Extending Matchgate Simulation Methods to Universal Quantum Circuits

2023/02/06 by Mocherla, Avinash, Lao, Lingling, Browne, Dan E. · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2302.02654

Abstract

Matchgates are a family of parity-preserving two-qubit gates, nearest-neighbour circuits of which are known to be classically simulable in polynomial time. In this work, we present a simulation method to classically simulate an \boldsymboln-qubit circuit containing \boldsymbolN gates, \boldsymbolm of which are universality-enabling gates and \boldsymbolN-m of which are matchgates, in the setting of single-qubit Pauli measurements and product state inputs. The universality-enabling gates we consider include the SWAP, CZ, and CPhase gates. For fixed \boldsymbolm as \boldsymboln → \boldsymbol∞, the resource cost, \boldsymbolT, scales as \boldsymbolO(((en)/(m+1))^2m+2). For \boldsymbolm scaling as a linear function of \boldsymboln, however, \boldsymbolT scale as \boldsymbolO(2^{2nH((m+1)/(n))}), where \boldsymbolH(λ) is the binary entropy function.

Cited by

• ExtraFerm: An Extended Matchgate Simulator
• Emergence of Generic Entanglement Structure in Doped Matchgate Circuits

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