Xanadu's latest quantum photonic chip

 The photonic quantum computing company Xanadu published an article in Nature last week reporting on the capabilities of their latest programmable Gaussian BosonSampling chip. Their device generates certain eight mode quantum states of light, which are detected (off-chip) using superconducting number-resolving photon detectors. In contrast to the much-publicised Gaussian BosonSampling experiment using 100 modes by the group of Jian-Wei Pan last year, this device is programmable. However, it will need to be scaled up to a much large number of modes in order to solve problems difficult for existing classical computers. Three proof-of-principle quantum algorithms were demonstrated using this chip:

1. Gaussian BosonSampling. BosonSampling is the problem of computing probabilities of obtaining multi-photon coincidences after applying a unitary transformation to quantum squeezed states of light. In the case of (Gaussian) squeezed states, the probabilities of individual detection events can be related to a property of the unitary transformation (Hafnians of its submatrices), which is hard to compute.

2. Molecular vibronic spectra. Here the problem is to compute the absorption or emission spectra of molecules, corresponding to changes in their internal (vibrational) states. These spectra can serve as molecular fingerprints. Although this task is not proven to be computationally hard, no efficient classical algorithms are known. By complementing the Gaussian BosonSampling circuit with an additional transformation (state displacement), the output photon number distribution can be used to simulate molecular vibronic spectra. Unfortunately, the present Xanadu chip does not implement displacements, and therefore was only used to solve a toy problem of this class (without displacements, and limited squeezing). In the case of coherent states, displacements can be implemented using a beamsplitter and an auxiliary mode. Another approach appears employ electro-optic modulators.

3. Graph similarity. This forms a variant of Gaussian BosonSampling. The connectivity of a graph is encoded by its adjacency matrix. This adjacency matrix is encoded into a multimode Gaussian state by suitably choosing the squeezing parameters and unitary matrix. Then, the distribution of output photon counts provides a fingerprint of the graph that can be used to compare the similarity of different graphs. In particular, the probability of a individual combination of output photons can be related to the number of perfect matchings of a subgraph of the graph. This is generally a hard task (related to the Hafnian), but if all the elements of the adjacency matrix have the same sign efficient approximate algorithms exist. I am not sure what important real-world problems involve adjacency matrices with elements with mixed signs...