodings. This allows qubitization of bosonic modes and generalization of QSP to hybrid CV-DV systems. We are interested to develop such hybrid CV-DV QSP into powerful framework to control and compile useful operations on hybrid qubit-oscillator quantum processors.