I think the factoring milestone table in section "1.1 The State of Play" contains at least two entries that should be corrected or clarified.
1. IBM superconducting (2019): "35 = 5 × 7"
The cited experiment did attempt a compiled implementation of Shor's algorithm for N = 35, but the paper itself explicitly concludes that the algorithm failed to factor 35:
"Eventually, the algorithm fails to factor N = 35."
For N = 35, the experimentally observed distribution actually matched the incorrect period r = 7 slightly better (SSO = 0.99) than the correct period r = 6 (SSO = 0.98).
Therefore, listing this simply as:
IBM superconducting | 2019 | 35 = 5 × 7
under "Largest Number Factored" seems misleading. At minimum, this should probably be marked as a failed / inconclusive experimental attempt rather than a successful factorization milestone.
Paper:
"An Experimental Study of Shor’s Factoring Algorithm on IBM Q"
arXiv:1903.00768
2. The 2023 "Variational hybrid" result is not Shor's algorithm, and the number is incorrect
The table appears under the heading "Shor's Algorithm in 50 Years: A Speculative Projection (2026 → 2076)", but the 2023 "Variational hybrid" entry is not an implementation or variant of Shor's algorithm.
The cited paper explicitly distinguishes its method from Shor's algorithm. The authors write:
"Up to now, the largest integer factorized by Shor's algorithm in current quantum systems is 21."
They then describe other approaches separately:
"Alternatively, integer factorization can be transformed into an optimization problem, which can be solved by adiabatic quantum computation (AQC) or QAOA."
And their own algorithm is explicitly described as being based on Schnorr's classical factoring algorithm:
"The algorithm is based on the classical Schnorr's algorithm, which uses lattice reduction to factor integers. We take advantage of QAOA to optimize the most time-consuming part of Schnorr's algorithm..."
Therefore, presenting this result as a milestone in a historical/prospective table about Shor's algorithm is misleading. It is a different hybrid classical-quantum factoring approach based on Schnorr's lattice algorithm and QAOA, not Shor's period-finding algorithm.
In fact, the paper itself explicitly compares the proposed algorithm against Shor's algorithm:
"This makes it the most qubit-saving quantum algorithm for integer factorization compared with the existing algorithms, including Shor's algorithm."
There is also a factual error in the number shown in the table. The paper reports:
"Using this algorithm, we have successfully factorized the integers 1961 (11-bit), 48567227 (26-bit) and 261980999226229 (48-bit), with 3, 5 and 10 qubits..."
So the reported integer is 261,980,999,226,229, not 261,980,999.
I suggest either removing this entry from a table specifically describing the progress of Shor's algorithm, or clearly separating non-Shor hybrid/variational factoring algorithms into a different category.
https://github.com/ruvnet/RuVector/blob/main/docs/research/quantum-crypto/shors-algorithm-50-year-projection.md
I think the factoring milestone table in section "1.1 The State of Play" contains at least two entries that should be corrected or clarified.
1. IBM superconducting (2019): "35 = 5 × 7"
The cited experiment did attempt a compiled implementation of Shor's algorithm for N = 35, but the paper itself explicitly concludes that the algorithm failed to factor 35:
For N = 35, the experimentally observed distribution actually matched the incorrect period r = 7 slightly better (SSO = 0.99) than the correct period r = 6 (SSO = 0.98).
Therefore, listing this simply as:
under "Largest Number Factored" seems misleading. At minimum, this should probably be marked as a failed / inconclusive experimental attempt rather than a successful factorization milestone.
Paper:
"An Experimental Study of Shor’s Factoring Algorithm on IBM Q"
arXiv:1903.00768
2. The 2023 "Variational hybrid" result is not Shor's algorithm, and the number is incorrect
The table appears under the heading "Shor's Algorithm in 50 Years: A Speculative Projection (2026 → 2076)", but the 2023 "Variational hybrid" entry is not an implementation or variant of Shor's algorithm.
The cited paper explicitly distinguishes its method from Shor's algorithm. The authors write:
They then describe other approaches separately:
And their own algorithm is explicitly described as being based on Schnorr's classical factoring algorithm:
Therefore, presenting this result as a milestone in a historical/prospective table about Shor's algorithm is misleading. It is a different hybrid classical-quantum factoring approach based on Schnorr's lattice algorithm and QAOA, not Shor's period-finding algorithm.
In fact, the paper itself explicitly compares the proposed algorithm against Shor's algorithm:
There is also a factual error in the number shown in the table. The paper reports:
So the reported integer is 261,980,999,226,229, not 261,980,999.
I suggest either removing this entry from a table specifically describing the progress of Shor's algorithm, or clearly separating non-Shor hybrid/variational factoring algorithms into a different category.
https://github.com/ruvnet/RuVector/blob/main/docs/research/quantum-crypto/shors-algorithm-50-year-projection.md