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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
|
Vol.13 No.1&2 January 2013 |
Quantum binary field inversion: improved circuit depth via choice of
basis representation
(pp0116-0134)
Brittanney
Amento, Martin Rotteler, and Rainer Steinwandt
doi:
https://doi.org/10.26421/QIC13.1-2-7
Abstracts:
Finite fields of the form F2m play an important role in coding theory
and cryptography. We show that the choice of how to represent the
elements of these fields can have a significant impact on the resource
requirements for quantum arithmetic. In particular, we show how the use
of Gaussian normal basis representations and of ghost-bit basis
representations can be used to implement inverters with a quantum
circuit of depth O(m log(m)). To the best of our knowledge, this is the
first construction with subquadratic depth reported in the literature.
Our quantum circuit for the computation of multiplicative inverses is
based on the Itoh-Tsujii algorithm which exploits that in normal basis
representation squaring corresponds to a permutation of the
coefficients. We give resource estimates for the resulting quantum
circuit for inversion over binary fields F2m based on an elementary gate
set that is useful for fault-tolerant implementation.
Key words:
quantum circuit; finite field; normal basis |
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