Hybrid bosonic codes combining bosonic codes with photon states offer a promising pathway for fault-tolerant quantum computation. However, the efficient generation of such states in optical setups remains technically challenging due to the requirement for complex non-Gaussian resources. In this paper, we propose a novel scheme to efficiently generate hybrid entangled states between a GKP qubit and a photon-number state using small-amplitude cat states as the primary resource. We apply a breeding process using small-amplitude cat states to increase the non-Gaussianity of the input states. This method requires only linear optical elements and homodyne measurements. Furthermore, we demonstrate that this protocol can be extended to generate hybrid qudit states. This scheme has the potential to provide a resource-efficient and experimentally attractive route toward implementing hybrid quantum error correction.
Hybrid bosonic codes combining bosonic codes with photon states offer a promising pathway for fault-tolerant quantum computation. However, the efficient generation of such states in optical setups remains technically challenging due to the requirement for complex non-Gaussian resources. In this paper, we propose a novel scheme to efficiently generate hybrid entangled states between a GKP qubit and a photon-number state using small-amplitude cat states as the primary resource. We apply a breeding process using small-amplitude cat states to increase the non-Gaussianity of the input states. This method requires only linear optical elements and homodyne measurements. Furthermore, we demonstrate that this protocol can be extended to generate hybrid qudit states. This scheme has the potential to provide a resource-efficient and experimentally attractive route toward implementing hybrid quantum error correction.
The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.
Large-amplitude squeezed cat states and high-quality Gottesman-Kitaev-Preskill (GKP) states are essential for effective quantum error correction, yet their optical preparation has been hindered by challenges such as low success probabilities, small amplitudes, and insufficient squeezing. Addressing these limitations, our research introduces scalable optical schemes for the deterministic preparation of large-amplitude squeezed cat states from photon-number states. Fock states have the benefit of producing consistent cat states across all measurement outcomes and intrinsically provides a degree of squeezing. Notably, these squeezed cat states facilitate the deterministic generation of high-quality approximate GKP states via "breeding," showing that GKP error correction in optics is technically feasible in near-term experiments. Our schemes allow fault-tolerant quantum computation through the use of GKP error correction.
To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available gate interactions be compatible with the code. A promising bosonic code is the Gottesman-Kitaev-Preskill (GKP) code, for which a linear beamsplitter-like coupling between two bosonic modes is fault-tolerant, making this a key primitive for building larger systems. Here, using two motional modes of a trapped ion, we demonstrate the generation of entangled states of GKP qubits by interfering two qunaught states, which have a grid structure but carry no logical information, on a beamsplitter. We generate all four Bell states with an average fidelity of 69%, and subsequently demonstrate an extension of the entangled state lifetime through the use of quantum error correction. These results complete the set of Gaussian operations required for quantum computing with GKP codes and enable explorations of multi-mode bosonic encodings as well as fundamental tests of information channels.
Optical system is an appealing system for quantum computation as it has tremendous scalability over typical matter-based qubit. This is thanks to its rich degree of freedom that allows multiplexing. A particularly promising approach is the time-domain multiplexing approach where large-scale entangled resources and their usages have been demonstrated. To achieve quantum computation, these resources have to be combined with a type of states called non-Gaussian states. Non-Gaussian state generation requires strong nonlinearity which is challenging in optical system, compared to the matter-based system. In this work, we explain our recent work in the generation of the non-Gaussian states for optical quantum computer. In the first half, we discuss the demonstration of cat-breeding protocol for the generation of Gottesman-Kitaev-Preskill (GKP) qubit. In the second half, we show the demonstration of generation of cat states from broadband light source. In the future, by combining these two techniques, we can achieve high-rate high-quality GKP states crucial for optical quantum computer.
GKP states enable fault-tolerant CV quantum computation, but their generation remains experimentally challenging due to their highly non-Gaussian and infinite-energy ideal structure. In this work, we present a realistic and scalable protocol for generating finite-energy resource states, specifically the qunaught state, using Schrodinger cat states generated in a strongly coupled quantum dot-cavity system. Our scheme combines deterministic squeezed cat-state generation, cat-breeding protocols, and homodyne measurements. Using numerical simulations, we analyze the role of various parameters of the quantum dot-cavity system in the generation of practical qunaught states. Furthermore, we quantify the trade-off between the fidelity and generation probability of these states and exploit the fact that accepting a structured set of homodyne outcomes can significantly enhance the overall success rate. The proposed approach is compatible with integrated photonics and telecom wavelengths, offering a promising route toward scalable CV quantum information processing.
Non-Gaussian quantum states of light are important resources for implementing quantum information tasks, ranging from fault-tolerant optical quantum information processing to long distance quantum communication. These states can be generated by applying non-Gaussian operations, such as photon addition and subtraction, to an input Gaussian quantum state. Also, the use of Gaussian operations (like homodyne measurement) allows the transformation of non-Gaussian input quantum states while maintaining their non-Gaussianity. It has been shown that in such context, iterative tailoring of arbitrary quantum states is possible, by cascading elementary operation blocks. This invitably comes at the cost of increasing the protocol complexity. Spectral modes, on the other hand, can be used to handily carry multiple quantum states in a single spatial mode. Moreover, multimode states populating such modes are readily available in commonly exploited processes such as spontaneous parametric down conversion.In this work, we propose a protocol to generate non-Gaussian quantum states using spectral multiplexing of input states and Gaussian operations. We give the analytical expression of the output non-Gaussian state as a function of the number of input state, the Gaussian operation and the properties of spectral modes carrying the input quantum states. Taking as an example the cat breeding operation, we show that with a single mixing and measurement operation, we can obtain an amplified output cat state comparable to the one obtained using iterative breeding scheme with multiple mixing operations and measurements with the same number of input states. We show also that the generation of approximated GKP states is possible with this protocol. We believe that the proposed protocol will have a major impact on the field of non-Gaussian quantum states generation, and can be used to extend the study beyond the cases considered in our work.