摘要: So far, we have discussed classical and particularly quantum algorithms for integer factoring, discrete logarithms elliptic curve logarithms. This does not mean can only be used to solve factorization problem, logarithm problem problem. In fact, computers in general other problems with either superpolynomially (exponentially) speedup or polynomially speedup. this last short chapter, shall discuss some various methods more number-theoretic problems. Unlike the previous chapters, will emphasize on introduction of details problems, rather concentrated new ideas developments
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sci-hub.st 参考文章(43)
Chris Lomont, THE HIDDEN SUBGROUP PROBLEM - REVIEW AND OPEN PROBLEMS arXiv: Quantum Physics. ,(2004)
Christoph Thiel, On the complexity of some problems in algorithmic algebraic number theory ,(1995)
Martin L. Brown, Heegner modules and elliptic curves ,(2004)
Hugh C. Williams, Michael J. Jr. Jacobson, Solving the Pell Equation ,(2008)
Jing-Run Chen, ON THE REPRESENTATION OF A LARGER EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES Scientia Sinica. ,vol. 16, pp. 157- 176 ,(1973) , 10.1360/YA1973-16-2-157
Henri Cohen, A Course in Computational Algebraic Number Theory ,(1993)
Gadiel Seroussi, Wim van Dam, Efficient Quantum Algorithms for Estimating Gauss Sums arXiv: Quantum Physics. ,(2002)
Paul Vitányi, The Quantum Computing Challenge Lecture Notes in Computer Science. ,vol. 2000, pp. 219- 233 ,(2001) , 10.1007/3-540-44577-3_15
Andris Ambainis, New developments in quantum algorithms mathematical foundations of computer science. ,vol. 6281, pp. 1- 11 ,(2010) , 10.1007/978-3-642-15155-2_1
Wim van Dam, Quantum Computing and Zeroes of Zeta Functions arXiv: Quantum Physics. ,(2004)