Extending Matchgate Simulation Methods to Universal Quantum Circuits

• URL: http://arxiv.org/abs/2302.02654v2
• Date: Sun, 16 Jun 2024 23:35:00 GMT
• Title: Extending Matchgate Simulation Methods to Universal Quantum Circuits
• Authors: Avinash Mocherla, Lingling Lao, Dan E. Browne,
• Abstract summary: Matchgates are a family of parity-preserving two-qubit gates, nearest-neighbour circuits of which are known to be classically simulable in time. We present a simulation method to simulate an $boldsymboln$-qubit circuit containing $boldsymbolN$ gates and $boldsymbolN-m$ of which are matchgates.
• Score: 4.342241136871849
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\boldsymbol{n}$-qubit circuit containing $\boldsymbol{N}$ gates, $\boldsymbol{m}$ of which are universality-enabling gates and $\boldsymbol{N-m}$ 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 $\boldsymbol{m}$ as $\boldsymbol{n} \rightarrow \boldsymbol{\infty}$, the resource cost, $\boldsymbol{T}$, scales as $\boldsymbol{\mathcal{O}\left(\left(\frac{en}{m+1}\right)^{2m+2}\right)}$. For $\boldsymbol{m}$ scaling as a linear function of $\boldsymbol{n}$, however, $\boldsymbol{T}$ scale as $\boldsymbol{\mathcal{O}\left(2^{2nH\left(\frac{m+1}{n}\right)}\right)}$, where $\boldsymbol{H}(\lambda)$ is the binary entropy function.

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