Boosting Gaussian Boson Sampling using Optical Parametric Amplification Networks

Abstract

Gaussian Boson Sampling (GBS) provides a route toward demonstrating quantum computational advantage. However, optical loss, which reduces the entanglement in the system, can render GBS results classically simulable. We propose a nonlinear photonic architecture based on optical parametric amplifiers (OPAs) arranged in an interferometer network. This active configuration amplifies quantum correlations within the circuit while preserving the #P-hard Hafnian structure of the output probabilities. Using logarithmic negativity, we numerically show that entanglement scales linearly with both the OPA gain and network depth in the lossless limit, and maintains linear scaling with the number of modes under realistic loss rate. These scaling behaviors suggest that classical simulation in lossy scenarios remains computationally intractable. Our results demonstrate that OPA-boosted GBS preserves computational hardness in noisy environments, offering a more effective implementations of near-term photonic quantum computers.

Figures (3)

• Figure 1: (a) depicts the model of a lossy GBS. The inputs are single-mode squeezed states (SMSS) going through a lossy linear interferometer composed of arranged beam splitters, and (a) is equivalent to (b), using weaker squeezed SMSS passing through a lossless linear interferometer followed by an array of displacement operators. (c) shows the proposed nonlinear interferometer where the beam splitters of GBS are replaced by OPAs described by elements of $\mathrm{SU(1,1)}$. Beam splitter between OPA layers are used to model loss. Instead of inputting the squeezed states, here an array of vacuum states is adopted as the source.
• Figure 2: Logarithmic negativity ($E_\mathcal{N}$) of the output state from an $8$ modes nonlinear interferometer network with vacuum input. The degree of squeezing is uniform across all OPAs. (a) shows $E_\mathcal{N}$ as a function of depth $d$ for two different degrees of squeezing $r=0.8$ (blue) and $r=1.6$ (red). The circle-solid, cross-dashed, square-dotted and diamond-dotted-dashed lines correspond to the four partition strategies: (4,4), (5,3), (6,2) and (7,1), respectively. (b) shows the corresponding $E_\mathcal{N}$ over the degree of squeezing with a typical range from 0 to 3. The evolution depth is set to $16$ to fully connect all modes.
• Figure 3: Logarithmic negativity ($E_\mathcal{N}$) of the output states in the presence of photon loss. a) $E_\mathcal{N}$ varying with the degree of squeezing ($r$) is shown for 8-mode vacuum inputs with transmission rate ($t$) of $0.8$ (yellow) and $0.9$ (blue) at a depth ($d$) of $4$, $8$, and $16$ corresponding to the dash, point dash, and solid line. For reference, the purple and green solid lines show the ideal case for $d=8$ and $d=16$ respectively. b) A comparison of $E_\mathcal{N}$ varying with the degree of squeezing for $n =2$, $4$, $6$, $8$, and $10$ modes with $t=0.8$ and $d= 12$ . The red and purple dashed lines show the ideal case for $n=8$ and $n=10$ respectively. c) Similar to b), for various transmission with $8$-mode and $d = 12$. d) The scaling of logarithm negativity in terms of depth for $n=8$, and $10$ modes with $t = 0.8$ and $r = 0.8$ e) The scaling of $E_\mathcal{N}$ with the number of modes is shown with $d = 8$ and $r = 0.8$ for $t=0.6$, $0.7$, $0.8$, and $0.9$ (solid-colored circles). The ideal scaling is shown as well for reference (dash line). f) The scaling of $E_\mathcal{N}$ in terms of the transmission rate for $r = 0.8$, $d=8$, and $n = 8$.