Factoring 2048-bit RSA Integers in 177 Days with 13436 Qubits and a Multimode Memory

TL;DR

This paper proposes a quantum computer architecture with a small processor and a large multiplexed memory, enabling the factorization of a 2048-bit RSA integer in 177 days using 13,436 qubits, significantly reducing the required processing qubits.

Contribution

It introduces a novel quantum architecture combining processing and multiplexed memory, reducing qubit requirements for large integer factorization tasks.

Findings

Factorization of 2048-bit RSA in 177 days with 13,436 qubits.

Reduction of processing qubits by leveraging multiplexed memory.

Feasibility of long-term quantum memory with photon echo in solids.

Abstract

We analyze the performance of a quantum computer architecture combining a small processor and a storage unit. By focusing on integer factorization, we show a reduction by several orders of magnitude of the number of processing qubits compared with a standard architecture using a planar grid of qubits with nearest-neighbor connectivity. This is achieved by taking advantage of a temporally and spatially multiplexed memory to store the qubit states between processing steps. Concretely, for a characteristic physical gate error rate of $10^{-3}$, a processor cycle time of 1 microsecond, factoring a 2048-bit RSA integer is shown to be possible in 177 days with 3D gauge color codes assuming a threshold of 0.75 % with a processor made with 13436 physical qubits and a memory that can store 28 million spatial modes and 45 temporal modes with 2 hours' storage time. By inserting additional error-correction steps, storage times of 1 second are shown to be sufficient at the cost of increasing the run-time by about 23 %. Shorter run-times (and storage times) are achievable by increasing the number of qubits in the processing unit. We suggest realizing such an architecture using a microwave interface between a processor made with superconducting qubits and a multiplexed memory using the principle of photon echo in solids doped with rare-earth ions.