Adaptive Non-Gaussian Quantum State Engineering

TL;DR

The paper tackles the challenge of efficiently generating non-Gaussian photonic states, such as Schrödinger cat and GKP grid states, by developing and numerically evaluating adaptive, multi-layer schemes based on Gaussian boson sampling (GBS). By comparing adaptive and non-adaptive architectures under equal resource budgets and optimizing a reward $\mathcal{F}+P$, the authors demonstrate that adaptivity—featuring feed-forward between layers and inline Gaussian operations—can substantially raise the probability of success $P$ while preserving high fidelity $\mathcal{F}$ for key targets. They present results for odd cat states and GKP states across three- and four-mode configurations, including scenarios with inline squeezing and Fock inputs, and show that concatenated adaptive layers can push overall success probabilities toward the ~10% range under favorable losses. The work also analyzes photon loss, showing that adaptive schemes can be more resilient under certain conditions and outlining practical considerations for implementing these schemes in integrated photonic platforms with high-gain squeezing, fast feed-forward, and efficient photon-number-resolving detection. Overall, the study offers a versatile framework for engineering non-Gaussian resource states with improved performance and a clear pathway toward experimental realization and applications in photonic quantum information processing.

Abstract

Non-Gaussian quantum states of bosons are a key resource in quantum information science with applications ranging from quantum metrology to fault-tolerant quantum computation. Generation of photonic non-Gaussian resource states, such as Schrödinger's cat and Gottesman-Kitaev-Preskill states, is challenging. In this work, we extend on existing passive architectures and explore a broad set of adaptive schemes. Our numerical results demonstrate a consistent improvement in the probability of success and fidelity of generating these non-Gaussian quantum states with equivalent resources. We also explore the effect of loss as the primary limiting factor and observe that adaptive schemes lead to more desirable outcomes in terms of overall probability of success and loss tolerance. Our work offers a versatile framework for non-Gaussian resource state generation with the potential to guide future experimental implementations.

Figures (9)

• Figure 1: GBS device with $N$ squeezed displaced input vacuum states and $N-1$ PNRDs.
• Figure 2: (a) Adaptive non-Gaussian state generation with GBS-like devices. Here, $S$ represents the squeezing operator, $U$ represents the unitary linear interferometers, and $n_i$ denotes the measurement outcome of the PNRD at the $i$-th mode. Single lines represent quantum channels, while double lines represent classical channels. (b) Adaptive scheme where the interferometer $U_2$ is the sole element in the adaptive stage. (c) Adaptive scheme analogous to (a) with general Gaussian operations instead of passive unitary interferometers. (d) General adaptive scheme with Gaussian operations.
• Figure 3: Scheme of the Bloch-Messiah decomposition.
• Figure 4: Adaptive scheme with loss occurring before and after $U_{1,2}$.
• Figure 5: Comparison between the (a) non-adaptive and (b) pseudo-adaptive schemes for generating the odd cat state. The squeezing is bounded by $r_{\text{max}}=0.5$. The darker shades in the squeezing boxes correspond to higher squeezing intensities, with the darkest blue representing $r=0.5$. The pseudo-adaptive scheme is equivalent to running the non-adaptive scheme a second time. The target state is the odd cat state with $\alpha=\sqrt{6}$. The plus sign indicates that the probabilities corresponding to the two possible outcomes of the adaptive sources can be summed.