Experimental linear optical computing of the matrix permanent
arXiv:1904.06673 · doi:10.1103/PhysRevA.99.052308
Abstract
Linear optical computing (LOC) with thermal light has recently gained attention because the problem is connected to the permanent of a Hermitian positive semidefinite matrix (HPSM), which is of importance in the computational complexity theory. Despite the several theoretical analyses on the computational structure of an HPSM in connection to LOC, the experimental demonstration and the computational complexity analysis via the linear optical system have not been performed yet. We present, herein, experimental LOC for estimating the permanent of an HPSM. From the linear optical experiments and theoretical analysis, we find that the LOC efficiency for a multiplicative error is dependent on the value of the permanent and that the lower bound of the computation time scales exponentially. Furthermore, our results are generalized and applied to LOC of permanents of unitary matrices, which can be implemented with a multi-port quantum interferometer involving single-photons at the input ports. We find that LOC with single-photons, for the permanent estimation, is on average less efficient than the most efficient classical algorithm known to date, even in ideal conditions.
References in corpus (17)
- Quantum Computing in the NISQ era and beyond
- Quantum Computing
- Boson Sampling on a Photonic Chip
- Quantum Computational Supremacy
- Experimental Boson Sampling
- Gaussian Boson Sampling
- Efficient experimental validation of photonic boson sampling against the uniform distribution
- Boson Sampling from Gaussian States
- Experimental Scattershot Boson Sampling
- Quantum Sampling Problems, BosonSampling and Quantum Supremacy
- What can quantum optics say about computational complexity theory?
- Sampling arbitrary photon-added or photon-subtracted squeezed states is in the same complexity class as boson sampling
- From the Physics to the Computational Complexity of Multiboson Correlation Interference
- Boson-sampling with photons of arbitrary spectral structure
- Experimental study of a photon as a subsystem of an entangled two-photon state
- A quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices
- The scaling of boson sampling experiments