Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Interpolation Methods for Binary and Multivalued Logical Quantum Gate Synthesis

Abstract : A method for synthetizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a family of logical operators corresponding to the one-argument logical connectives. Scaling-up to n-arity gates is obtained by using the Kronecker product and unitary transformations. The quantum version of the Fourier transform of Boolean function is presented and a method for Reed-Muller decomposition is derived. The common control gates can be easily obtained by considering the logical correspondence between the control logic operator and the binary logic operator. A new polynomial and exponential formulation of the Toffoli gate is presented. The method has parallels to quantum gate T optimization methods using powers of multilinear operator polynomials. The method is then applied naturally to alphabets greater than two for multi-valued logical gates used for quantum Fourier transform, min-max decision circuits and multivalued adders.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas
Contributor : Zeno Toffano <>
Submitted on : Monday, March 20, 2017 - 5:40:32 PM
Last modification on : Tuesday, June 30, 2020 - 2:38:03 PM
Document(s) archivé(s) le : Wednesday, June 21, 2017 - 12:17:26 PM


Files produced by the author(s)


  • HAL Id : hal-01490947, version 1


Zeno Toffano, François Dubois. Interpolation Methods for Binary and Multivalued Logical Quantum Gate Synthesis. 2017. ⟨hal-01490947v1⟩



Record views


Files downloads