Programmable Coherent Linear Quantum Operations with High-Dimensional Optical Spatial Modes

Abstract

A simple and flexible scheme for high-dimensional linear quantum operations is demonstrated on optical discrete spatial modes in the transverse plane. The quantum state tomography (QST) via symmetric informationally complete positive operator-valued measures (SIC POVMs) and quantum Fourier transformation (QFT) are implemented with dimensionality of 15. The statistical fidelity of SIC POVMs and fidelity of QST are ∼0.97 and up to 0.853, respectively, while the matrix fidelity of QFT is 0.85. We believe that our approach has the potential for further exploration of high-dimensional spatial entanglement provided by spontaneous parametric down conversion in nonlinear crystals.

An On-demand Photonic Ising Machine with Simplified Hamiltonian Calculation by Phase-encoding and Intensity Detection

“…Generating the phase-only patterns on SLMs. The phase-only patterns on SLM1-3 to conduct the beam-splitting and recombining operations are iteratively optimized based on a gradient-descent method, rather than simply taking the argument pattern of the superposed weighted blazed gratings in our previous work [40][41][42][43] . The loss function depending on complex-valued parameters is defined as the difference between the target field and the field modulated by the pattern to be optimized.…”

“…( 3) is complex and non-unitary, so that the OVMM employed in our architecture should be capable to achieve such non-unitary transformation. In our previous work [40][41][42][43] , a matrix transformation scheme has been demonstrated with discrete coherent spatial (DCS) modes and SLMs. With such scheme, arbitrary complex vector-matrix multiplications can be implemented for both unitary and non-unitary matrices.…”

“…Due to various unavoidable systematic errors such as misalignment in the OVMM system, the phase term and the beam-splitting and recombining ratios of all the patterns need to be calibrated. The calibration method is improved from our previous work 42…”

“…In our experimental implementation, the employed OVMM scheme is based on the discrete coherent spatial (DCS) mode and SLMs as our previous work [40][41][42][43] . To verify the feasibility of our proposal, the 20-dimensional antiferromagnetic Möbius-Ladder model as well as two fully connected, randomly generated spin-glass models are experimentally solved.…”

Emitting Laser Array of Coherent Beam Combination System Revisited: Angular Domain Perspective and the Fractal-Based Optimization

“…Despite the salient utility for the calculation of optical field distributions, the present theoretical model of emitting laser array configuration is difficult to elucidate the underlying principle for the formation of the mainlobe and sidelobes, and therefore, sidelobes suppression for CBC systems is always intuitively recognized as a long-standing engineering problem [5,7,30,33]. There is now increasing interest in exploring the theory of laser arrays in both classical and quantum regimes, and its important implications have been confirmed in developing a variety of advanced optics and photonic systems [34][35][36][37]. To fulfill the continuing desire in the enhancement of combining efficiency, it is thus essential to revisit the principle of the laser array in CBC systems with a deeper insight and further extend the optimization of the system design to a new perspective.…”