Extended Data Table 1 Comparison of large-scale boson sampling demonstrations
From: An atomic boson sampler
- For works involving Fock state boson sampling, n denotes both the particle number and the number of input modes. Works involving Gaussian boson sampling are marked with a *, in which case n corresponds only to the number of input modes. \({\mathcal{P}}=1-{g}^{(2)}(0)\) is typically referred to as the “purity” in photonics experiments, and is measured via second order correlations in Hanbury-Brown-Twiss-like experiments. †To the extent that these measurements characterize the single-particle nature of the input field9, in our experiments \({\mathcal{P}}\simeq 1\) and is lower-bounded by our imaging fidelity of 0.998(1). However, our state purity is primarily limited by thermal motional excitations normal to the lattice, and can be estimated using the measured particle indistinguishability of \({\mathcal{J}}=0.99{5}_{-16}^{+5}\), which is an estimate of the purity assuming that the single-particle density matrices in the out-of-plane motional DOF are equal. To characterize state preparation, we list \({\mathcal{J}}\) for Fock state boson sampling results and the squeezing parameter r for Gaussian boson sampling results. m denotes the number of output modes in the linear optical network. “Loss” denotes the fraction of particles lost during evolution, including incoupling from the source to the linear-optical network, loss in the network, and outcoupling to the detectors. Detection is characterized by the detection efficiency, and the type of measurement performed on each output mode. “Click” refers to detecting the presence or absence of particles, “parity” to detecting particle number parity, “PPNRD” to pseudo-photon-number-resolving detection, and “counting” to full particle number-resolved readout. The work marked with ‡ includes fiber coupling loss in the estimate of detection efficiency, and the work marked with § includes detection efficiency in the quoted value for loss. ∥The listed value for our work is a detection fidelity rather than an efficiency, and includes contributions from both particle loss and infidelity. Converting the other listed values to detection fidelities would involve including the effects of leakage light and dark counts, resulting in slightly lower values. “Input” refers to the class of states that can be prepared as inputs to the linear optical network, with “phase” referring to tunability of the phases of the prepared squeezed states, and “pattern” to nearly arbitrary Fock states with occupations of 0 or 1 on each input mode (see Methods). “Evolution” refers to the family of linear optical networks that can be applied in a given system, with “Hamiltonian” referring to unitary evolution for variable time under a fixed Hamiltonian. For both “input” and “evolution”, “fixed” refers to a single instance, and “tunable” to flexible, but not universal, programmability. The numbers appearing in this table are representative values for approximate comparison only, please refer to the original publications for details.
