All-optical quantum computing using cubic phase gates

Abstract

If suitable quantum optical interactions were available, transforming optical field mode operators in a nonlinear fashion, the all-photonics platform could be one of the strongest contenders for realizing a quantum computer. Unlike other, matter-based (solid-state or atomic) platforms, photonic qubits can be operated at room temperature and high clock rates (GHz or, in principle, even THz). In addition, recent continuous-variable time-domain approaches are extremely well scalable. Moreover, while single-photon qubits may be processed directly, "brighter" logical qubits may be embedded in individual oscillator modes, using so-called bosonic codes, for an in-principle fault-tolerant processing. In this work, we show how elements of all-optical, universal, and fault-tolerant quantum computation can be implemented using only beam splitters together with single-mode cubic phase gates in reasonable numbers, and possibly offline squeezed-state or single-photon resources. Our approach is based on a novel decomposition technique combining exact gate decompositions and approximate trotterization. This allows for efficient decompositions of certain nonlinear continuousvariable multi-mode gates into the elementary gates, where the few cubic gates needed may even be weak or all identical, thus facilitating potential experiments. The final gate operations include two-mode controlled phase rotation and three-mode Rabi-type Hamiltonian gates, which are shown to be employable for realizing high-fidelity single-photon two-qubit entangling gates or, as a bosoniccode example, creating high-quality Gottesman-Kitaev-Preskill states. We expect our method of general use with various applications, including those that rely on quartic Kerr-type interactions.

Error-corrected quantum repeaters with GKP qudits

“…To shift the experimental burden associated with this, alternative approaches have been proposed [11,12]. If non-Gaussian resource states or non-Gaussian optical elements are available, a recursive application of short linear circuits and homodyne measurements is sufficient for the preparation of GKP states [13][14][15]. There also exist alternatives which do not rely on measurements at all [15,16].…”

“…If non-Gaussian resource states or non-Gaussian optical elements are available, a recursive application of short linear circuits and homodyne measurements is sufficient for the preparation of GKP states [13][14][15]. There also exist alternatives which do not rely on measurements at all [15,16]. A final option is to combine photon-subtraction-and homodyne-based elements to convert many-mode Gaussian cluster states into non-Gaussian few-mode states, which can be further processed into GKP states [17].…”

“…A final option is to combine photon-subtraction-and homodyne-based elements to convert many-mode Gaussian cluster states into non-Gaussian few-mode states, which can be further processed into GKP states [17]. Such an approach is compatible with measurement-based, continuous-variable quantum computation [15,18].…”