Oversimplifying quantum factoring

Shor’s quantum factoring algorithm exponentially outperforms known classical methods. Previous experimental implementations have used simplifications dependent on knowing the factors in advance. However, as we show here, all composite numbers admit simplification of the algorithm to a circuit equivalent to flipping coins. The difficulty of a particular experiment therefore depends on the level of simplification chosen, not the size of the number factored. Valid implementations should not make use of the answer sought.

[1]  Thomas L. Heath,et al.  Thirteen Books of Euclid's Elements , 1911, The Mathematical Gazette.

[2]  W. Zurek.  Pointer Basis of Quantum Apparatus: Into What Mixture Does the Wave Packet Collapse? , 1981 .

[3]  Lam Lay Yong,et al.  Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China , 1992 .

[4]  Lam Lay Yong,et al.  10. Translation of Sun Zi Suanjing (The Mathematical Classic of Sun Zi) , 1992 .

[5]  Griffiths,et al.  Semiclassical Fourier transform for quantum computation. , 1995, Physical review letters.

[6]  Michele Mosca,et al.  The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer , 1998, QCQC.

[7]  Colin P. Williams.  Quantum Computing and Quantum Communications , 1999, Lecture Notes in Computer Science.

[8]  M B Plenio,et al.  Efficient factorization with a single pure qubit and logN mixed qubits. , 2000, Physical review letters.

[9]  I. Chuang,et al.  Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance , 2001, Nature.

[10]  Christof Zalka.  Shor's algorithm with fewer (pure) qubits , 2006, quant-ph/0601097.

[11]  B. Lanyon,et al.  Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement. , 2007, Physical review letters.

[12]  Jian-Wei Pan,et al.  Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits. , 2007, Physical review letters.

[13]  John Preskill,et al.  Accuracy threshold for postselected quantum computation , 2007, Quantum Inf. Comput..

[14]  A. Politi,et al.  Shor’s Quantum Factoring Algorithm on a Photonic Chip , 2009, Science.

[15]  E. Lucero,et al.  Computing prime factors with a Josephson phase qubit quantum processor , 2012, Nature Physics.

[16]  Michael R. Geller,et al.  Factoring 51 and 85 with 8 qubits , 2013, Scientific Reports.

[17]  X-Q Zhou,et al.  Experimental realization of Shor's quantum factoring algorithm using qubit recycling , 2011, Nature Photonics.