# Simulating Universal Quantum Gate Sets on Photonic OAM Qubits: Single-Qubit and Multi-Qubit Operations via Spatial Light Modulator Phase Holography

**Authors:** Saleha Maqsood, Muhammad Kamran, Tahir Malik  
**arXiv:** [2606.26088](https://arxiv.org/abs/2606.26088)  
**Date:** 2026-06-24  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2606.26088v1/

## Key points

- Spatial light modulators (SLMs) are essential for reconfigurable photonic quantum information processing
- SLMs enable precise control over the orbital angular momentum (OAM) of light encoded in Laguerre-Gaussian (LG) beams
- Thorough analysis of quantum gate operations on the HOLOEYE LC 2012 transmissive SLM with a realistic three-channel noise model
- Total noise quantified at $σ_{\text{total}} = 92.4\text{mrad}$, including 8-bit quantisation noise, TN electronic and thermal noise, and phase-wrap clipping error
- Simulation of universal single-qubit gate set $\{X, Y, Z, S, T, H\}$ and two-qubit entangling gates $\{\text{CNOT}, \text{CZ}, \text{SWAP}\}$ on a $512 \times 512$ computational grid
- Predicted gate fidelities range from $F = 0.9914$ to $0.9936$, with Bell state preparation achieving a fidelity of $F(Φ^+) = 0.9914$
- TN electronic noise identified as primary factor limiting fidelity in gate operations on this SLM platform
- Successful encoding of two logical qubits in four orthogonal OAM modes and demonstration of fundamental two-qubit gates with high fidelity in simulation
- Future directions include experimental validation using quantum state tomography, exploring machine learning-based hologram optimization routines, and investigating applications in variational quantum eigensolver (VQE) circuit implementations

## Summary

Spatial light modulators (SLMs) have become essential tools for reconfigurable photonic quantum information processing. They enable precise control over the orbital angular momentum (OAM) of light encoded in Laguerre-Gaussian (LG) beams. This paper presents a thorough analysis of quantum gate operations implemented on the HOLOEYE LC 2012 transmissive SLM. It incorporates a realistic three-channel noise model derived from the manufacturer's datasheet without any free-parameter fitting. The total noise is quantified at $σ_{\text{total}} = 92.4\text{mrad}$, encompassing 8-bit quantisation noise, twisted-nematic (TN) electronic and thermal noise, and phase-wrap clipping error. The study simulates the complete universal single-qubit gate set $\{X, Y, Z, S, T, H\}$ and two-qubit entangling gates $\{\text{CNOT}, \text{CZ}, \text{SWAP}\}$ on a $512 \times 512$ computational grid. Results indicate that predicted gate fidelities range from $F = 0.9914$ to $0.9936$, with fork grating gates primarily limited by TN noise and phase gates achieving higher fidelity due to zero phase-wrap clipping error. Notably, Bell state preparation via the H-CNOT circuit achieves a fidelity of $F(Φ^+) = 0.9914$ after two SLM interactions within the wavelength range of 450--532 nm which was found to be optimal for operation of the HOLOEYE LC 2012 device. The paper also benchmarks its results against six experimental studies spanning a fidelity range of 78%--99.6%, showcasing the physical realism of the simulation model. In conclusion and future work, it is highlighted that TN electronic noise emerges as the primary factor limiting fidelity in gate operations on this SLM platform. Additionally, degradation above 630nm is observed due to limited phase retardation at longer wavelengths. The study successfully encodes two logical qubits in four orthogonal OAM modes and demonstrates fundamental two-qubit gates with high fidelity in simulation. Future directions include experimental validation using quantum state tomography with the HOLOEYE LC 2012 device, integrating far-field Fourier propagation models for beam evolution considerations, extending multi-qubit frameworks to higher-dimensional OAM qudit spaces for error-correction code demonstrations, exploring machine learning-based hologram optimization routines for minimizing errors during gate operations, and investigating applications of the SLM-OAM platform in variational quantum eigensolver (VQE) circuit implementations. The authors acknowledge support from the Centre for Quantum Technologies (CQT) at NED University of Engineering and Technology for providing facilities and resources for this research project. Overall contributions were made by S.M., M.K., and T.M., who collectively developed theoretical frameworks, conducted data analysis, interpreted results, drafted manuscripts collaboratively while ensuring scientific accuracy throughout all stages of research.