Addition on a Quantum Computer

By Thomas G. Draper. 2000

400 citations recorded by the source corpus.

A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also allows the addition of a classical number to a quantum superposition without encoding the classical number in the quantum register. This method also allows for massive parallelization in its execution.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9bf9c29d3d1bebf026d8d13f662af7820950299e

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Option Pricing using Quantum Computers (2019, methodology): “The addition of the values in two quantum registers |a, b〉 → |a, a+ b〉 may be calculated in quantum computers with adder circuits based on CNOT and Toffoli gates [38–40].”
A logarithmic-depth quantum carry-lookahead adder (2004, background): “Previous quantum addition circuits include the quantum ripple-carry adder of Vedral, Barenco, and Ekert [7], which has recently been improved [1], and the transform adder [2].”
ProjectQ: An Open Source Software Framework for Quantum Computing (2016, methodology): “Out of several implementations [11, 12, 13], we focus on Draper’s addition in Fourier space [13], due to the large potential for optimization when executing several additions in sequence, which happens when using the construction in [10] to achieve modular addition.”
A new quantum ripple-carry addition circuit (2004, background): “know whether we can add in linear depth with no ancillae and without this restriction on the output bit. It would be interesting to compare the ripple-carry adder of this paper to the transform adder [2]. Both circuits have linear depth. It is unclear which adder would be easier to 7 implement in pr”
Shor's discrete logarithm quantum algorithm for elliptic curves (2003, background): “. Unfortunately we haven’t found any way of doing this. A quantum solution to arithmetic in GF(p) With an (approximate) quantum Fourier transform of size p, addition modulo p in a way becomes simpler [24]. It would be nice to ﬁnd such a “quantum solution” to both, addition and multiplication. But to”
Circuit for Shor's algorithm using 2n+3 qubits (2002, methodology): “Figure 2: The quantum addition as described by Draper [ 6 ].”
Automated optimization of large quantum circuits with continuous parameters (2017, methodology): “It is well known that one can perform a highly accurate approximate QFT by omitting gates with very small rotation angles [7].”