Galois fields Archives - IEEE Transactions on Quantum Engineering

Encoder Circuit Optimization for Nonbinary Quantum Error Correction Codes in Prime Dimensions: An Algorithmic Framework

March 2, 2026Aditya Sodhani, Keshab K. ParhiQuantum InformationCodes, Encoding, Galois fields, Hardware, Hilbert space, Logic gates, Quantum system, Qubit, Urban areas, Vectors

Abstract: Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically operate on qubits—quantum information elements that can occupy superpositions of the basis |0⟩ and |1⟩ states—recent advances have demonstrated the practical implementation of higher dimensional […]

Private Product Computation Using Quantum Entanglement

In this article, we show that a pair of entangled qubits can be used to compute a product privately. More precisely, two participants with a private input from a finite field can perform local operations on a shared, Bell-like quantum state, and when these qubits are later sent to a third participant, the third participant […]