Ground State Nature and Nonlinear Squeezing of Gottesman-Kitaev-Preskill States.

The main bottleneck for universal quantum computation with traveling light is the preparation of Gottesman-Kitaev-Preskill states of sufficient quality. This is an extremely challenging task, experimental as well as theoretical, also because there is currently no single easily computable measure of quality for these states. We introduce such a measure, Gottesman-Kitaev-Preskill squeezing, and show how it is related to the current ways of characterizing the states. The measure is easy to compute and can be easily employed in state preparation as well as verification of experimental results.

Logical states for fault-tolerant quantum computation with propagating light.

To harness the potential of a quantum computer, quantum information must be protected against error by encoding it into a logical state that is suitable for quantum error correction. The Gottesman-Kitaev-Preskill (GKP) qubit is a promising candidate because the required multiqubit operations are readily available at optical frequency. To date, however, GKP qubits have been demonstrated only at mechanical and microwave frequencies. We realized a GKP state in propagating light at telecommunication wavelength and verified it through homodyne measurements without loss corrections. The generation is based on interference of cat states, followed by homodyne measurements. Our final states exhibit nonclassicality and non-Gaussianity, including the trident shape of faint instances of GKP states. Improvements toward brighter, multipeaked GKP qubits will be the basis for quantum computation with light.

Nonlinear feedforward enabling quantum computation.

Measurement-based quantum computation with optical time-domain multiplexing is a promising method to realize a quantum computer from the viewpoint of scalability. Fault tolerance and universality are also realizable by preparing appropriate resource quantum states and electro-optical feedforward that is altered based on measurement results. While linear feedforward has been realized and become a common experimental technique, nonlinear feedforward was unrealized until now. In this paper, we demonstrate that a fast and flexible nonlinear feedforward realizes the essential measurement required for fault-tolerant and universal quantum computation. Using non-Gaussian ancillary states, we observed 10% reduction of the measurement excess noise relative to classical vacuum ancilla.

Non-Gaussian quantum state generation by multi-photon subtraction at the telecommunication wavelength.

In the field of continuous-variable quantum information processing, non-Gaussian states with negative values of the Wigner function are crucial for the development of a fault-tolerant universal quantum computer. While several non-Gaussian states have been generated experimentally, none have been created using ultrashort optical wave packets, which are necessary for high-speed quantum computation, in the telecommunication wavelength band where mature optical communication technology is available. In this paper, we present the generation of non-Gaussian states on wave packets with a short 8-ps duration in the 1545.32 nm telecommunication wavelength band using photon subtraction up to three photons. We used a low-loss, quasi-single spatial mode waveguide optical parametric amplifier, a superconducting transition edge sensor, and a phase-locked pulsed homodyne measurement system to observe negative values of the Wigner function without loss correction up to three-photon subtraction. These results can be extended to the generation of more complicated non-Gaussian states and are a key technology in the pursuit of high-speed optical quantum computation.

Cubic nonlinear squeezing and its decoherence.

Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators below threshold for all possible up-to-quadratic Hamiltonians, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often more vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. Therefore, a stability of nonlinear squeezing is essential. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters which can be optimized and adjusted to achieve the maximal robustness for the potential applications.

Taming numerical errors in simulations of continuous variable non-Gaussian state preparation.

Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the Fock state representation. It unavoidably uses an approximation of the infinite-dimensional Fock space by finite complex vector spaces implementable with classical digital computers. In this approximation we analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. To overcome their limitations we propose an alternative with improved accuracy based on the standard matrix exponential. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement. We compare different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors in the context of engineering non-linearly squeezed cubic states and construction of qubit-like superpositions between vacuum and single photon states.

Generation of quantum states with nonlinear squeezing by Kerr nonlinearity.

In quantum optics, squeezing corresponds to the process in which fluctuations of a quadrature operator are reduced below the shot noise limit. In turn, nonlinear squeezing can be defined as reduction of fluctuations related to nonlinear combination of quadrature operators. Quantum states with nonlinear squeezing are a necessary resource for deterministic implementation of high-order quadrature phase gates that are, in turn, sufficient for advanced quantum information processing. We demonstrate that this class of states can be deterministically prepared by employing a single self-Kerr gate accompanied by suitable Gaussian processing. The required Kerr coupling depends on the energy of the initial system and can be made arbitrarily small. We also employ numerical simulations to analyze the effects of imperfections and to show to which extent can they be neglected.

