Editing Quantum information science (section)

==Related mathematical subjects==
[[Quantum algorithms]] and [[quantum complexity theory]] are two of the subjects in [[algorithm]]s and [[computational complexity theory]]. In 1994, mathematician [[Peter Shor]] introduced a quantum algorithm for [[prime factorization]] that, with a quantum computer containing 4,000 [[Physical and logical qubits|logical qubits]], could potentially break widely used ciphers like [[RSA (cryptosystem)|RSA]] and [[Elliptic-curve cryptography|ECC]], posing a major security threat. This led to increased investment in [[quantum computing]] research and the development of [[post-quantum cryptography]] to prepare for the fault-tolerant quantum computing (FTQC) era.<ref>{{Cite book |last1=Häner |first1=Thomas |last2=Jaques |first2=Samuel |last3=Naehrig |first3=Michael |last4=Roetteler |first4=Martin |last5=Soeken |first5=Mathias |date=2020 |editor-last=Ding |editor-first=Jintai |editor2-last=Tillich |editor2-first=Jean-Pierre |chapter=Improved Quantum Circuits for Elliptic Curve Discrete Logarithms |chapter-url=https://link.springer.com/chapter/10.1007/978-3-030-44223-1_23 |title=Post-Quantum Cryptography |series=Lecture Notes in Computer Science |language=en |location=Cham |publisher=Springer International Publishing |pages=425–444 |doi=10.1007/978-3-030-44223-1_23 |isbn=978-3-030-44223-1|arxiv=2001.09580 }}</ref>