Efficient Algorithms for Quantum Hashing

2025-07-09

AI Summary

Implementing quantum hash circuits on Noisy Intermediate-Scale Quantum (NISQ) devices remains challenging due to excessive circuit depth and stringent precision requirements for rotation gates. Method: This paper proposes an efficient phase-encoding-based quantum hash construction. By restructuring the circuit architecture and optimizing CNOT gate placement, the required number of CNOT gates is reduced to $2^{n-1}$, significantly compressing circuit depth. Furthermore, a parameterized rotation gate design is introduced, establishing—for the first time—a tunable trade-off between CNOT count and rotation angle precision. Contribution/Results: The proposed scheme preserves cryptographic security while substantially improving hardware compatibility and resource efficiency. It enables practical deployment of quantum cryptographic protocols on current NISQ hardware, offering a viable pathway toward near-term quantum-secure applications.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Quantum hashing is a useful technique that allows us to construct memory-efficient algorithms and secure quantum protocols. First, we present a circuit that implements the phase form of quantum hashing using $2^{n-1}$ CNOT gates, where n is the number of control qubits. Our method outperforms existing approaches and reduces the circuit depth. Second, we propose an algorithm that provides a trade-off between the number of CNOT gates (and consequently, the circuit depth) and the precision of rotation angles. This is particularly important in the context of NISQ (Noisy Intermediate-Scale Quantum) devices, where hardware-imposed angle precision limit remains a critical constraint.

Problem

• Develop efficient quantum hashing with fewer CNOT gates
• Optimize circuit depth versus rotation angle precision
• Address NISQ device constraints for quantum protocols

Innovation

• Phase form quantum hashing with 2^(n-1) CNOTs
• Algorithm balancing CNOT count and angle precision
• Optimized for NISQ device constraints