发表于 2023-4-19 09:24:11
Records for efforts by quantum computers
The largest number reliably factored by Shor's algorithm is 21 which was factored in 2012. 15 had previously been factored by several labs.
In April 2012, the factorization of by a room temperature (300K) NMR adiabatic quantum computer was reported by a group led by Xinhua Peng. In November 2014 it was discovered that the 2012 experiment had in fact also factored much larger numbers without knowing it.[clarification needed] In April 2016 the 18-bit number 200,099 was factored using quantum annealing on a D-Wave 2X quantum processor. Shortly after, 291 311 was factored using NMR at higher than room temperature. In late 2019, Zapata computing claimed to have factored 1,099,551,473,989, and in 2021 released a paper describing this computation.
In December 2022, the 48-bit factorisation was completed using a 10-qubit flip-chip superconducting quantum processor by a team in China.  The team also factored the 11-bit integer 1961 and 26-bit integer 48567227 with 3 and 5 superconducting qubits respectively. However, the approach was described by the team as a "classical-quantum hybrid", using the quantum approximate optimization algorithm to optimize the time-consuming sr-pair generation used in Schnorr's factoring algorithm,  and a classical computer to solve the resulting linear equations.
As such, claims of factoring with quantum computers have however been criticized for depending heavily on classical computation to reduce the number of qubits required.  For example, the factorization of 1,099,551,473,989 relied on classical pre-processing to reduce the problem to a three-qubit quantum circuit. Furthermore, the three numbers factored in this paper (200,099, 291,311, and 1,099,551,473,989) can easily be factored using Fermat's factorization method, requiring only 3, 1, and 1 iterations of the loop respectively.