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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
  • P. Shor
  • Computer Science, Mathematics
  • SIAM Rev.
  • 30 August 1995
Efficient randomized algorithms are given for factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Expand
Algorithms for quantum computation: discrete logarithms and factoring
  • P. Shor
  • Mathematics, Computer Science
  • Proceedings 35th Annual Symposium on Foundations…
  • 20 November 1994
Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given. Expand
Quantum Error Correction Via Codes Over GF(4)
In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Expand
Quantum error correction via codes over GF(4)
The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. ThisExpand
Fault-tolerant quantum computation
  • P. Shor
  • Computer Science, Physics
  • Proceedings of 37th Conference on Foundations of…
  • 13 May 1996
For any quantum computation with t gates, it is shown how to build a polynomial size quantum circuit that tolerates O(1/log/sup c/t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O( 1/t). Expand
Quantum Error Correction and Orthogonal Geometry
A quantum error-correcting code is a way of encoding quantum states into qubits (two-state quantum systems) so that error or decoherence in a small number of individual qubits has little or no effectExpand
Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem
In the classical analog of entanglement-assisted communication - communication over a discrete memoryless channel (DMC) between parties who share prior random information - one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMCs of equal capacity can simulate one another with unit asymptotic efficiency. Expand
The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information
An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both theExpand
Chip-firing Games on Graphs
The number of steps in a finite game is related to the least positive eigenvalue of the Laplace operator of the graph to show that the finiteness of the game and the terminating configuration are independent of the moves made. Expand
Geometric Applications of a Matrix Searching Algorithm
The Θ(m) bound on finding the maxima of wide totally monotone matrices is used to speed up several geometric algorithms by a factor of logn. Expand