Matchgate and space-bounded quantum computations are equivalent

Matchgate and space-bounded quantum computations are equivalent

Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional spin chains. We show that the computational power of circuits of matchgates is equivalent to that of space-bounded quantum computation with unita...

Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur, for example, in 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 probabil...

Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur, for example, in 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 probabil...

Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur, for example, in 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 probabil...

Unambiguous Logarithmic Space Bounded Computations