Geometries for universal quantum computation with matchgates

Abstract

Matchgates are a group of two-qubit gates associated with free fermions. They are classically simulatable if restricted to act between nearest neighbors on a one-dimensional chain, but become universal for quantum computation with longer-range interactions. We describe various alternative geometries with nearest-neighbor interactions that result in universal quantum computation with matchgates only, including subtle departures from the chain. Our results pave the way for new quantum computer architectures that rely solely on the simple interactions associated with matchgates.

6 pages, 4 figures. Updated version includes an appendix extending one of the results

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Cited by in corpus (11)

• Computational power of one- and two-dimensional dual-unitary quantum circuits
• Efficient classical simulation of matchgate circuits with generalized inputs and measurements
• Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states
• All pure fermionic non-Gaussian states are magic states for matchgate computations
• Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers
• Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking
• Computational power of matchgates with supplementary resources
• The computational power of matchgates and the XY interaction on arbitrary graphs
• Entanglement spectrum of matchgate circuits with universal and non-universal resources
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• The Computational Power of Non-interacting Particles