Factoring with n+2 clean qubits and n-1 dirty qubits

Elementary gates for quantum computation

Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter · 1995

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Efficient networks for quantum factoring

David Beckman, Amalavoyal N. Chari, Srikrishna Devabhaktuni, and John Preskill · 1996

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Quantum Networks for Elementary Arithmetic Operations

Vlatko Vedral, Adriano Barenco, and Artur Ekert · 1996

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Fast versions of Shor’s quantum factoring algorithm , 1998

Christof Zalka · 1998

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The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer

Michele Mosca and Artur Ekert · 1999

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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Peter W. Shor · 1999

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Addition on a Quantum Computer , 2000

Thomas G. Draper · 2000

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Efficient Factorization with a Single Pure Qubit and log N Mixed Qubits

S. Parker and M. B. Plenio · 2000

Cited alongside, same era.

Circuit for Shor’s algorithm using 2n+3 qubits

Stephane Beauregard · 2003

Cited alongside, same era.

Optimal Design of A Reversible Full Adder

Yvan Van Rentergem and Alexis De Vos · 2004

Cited alongside, same era.

A linear-size quantum circuit for addition with no ancillary qubits

Yasuhiro Takahashi and Noboru Kunihiro · 2005

Cited alongside, same era.

A quantum circuit for Shor’s factoring algorithm using 2n+2 qubits

Yasuhiro Takahashi and Noboru Kunihiro · 2006

Cited alongside, same era.

Shor’s algorithm with fewer (pure) qubits, 2006

Christof Zalka · 2006

Cited alongside, same era.

Faster integer multiplication

Martin Fürer · 2007

Later among the works it cites.

ISO/IEC 9899:2011 (C11 Standard) , §3.4.3 undefined behavior

International Organization for Standardization · 2011

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Media for thinking the unthinkable

Brett Victor · 2013

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Quirk: A drag-and-drop quantum circuit simulator for exploring small quantum circuits

Craig Gidney · 2016

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Factoring using 2n+2 qubits with Toffoli based modular multiplication , 2016

Original

Thomas Häner, Martin Roetteler, and Krysta M. Svore · 2016

Later among the works it cites.

ProjectQ: An Open Source Software Framework for Quantum Computing , 2016

Original