Photon sieve lights a smooth path to entangled quantum weirdness

Adrian Cho

Entanglement, a seemingly impossible link between distant particles, is key to physicists' plans for revolutionary quantum computers and uncrackable quantum communications systems. Creating entangled pairs of light particles, or photons, is a delicate business. Now, physicists from Japan and the United Kingdom have found a way to do it by simply passing ordinary photons through a novel optical filter.

Luiz Carlos Ryff

Yoon‐Ho Kim

Jie Yang, Wenjia Zhang, Junjie Yu +2 more

Integer factorization, a cryptographic cornerstone, remains exponentially hard for classical computers, while quantum approaches, though theoretically polynomial-time, still face hardware limitations. We propose an Ising-accelerated lattice sieve method using a photonic Ising machine to solve the NP-hard closest vector problem efficiently. Our approach requires only sub-linear growth in spin number and stable dynamic range of the interaction matrix as integer bit-length increases, minimizing hardware demands. We construct a programmable spatial photonic Ising machine based on a Dammann grating. Through multi-path simulated annealing experiments on the constructed SPIM, we experimentally achieved the complete factorization of a 32-bit integer and demonstrated the identification of multiple distinct smooth relation pairs required for factorizing a 100-bit integer. To further validate the generality and scalability of the proposed method, we performed classical computer simulations of the multi-path annealing process, achieving factorization of integers up to 120 bits and establishing a benchmark for lattice sieve-based factorization.

Mark Buchanan

Michele Mosca, Joao Basso, Sebastian R. Verschoor

There have been several efforts to apply quantum SAT solving methods to factor large integers. While these methods may provide insight into quantum SAT solving, to date they have not led to a convincing path to integer factorization that is competitive with the best known classical method, the Number Field Sieve. Many of the techniques tried involved directly encoding multiplication to SAT or an equivalent NP-hard problem and looking for satisfying assignments of the variables representing the prime factors. The main challenge in these cases is that, to compete with the Number Field Sieve, the quantum SAT solver would need to be superpolynomially faster than classical SAT solvers. In this paper the use of SAT solvers is restricted to a smaller task related to factoring: finding smooth numbers, which is an essential step of the Number Field Sieve. We present a SAT circuit that can be given to quantum SAT solvers such as annealers in order to perform this step of factoring. If quantum SAT solvers achieve any asymptotic speedup over classical brute-force search for smooth numbers, then our factoring algorithm is faster than the classical NFS.