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

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 2 048-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 13 436 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.

Figure 1

Quantum computer architecture using a processor made with a 2D grid of qubits and a memory operating as a qubit register where the address of each qubit is specified by a temporal and spatial index. Only (dressed) logical qubits are represented; additional ancillary qubits are used for measuring the operators for error correction.

Figure 2

Number of qubits in the processor and run-time to factor $n$-bit RSA integers with a computer architecture using a multimode memory.