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Good Quantum Error-Correcting Codes Exist
A. R. Calderbank, Peter W. Shor
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that…
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
Peter W. Shor
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in c…
Elementary gates for quantum computation
A. Barenco, C. H. Bennett, R. Cleve +6
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values to ) is universal…
Quantum Computers, Factoring, and Decoherence
I. Chuang, Raymond Laflamme, P. Shor +1
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can drama…