143 research outputs found
Quantum matchgate computations and linear threshold gates
The theory of matchgates is of interest in various areas in physics and
computer science. Matchgates occur in e.g. the study of fermions and spin
chains, in the theory of holographic algorithms and in several recent works in
quantum computation. In this paper we completely characterize the class of
boolean functions computable by unitary two-qubit matchgate circuits with some
probability of success. We show that this class precisely coincides with that
of the linear threshold gates. The latter is a fundamental family which appears
in several fields, such as the study of neural networks. Using the above
characterization, we further show that the power of matchgate circuits is
surprisingly trivial in those cases where the computation is to succeed with
high probability. In particular, the only functions that are
matchgate-computable with success probability greater than 3/4 are functions
depending on only a single bit of the input
A Theory for Valiant's Matchcircuits (Extended Abstract)
The computational function of a matchgate is represented by its character
matrix. In this article, we show that all nonsingular character matrices are
closed under matrix inverse operation, so that for every , the nonsingular
character matrices of -bit matchgates form a group, extending the recent
work of Cai and Choudhary (2006) of the same result for the case of , and
that the single and the two-bit matchgates are universal for matchcircuits,
answering a question of Valiant (2002)
A Recursive Definition of the Holographic Standard Signature
We provide a recursive description of the signatures realizable on the
standard basis by a holographic algorithm. The description allows us to prove
tight bounds on the size of planar matchgates and efficiently test for standard
signatures. Over finite fields, it allows us to count the number of n-bit
standard signatures and calculate their expected sparsity.Comment: Fixed small typo in Section 3.
- …