Traversing Gaussian and non-Gaussian regimes in photonic quantum simulators: a review

Abstract Quantum photonic simulators are pivotal for designing and analyzing quantum photonic circuits that utilize both continuous-variable (CV) and discrete-variable (DV) encodings. This review critically examines the transition from Gaussian to non-Gaussian photonic models and the computational overhead that emerges from simulating systems with more than 20 modes or photon numbers exceeding 10 per mode. Gaussian states; such as coherent and squeezed states, are modeled efficiently using first-moment vectors and covariance matrices of dimension $2n \times 2n$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:math> , where n is the number of modes. Non-Gaussian elements like the cubic phase gate $U = \exp (i \gamma \hat{x}^{3})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>U</mml:mi> <mml:mo>=</mml:mo> <mml:mo>exp</mml:mo> <mml:mo>(</mml:mo> <mml:mi>i</mml:mi> <mml:mi>γ</mml:mi> <mml:msup> <mml:mover> <mml:mi>x</mml:mi> <mml:mo>ˆ</mml:mo> </mml:mover> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:math> and photon-subtracted states demand full Fock space representations and scale exponentially with photon number $d^{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , where d is the Hilbert space dimension. We analyze simulators including , , and , benchmarking their support for tensor networks (bond dimension D &gt;100), GPU acceleration, thus NVIDIA A100 with 1555 GB/s bandwidth, and SoC implementations such as Edge TPU with 8 TFLOPS. Special focus is given to noise models such as photon loss with transmissivity η , thermal noise modeled with $\bar{n} = 1.5$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>n</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mn>1.5</mml:mn> </mml:math> , and dark count Poisson distributions ( $\lambda = 0.1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.1</mml:mn> </mml:math> ). The review underscores scalable techniques and hybrid quantum-classical workflows vital for near-term photonic quantum computing.