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arXiv:2105.11035

All-optical Quantum State Engineering for Rotation-symmetric Bosonic States

Rajveer Nehra, Miller Eaton, Olivier Pfister, Alireza Marandi

Published May 23, 2021• 1 citation
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Abstract

Continuous-variable quantum information processing through quantum optics offers a promising platform for building the next generation of scalable fault-tolerant information processors. To achieve quantum computational advantages and fault tolerance, non-Gaussian resources are essential. In this work, we propose and analyze a method to generate a variety of non-Gaussian states using coherent photon subtraction from a two-mode squeezed state followed by photon-number-resolving measurements. The proposed method offers a promising way to generate rotation-symmetric states conventionally used for quantum error correction with binomial codes and truncated Schrödinger cat codes. We consider the deleterious effects of experimental imperfections such as detection inefficiencies and losses in the state engineering protocol. Our method can be readily implemented with current quantum photonic technologies.

DOI
10.48550/arxiv.2105.11035

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Continuous-variable quantum information processing through quantum optics offers a promising platform for building the next generation of scalable fault-tolerant information processors. To achieve quantum computational advantages and fault tolerance, non-Gaussian resources are essential. In this work, we propose and analyze a method to generate a variety of non-Gaussian states using coherent photon subtraction from a two-mode squeezed state followed by photon-number-resolving measurements. The proposed method offers a promising way to generate rotation-symmetric states conventionally used for quantum error correction with binomial codes and truncated Schrödinger cat codes. We consider the deleterious effects of experimental imperfections such as detection inefficiencies and losses in the state engineering protocol. Our method can be readily implemented with current quantum photonic technologies.
We propose a high-rate generation method of optical Schr\"odinger cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, allowing us to optimize them and attain a high generation rate. Supposing realistic experimental conditions, the generation rate of cat states with large amplitudes ($|\ensuremath{\alpha}|\ensuremath{\ge}2)$ can exceed megacounts per second, about 103{10}^{3}103 to 106{10}^{6}106 times better than typical rates of conventional photon subtraction. This rate would be improved further by the progress of related technologies. The ability to generate non-Gaussian states at a high rate is important in quantum computing using optical continuous variables, where scalability has been demonstrated but preparation of non-Gaussian states of light remains as a challenging task for universality and fault tolerance. Our proposal reduces the difficulty of the state preparation and opens a way for practical applications in quantum optics.
Continuous-variable quantum computing (CVQC) boasts, by way of quantum optics, one of the largest scalability potentials of all quantum computing platforms. In order to enable universal CVQC, i.e., exponential speedup as well as fault tolerance, one requires quantum resources (states and/or gates) with a non-Gaussian Wigner function. We present several state preparation techniques, using photon-number-resolving detection, that enable the generation of resource states such as GKP or binomial error encodings.
A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.
We propose a high-rate generation method of optical Schrödinger cat states [1] . More than a decade, the standard method of cat-state generation has been photon subtraction from squeezed vacuum states [2] . Its constraints on experimental parameters, however, limit the generation rate. We overcome the problem by considering photon-number measurement in one mode of arbitrary two-mode Gaussian states, which we call "generalized photon subtraction". Analysis of such a general situation is challenging, but we analytically derive an efficient condition by describing the state-generation process using wave functions. Supposing realistic experimental conditions, the generation rate of cat states with large-amplitude (| α| ≥ 2) is improved by multiple orders from the conventional photon subtraction. Our proposal would open a way for quantum error correction and coherent-state-based quantum computing.
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.