TY - JOUR

T1 - All Pure Fermionic Non-Gaussian States Are Magic States for Matchgate Computations

AU - Hebenstreit, M.

AU - Jozsa, R.

AU - Kraus, B.

AU - Strelchuk, S.

AU - Yoganathan, M.

N1 - Publisher Copyright:
© 2019 American Physical Society. © 2019 American Physical Society.

PY - 2019

Y1 - 2019

N2 - Magic states were introduced in the context of Clifford circuits as a resource that elevates classically simulatable computations to quantum universal capability, while maintaining the same gate set. Here we study magic states in the context of matchgate (MG) circuits, where the notion becomes more subtle, as MGs are subject to locality constraints. Nevertheless a similar picture of gate-gadget constructions applies, and we show that every pure fermionic state which is non-Gaussian, i.e., which cannot be generated by MGs from a computational basis state, is a magic state for MG computations. This result has significance for prospective quantum computing implementation in view of the fact that MG circuit evolutions coincide with the quantum physical evolution of noninteracting fermions.

AB - Magic states were introduced in the context of Clifford circuits as a resource that elevates classically simulatable computations to quantum universal capability, while maintaining the same gate set. Here we study magic states in the context of matchgate (MG) circuits, where the notion becomes more subtle, as MGs are subject to locality constraints. Nevertheless a similar picture of gate-gadget constructions applies, and we show that every pure fermionic state which is non-Gaussian, i.e., which cannot be generated by MGs from a computational basis state, is a magic state for MG computations. This result has significance for prospective quantum computing implementation in view of the fact that MG circuit evolutions coincide with the quantum physical evolution of noninteracting fermions.

UR - http://www.scopus.com/inward/record.url?scp=85071896610&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.123.080503

DO - 10.1103/PhysRevLett.123.080503

M3 - Article

C2 - 31491201

AN - SCOPUS:85071896610

SN - 0031-9007

VL - 123

JO - Physical Review Letters

JF - Physical Review Letters

IS - 8

M1 - 080503

ER -