Quantum computing

A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks.

Here qD is the dark count probability of the detectors, η is the overall transmittance of the interferometer, r is the squeezing parameter of the M input squeezed states (assumed to be identical) and ϵ is a bound in the TVD of the photon-number probability distributions of GBS instance and the classical adversary. To estimate the round-trip transmittance of a particular loop \({\ell }\), we bypass the other loop delays and compare the amount of light detected when light undergoes a round-trip through a particular loop, relative to when all the round-trip channels are closed, that is, all loops in a ‘bar’ state. The transmittance η = 1 − NRFTMSV = ηC × η0 × ηdemux is the product of the common transmittance ηC, the round-trip in the first loop η0 and the average transmittance associated with two demux-detector channels used to detect the two halves of the two-mode squeezed vacuum \({\eta }_{{\rm{demux}}}=\frac{1}{2}\{{\eta }_{{\rm{demux}},i}+{\eta }_{{\rm{demux}},j}\}\). From this relation, we can find We obtain \({\eta }_{{\ell }}\), which we can then plug in equation ( 7) to complete the calibration sequence. For the purposes of sampling, a threshold detection event that in an experiment can be caused by one or many photons, can always be assumed to have been caused by a single photon, thus threshold samples have the same complexity as in the formula above with G = 2 (ref. 30), which is quadratically faster than the estimates in refs. Given that all the squeezed states come from the same squeezer and the programmability of our system, we can parametrize and characterize the loss budget of our system using a very small set of parameters. We cover the output pattern of all possible permutations \((\begin{array}{c}N+M-1\\ N\end{array})\), in which N is the number of photons, from 3 to 6, and M = 16 is the number of modes. Equation ( 4) captures the collision-free complexity of the hafnian of an N × N matrix of \(O({N}_{c}^{3}{2}^{{N}_{c}/2})\) because in that case G = 2. To quantify the performance of Borealis we calculate the fidelity (F) and total variation distance (TVD) of the 3, 4, 5 and 6 total photon-number probabilities relative to the ground truth. Overall, it is clear that the statistics of experimental samples diverge from the adversarial hypotheses considered and agree with the ground truth of our device (as seen in the top left panel of Fig. 4b) where they cluster around the identity line at 45°. For this reason, and the lack of evidence that the scores may change in favour of any alternative to the ground truth, we are confident that the studied range of N = [10,26] is sufficient to rule out all classical spoofers considered, even in the regime in which it is unfeasible to perform these benchmarks. In previous experiments 1, 2 the results were benchmarked against a ground truth obtained from tomographic measurements of a static interferometer, whereas for Borealis, the ground truth is obtained from the quantum program specified by the user, that is the squeezing parameters and phases sent to the VBS components in the device.