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Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor's algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms.
Multiplication of many-digital numbers by automatic computers
Anatoly Karatsuba and Yuri Ofman · 1962
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Logical reversibility of computation
Charles H. Bennett · 1973
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Time/space trade-offs for reversible computation
Charles H. Bennett · 1989
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Algorithms for quantum computation: discrete logarithm and factoring
Peter W. Shor · 1994
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Fast parallel circuits for the quantum Fourier transform
Richard Cleve and John Watrous · 2000
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Reversible space equals deterministic space
Klaus-Jörn Lange, Pierre McKenzie, and Alain Tapp · 2000
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Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang · 2000
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A new quantum ripple-carry addition circuit
Steven A. Cuccaro, Thomas G. Draper, Samuel A. Kutin, and David Petrie Moulton · 2004
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Reversible Karatsuba’s algorithm
Luis Antonio Brasil Kowada, Renato Portugal, and Celina Miraglia Herrera de Figueiredo · 2006
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Quantum algorithms for hidden nonlinear structures
Andrew M. Childs, Leonard J. Schulman, and Umesh V. Vazirani · 2007
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Polynomial-time quantum algorithms for Pell’s equation and the principal ideal problem
Sean Hallgren · 2007
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Quantum algorithm for solving linear systems of equations
Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
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Constant-optimized quantum circuits for modular multiplication and exponentiation
Mehdi Saeedi and Igor L. Markov · 2012
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A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
Matt Amy, Dmitri Maslov, Michele Mosca, and Martin Roetteler · 2013
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Pebble games and complexity
Siu Man Chan · 2013
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Preconditioned quantum linear system algorithm
Brian D. Clader, Bryan C. Jacobs, and Chad R. Sprouse · 2013
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A quantum algorithm for computing the unit group of an arbitrary degree number field
Kirsten Eisenträger, Sean Hallgren, Alexei Y. Kitaev, and Fang Song · 2014
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Hamiltonian simulation with nearly optimal dependence on all parameters
Dominic W. Berry, Andrew M. Childs, and Robin Kothari · 2015
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Efficient synthesis of probabilistic quantum circuits with fallback
Alex Bocharov, Martin Roetteler, and Krysta M. Svore · 2015
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Efficient synthesis of universal Repeat-Until-Success circuits
Alex Bocharov, Martin Roetteler, and Krysta M. Svore · 2015
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Quantum circuits for GF 2 n {\rm GF}_{2^{n}} -multiplication with subquadratic gate count
Shane Kepley and Rainer Steinwandt · 2015
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Efficient Clifford + T +T approximation of single-qubit operators
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Asymptotically optimal approximation of single qubit unitaries by Clifford and T T circuits using a constant number of ancillary qubits
Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca · 2013
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Synthesis and optimization of reversible circuits - a survey
Mehdi Saeedi and Igor L. Markov · 2013
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Quantum circuits of T T -depth one
Peter Selinger · 2013
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Exponential improvement in precision for simulating sparse Hamiltonians
Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma · 2014
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An analysis of Bennett’s pebble game
Emanuel Knill
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Pebbling meets coloring: reversible pebble game on trees
Balagopal Komarath, Jayalal Sarma, and Saurabh Sawlani
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Peter Selinger · 2015
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Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields
Jean-François Biasse and Fang Song · 2016
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Hamiltonian simulation by qubitization, 2016
Guang Hao Low and Isaac L. Chuang · 2016
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Optimal ancilla-free Clifford + T +T approximation of z -rotations
Neil J. Ross and Peter Selinger · 2016
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