Exact and approximate synthesis of quantum circuits

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GPL-3 licensed by Neil J. Ross, Peter Selinger

A library of algorithms for exact and approximate synthesis of quantum circuits over the Clifford+T gate set. This includes, among other things:

  • Quantum.Synthesis.GridSynth: an efficient single-qubit approximate synthesis algorithm. From N. J. Ross and P. Selinger, "Optimal ancilla-free Clifford+T approximation of z-rotations",

  • Quantum.Synthesis.MultiQubitSynthesis: multi-qubit exact synthesis algorithms. From B. Giles and P. Selinger, "Exact synthesis of multiqubit Clifford+T circuits", Physical Review A 87, 032332, 2013,

  • Quantum.Synthesis.CliffordT: the computation of Matsumoto-Amano normal forms. From K. Matsumoto and K. Amano, "Representation of Quantum Circuits with Clifford and π/8 Gates",

  • Quantum.Synthesis.RotationDecomposition: an algorithm for decomposing multi-qubit unitary operators into one- and two-level unitaries. See e.g. Section 4.5.1 of M. A. Nielsen and I. L. Chuang, "Quantum Computation and Quantum Information", Cambridge University Press, 2002.

This package also provides an easy-to-use command line tool for single-qubit approximate synthesis.



v0.3.0.3 2016/07/27
(2016/07/27) PS1 - relaxed package dependencies to accommodate
older versions of ghc and base.

v0.3.0.2 2015/08/15
(2015/08/15) PS1 - relaxed dependencies.
(2015/08/15) PS1 - added IncoherentInstances to

v0.3.0.1 2015/05/15
(2015/05/15) PS1 - added a missing source file

v0.3 2015/05/15
(2015/05/15) NJR, PS1 - added a new --phase option for
approximation up to a phase.
(2015/05/15) NJR, PS1 - various bug fixes.

v0.2.0.1 2014/10/08
(2014/10/07) PS1 - added Applicative and Functor instances to
silence compiler warnings.
(2014/10/06) PS1 - updated dependencies for compatibility with
base 4.7 and random 1.1.
(2014/09/05) PS1 - fixed a bug where the actual T-count was output
instead of the lower bound.

v0.2 2014/03/12
(2014/03/12) NJR, PS1 - Added the new gridsynth algorithm from
N. J. Ross and P. Selinger, "Optimal ancilla-free Clifford+T
approximation of z-rotations", arXiv:1403.2975. Added a module
GridProblem for solving one- and two-dimensional grid equations,
and a module Diophantine for solving a Diophantine equation.
Removed the now obsolete Newsynth algorithm, and replaced it by a
backward compatibile interface to the new algorithm. New modules
GridSynth, QuadraticEquation, and StepComp. Additions and minor
improvements to EuclideanDomain, LaTeX, Matrix, and Ring. New
executable gridsynth.

v0.1.1.0 2014/02/05
(2014/02/04) PS1 - new functions euclid_divides and euclid_associates.
(2014/02/04) PS1 - changed 'lobit' and improved its asymptotic
(2014/02/04) PS1 - fixed a bug in the ShowLaTeX instance of Rational.
(2014/02/04) PS1 - added profiling options.
(2014/02/03) PS1 - eliminated common subexpressions in gridpoints.
(2014/02/03) PS1 - made fromDyadic an operation of the HalfRing
class, and improved its efficiency.

v0.1.0.0 2013/12/14
(2013/12/13) PS1 - added new rings DComplex and QComplex.
Improvements to the ring QOmega.
(2013/12/13) PS1 - more uniform naming of rings. Old names
DInteger, DReal, EReal, DComplex, EComplex have become ZRootTwo,
DRootTwo, QRootTwo, DRComplex, and QRComplex, respectively.
(2013/12/13) PS1 - adjusted output syntax to remove Unicode and
make output parseable.
(2013/12/13) PS1 - refactored as a Cabal package.
(2013/12/11) PS1 - removed erroneous Adjoint2 instances for Double
and Float.
(2013/12/11) PS1 - removed dependency on numbers package, removed
Random instance for FixedPrec (this is now in fixedprec package).
(2013/12/11) PS1 - added EmptyDataDecls pragma, to keep GHC happy.
(2013/12/10) PS1 - removed some unnecessary type class
(2013/09/25) PS1 - added "alternate" version of multi-qubit
synthesis algorithm, using only generators of determinant 1 if
(2013/09/25) PS1 - renamed some constructors and deconstructors
for matrices.

Release 2013/09/02
Released as part of Quipper 0.5.
(2013/07/08) PS1 - moved definitions of U2 and SO3 to Matrix.hs.
(2013/07/05) PS1 - added RotationDecomposition module.

Release 2013/06/19
Initial public release, as part of Quipper 0.4.
Used by 1 package:
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