Factoring 2048-bit RSA Integers in 177 Days with 13 436 Qubits and a Multimode Memory

Area of Science:

• Quantum computing
• Quantum architecture
• Quantum error correction

Background:

• Standard quantum computer architectures often require a large number of qubits for complex computations like integer factorization.
• Efficiently storing and retrieving qubit states is crucial for reducing the overhead of quantum algorithms.

Purpose of the Study:

• To analyze the performance of a quantum computer architecture that integrates a small processor with a memory unit.
• To demonstrate a significant reduction in the number of processing qubits required for integer factorization compared to standard architectures.

Main Methods:

• The study focuses on integer factorization, specifically factoring a 2048-bit RSA integer.
• A quantum architecture utilizing a temporally and spatially multiplexed memory to store qubit states between processing steps is analyzed.
• Performance is evaluated using 3D gauge color codes with a physical gate error rate of 10^-3 and a processor cycle time of 1 microsecond.

Main Results:

• The proposed architecture reduces the number of processing qubits by several orders of magnitude compared to standard planar grid architectures.
• Factoring a 2048-bit RSA integer is shown to be feasible in 177 days using 13,436 physical qubits and a memory with 28 million spatial and 45 temporal modes.
• Storage times of 1 second are sufficient with additional error correction, increasing runtime by 23%.

Conclusions:

• The developed quantum computer architecture offers a more qubit-efficient approach to integer factorization.
• The integration of a multiplexed memory system is key to reducing the processing qubit requirements.
• The architecture is proposed to be realized using superconducting qubits and a rare-earth ion-based memory system.