Deterministic multi-mode nonlinear coupling for quantum circuits

Abstract

We present a general technique for deterministically implementing a multi-mode nonlinear coupling between several propagating microwave or optical modes in quantum circuits. The measurement induced technique combines specifically prepared resource states together with feasible feed-forward operations. We explore several ways of generating the suitable resource states and discuss their difference on an illustrative example of cubic coupling between two modes. We also show that the required entangled states with requisite nonlinear properties can be already generated in the present day experiments.

Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors

“…The cubic phase state is essential in CV quantum computation [18], e.g., it can be used as a resource state to implement a cubic phase gate through gate teleportation [61]. A recent proposal has also extended this notion to a two-mode gate that is non-Gaussian [69]. A cubic phase state with a large phase parameter is usually difficult to generate, however, it can be generated by concatenating a sequence of weak cubic phase gates.…”

Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics

“…We also mention the possibility to obtain the cross-Kerr interaction by using the decomposition technique [78][79][80] and the multi-mode nonlinear coupling [81]. For the decomposition technique, the quantum gate for the n-order Hamiltonian with n > 3 can be approximated by the sequential gates consisting of less than the n -order Hamiltonians with n < n. Thus, our proposed scheme can be implemented in an optical setup, by replacing the cross-Kerr interaction with the cubic phase gate and Gaussian operations.…”

“…For the multi-mode nonlinear coupling, Ref. [81] introduced the multi-mode gate for modes 1 and 2, which is composed of only q operators such as e i q1 n q2 n with n + n > 3. Although the cross-Kerr gate is composed of q and p operators, which is described as e i( q1 2 + p1 2 )( q2 2 + p2 2 ) , we may obtain the cross-Kerr interaction by applying multi-mode nonlinear coupling to the cross-Kerr gate.…”

Cubic nonlinear squeezing and its decoherence

“…There are two parameters, z and χ. Final cubicity z relates to decohered state which is either measured or utilized for further processing [31,53]. In turn, the initial cubicity χ relates to the initially prepared cubic nonlinear state.…”

“…This sets it apart from the usual probabilistic methods for injecting non-Gaussianity into quantum system that rely on approximating addition or subtraction of individual photons by using single photon detectors [13,33,43,58,64,68,69]. Direct implementation of the quadrature phase gates by nonlinear crystals, optical fibers and atomic ensembles is currently unavailable, but they can be deterministically realized in a measurement induced fashion [31,39,53]. Using this approach, the required cubic nonlinearity is imprinted on the target system by coupling it to a different system in a specific quantum state, measuring this auxiliary system, and completing the process by deterministic nonlinear feed-forward.…”