Composite Pulses in Phase Space: Measurement-Free Gate Teleportation with Hybrid Oscillator-Qubit Systems

The quantum operations required to manipulate states encoded in the phase space of an oscillator can be challenging to implement. Recent experimental work has realized universal control of a quantum system by combining fast single-qubit rotations with high-fidelity echoed conditional displacements (ECD), indicating the potential of achieving universal quantum computation with continuous variable (CV) qubits using two-level ancillary qubits. In this talk, we present a framework consisting of entangling and disentangling gadgets for a hybrid oscillator-qubit system that provides an analytical method for constructing these ECD-based circuits. Our method can be seen as composite pulse sequences in phase space for operations which entangle and disentangle oscillator-qubit states without any measurement. By combining these gadgets with single-qubit rotations, one can achieve measurement-free control over certain CV states. As an example, we introduce a measurement-free gate teleportation scheme that provides universal control on finite-energy GKP qubits.