Benchmarking photon number resolving detectors.

Photon number resolving detectors are the ultimate measurement of quantum optics, which is the reason why developing the technology is getting significant attention in recent years. With this arises the question of how to evaluate the performance of the detectors. We suggest that performance of a photon number detector can be evaluated by comparing it to a multiplex of on-off detectors in a practical scenario: conditional preparation of a photon number state. Here, both the quality of the prepared state and the probability of the preparation are limited by the number of on-off detectors in the multiplex, which allows us to set benchmarks that can be achieved or surpassed by the photon number resolving detectors.

Loop-based subtraction of a single photon from a traveling beam of light.

Manipulating light by adding and subtracting individual photons is a powerful approach with a principal drawback: the operations are fundamentally probabilistic and the probability is often small. This limits not only the fundamental scalability but also the number of operations that can be applied in realistic experimental settings. We propose and analyze a loop-based technique which can significantly increase the probability of success while preserving the quality of the photon subtraction. We show the improvement both in single mode preparation and manipulation of non-Gaussian states with negative Wigner functions and in two-mode entanglement distillation protocol with Gaussian states of light.

Qubit-mediated deterministic nonlinear gates for quantum oscillators.

Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since strong highly nonlinear operations are often unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, it is possible to resolve these issues and implement a nonlinear operation both nearly deterministically and nearly perfectly. We explicitly demonstrate the approach by constructing self-Kerr and cross-Kerr couplings in a realistic situation, which require a feasible dispersive coupling between the two-level system and the oscillator.

Experimental characterization of a non-local convertor for quantum photonic networks.

We experimentally characterize a quantum photonic gate that is capable of converting multiqubit entangled states while acting only on two qubits. It is an important tool in large quantum networks, where it can be used for re-wiring of multipartite entangled states or for generating various entangled states required for specific tasks. The gate can be also used to generate quantum information processing resources, such as entanglement and discord. In our experimental demonstration, we characterized the conversion of a linear four-qubit cluster state into different entangled states, including GHZ and Dicke states. The high quality of the experimental results show that the gate has the potential of being a flexible component in distributed quantum photonic networks.

Noiseless Conditional Teleportation of a Single Photon.

We experimentally demonstrate the noiseless teleportation of a single photon by conditioning on quadrature Bell measurement results near the origin in phase space and thereby circumventing the photon loss that otherwise occurs even in optimal gain-tuned continuous-variable quantum teleportation. In general, thanks to this loss suppression, the noiseless conditional teleportation can preserve the negativity of the Wigner function for an arbitrary pure input state and an arbitrary pure entangled resource state. In our experiment, the positive value of the Wigner function at the origin for the unconditional output state, W(0,0)=0.015±0.001, becomes clearly negative after conditioning, W(0,0)=-0.025±0.005, illustrating the advantage of noiseless conditional teleportation.

Exploring a new regime for processing optical qubits: squeezing and unsqueezing single photons.

We implement the squeezing operation as a genuine quantum gate, deterministically and reversibly acting "online" upon an input state no longer restricted to the set of Gaussian states. More specifically, by applying an efficient and robust squeezing operation for the first time to non-Gaussian states, we demonstrate a two-way conversion between a particlelike single-photon state and a wavelike superposition of coherent states. Our squeezing gate is reliable enough to preserve the negativities of the corresponding Wigner functions. This demonstration represents an important and necessary step towards hybridizing discrete and continuous quantum protocols.

Generating superposition of up-to three photons for continuous variable quantum information processing.

We develop an experimental scheme based on a continuous-wave (cw) laser for generating arbitrary superpositions of photon number states. In this experiment, we successfully generate superposition states of zero to three photons, namely advanced versions of superpositions of two and three coherent states. They are fully compatible with developed quantum teleportation and measurement-based quantum operations with cw lasers. Due to achieved high detection efficiency, we observe, without any loss correction, multiple areas of negativity of Wigner function, which confirm strongly nonclassical nature of the generated states.