Simulations of Probabilities for Quantum Computing

Tzvetan S. Metodi, Arvin I. Faruque, Frederic T. Chong

Santana Yuda Pradata, M 'Anin N. 'Azhiim, Hendry M. Lim +4 more

Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available methods, the classical simulation of quantum circuits inspired by density functional theory -- the so-called QC-DFT method, shows promise for large circuit simulations as it approximates the quantum circuits using single-qubit reduced density matrices to model multi-qubit systems. However, the QC-DFT method performs very poorly when dealing with multi-qubit gates. In this work, we introduce a novel CNOT "functional" that leverages neural networks to generate unitary transformations, effectively mitigating the simulation errors observed in the original QC-DFT method. For random circuit simulations, our modified QC-DFT enables efficient computation of single-qubit marginal measurement probabilities, or single-qubit probability (SQPs), and achieves lower SQP errors and higher fidelities than the original QC-DFT method. Despite some limitations in capturing full entanglement and joint probability distributions, we find potential applications of SQPs in simulating Shor's and Grover's algorithms for specific solution classes. These findings advance the capabilities of classical simulations for some quantum problems and provide insights into managing entanglement and gate errors in practical quantum computing.

Jincheng Zhang

This paper explores the integration of probability logic and quantum computing to develop a novel computational model. We propose a framework that leverages quantum entanglement and quantum masking to enhance probabilistic reasoning and simulation capabilities. The core mechanism centers on combining the inherent uncertainty of probability logic with the superposition and entanglement properties of quantum computation. This model aims to provide a comprehensive computational engine capable of tackling complex probability problems and simulating quantum systems, facilitating quantum algorithm optimization and performance prediction. The study highlights the potential of this integrated approach to advance computational power and explore novel applications within the field of quantum information science.

Nicolas J. Cerf, S. E. Koonin

Tzvetan S. Metodi, Frederic T. Chong

Jincheng Zhang

This paper introduces a novel probabilistic space quantum entanglement simulator designed to efficiently model and simulate complex quantum entanglement states. Traditional quantum computation approaches often struggle with the inherent complexity of entangled states. This paper proposes a new algorithm that leverages a probability distribution to model entangled states, enabling direct calculation of entanglement probabilities rather than relying on complex quantum calculations. The core mechanism involves mapping the quantum state to a probability distribution, then using this distribution to simulate the evolution of the entangled state. This approach offers a significant improvement in computational efficiency and the potential for enhanced quantum algorithm capabilities. The paper details the design of this simulator, its performance evaluation, and its implications for future quantum computing advancements.