Quantum matchgate computations and linear threshold gates

Abstract

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.

References in corpus (3)

• Instantaneous non-local computation of low T-depth quantum circuits
• Matchgates and classical simulation of quantum circuits
• Matchgate and space-bounded quantum computations are equivalent

Cited by in corpus (7)

• Efficient classical simulation of matchgate circuits with generalized inputs and measurements
• Extending matchgates into universal quantum computation
• Solving search problems by strongly simulating quantum circuits
• Geometries for universal quantum computation with matchgates
• Dequantizing read-once quantum formulas
• Classical simulation of dissipative fermionic linear optics
• Clifford Gates in the Holant Framework