Evidence for the conjecture that sampling generalized cat states with linear optics is hard

Abstract

Boson-sampling has been presented as a simplified model for linear optical quantum computing. In the boson-sampling model, Fock states are passed through a linear optics network and sampled via number-resolved photodetection. It has been shown that this sampling problem likely cannot be efficiently classically simulated. This raises the question as to whether there are other quantum states of light for which the equivalent sampling problem is also computationally hard. We present evidence, without using a full complexity proof, that a very broad class of quantum states of light -arbitrary superpositions of two or more coherent states -when evolved via passive linear optics and sampled with number-resolved photodetection, likely implements a classically hard sampling problem.

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

“…The sampling problem possesses well-understood limiting cases: semi-classical sampling in the many-particle limit n m [33,34], classical sampling for distinguishable particles, Fourier-sampling for structured scattering matrices [5,32] and computationally hard BosonSampling [2], possibly realized with an input beyond multi-mode Fock-states [23][24][25]. These discrete cases constitute the corners of the high-dimensional and widely unexplored phase diagram of sampling complexity, whose precise demarkation from a physical and computerscience perspective constitutes an ambitious desideratum.…”

“…From a physical perspective, the successful experimental implementation of Boson-Sampling [6][7][8][9] has raised questions encompassing the scalability [16] and tolerance towards errors [15,[17][18][19], the generalization to experimentally more accessible systems [20,21] and alternative physical implementations of the original problem [22][23][24][25][26]. Bridging the fields of physics and computer science, the problem of verifying the functionality of an alleged Boson-Sampler arose [27][28][29].…”

Generalized Multiphoton Quantum Interference

“…The second issue is the handling of possible errors [18][19][20]. BosonSampling is a purely passive optical scheme and therefore lacks error-correction capabilities [21]. Only in the ideal case where the interfering photons are indistinguishable in all degrees of freedom is the resulting output probability distribution proportional to the permanent only.…”

Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states: The quantum-classical divide and computational-complexity transitions in linear optics

“…To further elaborate, while the sampling of thermal states can be simulated efficiently by a classical algorithm [25], it has been shown that the sampling of squeezed vacuum states is likely hard to efficiently simulate classically at least in some special cases [24,26]. Among non-Gaussian inputs (other than the Fock states), the photon-added and subtracted squeezed vacuum states [27] and generalized cat states (arbitrary superpositions of coherent states) [28], along with photon number detection, have been shown to likely implement computationally hard sampling problems similar to boson sampling.…”