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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Effective prime factorization via quantum annealing by modular locally-structured embedding.

Jingwen Ding1, Giuseppe Spallitta1, Roberto Sebastiani2

  • 1Department of Computer Science and Engineering, University of Trento, Trento, Italy.

Scientific Reports
|February 12, 2024
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Summary
This summary is machine-generated.

This study introduces compact quantum annealing (QA) encoding for prime factorization (PF). Researchers successfully factored 8,219,999 using a D-Wave quantum annealer, marking a significant advancement in quantum computing for cryptography.

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Area of Science:

  • Quantum Computing
  • Computational Mathematics
  • Cryptography

Background:

  • Prime factorization is a computationally intensive problem crucial for modern cryptography.
  • Quantum annealing (QA) offers a potential approach to accelerate complex computations like prime factorization.
  • Current quantum annealer architectures present challenges for encoding large-scale problems.

Purpose of the Study:

  • To develop novel, compact encoding techniques for prime factorization problems on quantum annealers.
  • To experimentally evaluate the performance of these encodings and factorization methods on a D-Wave quantum annealer.
  • To establish new benchmarks for the largest numbers factorized by quantum devices without classical pre-processing.

Main Methods:

  • Developed a compact modular encoding of a multiplier circuit using Optimization Modulo Theories for D-Wave's Pegasus topology.
  • Synthesized an 8-qubit module for a controlled full-adder, enabling the encoding of larger multiplication problems.
  • Conducted extensive experimental evaluations on a D-Wave Advantage 4.1 quantum annealer, testing different qubit initialization and performance enhancement techniques.

Main Results:

  • Successfully encoded up to a 21 × 12-bit multiplier into the D-Wave Pegasus 5760-qubit topology.
  • Factored the number 8,219,999 (32,749 × 251) as the highest prime product within QPU resource limitations.
  • Achieved the largest factorization by a quantum annealer and any quantum device without classical assistance.

Conclusions:

  • The developed compact encoding techniques significantly increase the scale of prime factorization problems addressable by current quantum annealers.
  • Experimental results demonstrate the feasibility and growing capability of quantum annealing for tackling cryptographic-relevant computations.
  • This work represents a substantial step towards practical quantum advantage in number theory and secure communication.