Simulation of quantum optics by coherent state decomposition

Abstract

We introduce a framework for simulating quantum optics by decomposing the system into a finite rank (number of terms) superposition of coherent states. This allows us to define a resource theory, where linear optical operations are 'free' (i.e., do not increase the rank), and the simulation complexity for an $m$-mode system scales quadratically in $m$, in stark contrast to the Hilbert space dimension. We outline this approach explicitly in the Fock basis, relevant in particular for Boson sampling, where the simulation time (space) complexity for computing output amplitudes, to arbitrary accuracy, scales as $O(m^2{2}^n)$ ($O(m{2}^n)$), for $n$ photons distributed amongst $m$ modes. We additionally demonstrate that linear optical simulations with the $n$ photons initially in the same mode scales efficiently, as $O(m^{2}n)$. This paradigm provides a practical notion of 'non-classicality', i.e., the classical resources required for simulation. Moreover, by making connections to the stellar rank formalism, we show this comes from two independent contributions, the number of single-photon additions, and the amount of squeezing.

25+9 pages. 6 figures. V2: Improvements to main text and additional references. V3: Updated to published version; additional discussion in Sect. 3.5, and other minor changes

References in corpus (10)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Optical Metrology -- The Lowdown on High-N00N States
• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Wigner function negativity and contextuality in quantum computation on rebits
• Leveraging Secondary Storage to Simulate Deep 54-qubit Sycamore Circuits
• Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
• Faster classical Boson Sampling
• BQP and the Polynomial Hierarchy
• Simulating Gaussian Boson Sampling with Tensor Networks in the Heisenberg picture

Cited by in corpus (13)

• Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study
• Classical simulation of non-Gaussian bosonic circuits
• Seeding Gaussian boson samplers with single photons for enhanced state generation
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Classical simulation and quantum resource theory of non-Gaussian optics
• General protocols for the efficient distillation of indistinguishable photons
• Quadrature Coherence Scale of Linear Combinations of Gaussian Functions in Phase Space
• Bosonic randomized benchmarking with passive transformations
• What's my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution
• Adaptive Non-Gaussian Quantum State Engineering
• Advancing Quantum Networking: Some Tools and Protocols for Ideal and Noisy Photonic Systems
• Classical algorithms for measurement-adaptive Gaussian circuits
• Non-Gaussianity from superselection rules