Efficient Classical Computation of Single-Qubit Marginal Measurement Probabilities to Simulate Certain Classes of Quantum Algorithms

TL;DR

This paper introduces a neural network-based modification to the QC-DFT method, significantly improving the classical simulation of single-qubit measurement probabilities in certain quantum circuits, aiding in quantum algorithm verification.

Contribution

The paper presents a novel CNOT functional using neural networks that enhances the QC-DFT method's accuracy in simulating quantum circuits, especially for multi-qubit gates.

Findings

Lower single-qubit probability errors

Higher fidelities in simulations

Potential for simulating specific quantum algorithms

Abstract

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.