Generation of continuous-variable spatial cluster entangled states in optical mode comb

Spatiotemporal graph states from a single optical parametric oscillator

“…(iii) Such cluster states can also be produced in parallel, by use of higher order spatial modes lg ±2, lg ±3, ... Although the effective coupling strength ξ will initially be expected to be smaller for these modes due to the smaller overlap between the pump, signal and idler modes [34,35], ξ can be effectively enhanced by introducing a specially designed nonlinear crystal structure for matching the property of LG modes and the structured transverse mode of pump [43]. Here we provide the details on how we obtain the eigenvalues/eigenvectors of the G matrix and the analytical expression of the A matrix.…”

“…The generation of a CV dual-rail cluster state based on an optical spatial mode comb was proposed via a four-wave-mixing process [33]. Proposals were also made for large-scale CV dual-rail cluster state generation involving Laguerre-Gaussian (LG) modes in a large-Fresnel-number degenerate OPO [34], and in a spatial mode comb pumped by two spatial LG modes [35]. A CV square quadripartite cluster state was experimentally produced by multiplexing orthogonal spatial modes in a single optical parametric amplifier (OPA) [36].…”

Logical measurement-based quantum computation in circuit-QED

“…The MBQC in continuous variables (CVs) has been firstly well developed in quantum optics since such CV cluster states are achievable using traveling squeezed states through optical parametric amplifiers 4–7 . For example, the recent development of creating one-dimensional (1D) and 2D CV cluster states has been demonstrated in quantum optics using quantum memory and in time/frequency domain 8–11 . In these methods, a phase-space translation operator is in general used for single-qubit gates while a two-qubit controlled-Z gate is implemented in a sequence of beam-splitters 12,13 .…”

Time-Domain Multiplexed 2-Dimensional Cluster State: Universal Quantum Computing Platform

“…Despite its importance and many proposals on a variety of physical systems 4,8,[15][16][17][18][19][20][21] , 2-dimensional cluster states have not been realized up until now due to their complexity. For stationary qubits [18][19][20][21] , such as superconducting qubits and ion-trap qubits, we would have to prepare and spatially arrange a large number of qubits.…”

“…For CV optical systems, a flying qumode possesses rich degrees of freedom and the ability to deterministically generate entanglement. There are many schemes for scalable generation of cluster states with constant physical resources 4,8,[15][16][17] . Among them, in the TDM approach 4,8 , we utilize temporally localized wave packets as modes of quantum states allowing the generation of large-scale cluster states.…”