Extending Matchgate Simulation Methods to Universal Quantum Circuits
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917695550652416 |
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| author | Mocherla, Avinash Lao, Lingling Browne, Dan E. |
| author_facet | Mocherla, Avinash Lao, Lingling Browne, Dan E. |
| contents | 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 $\boldsymbol{H}(λ)$ is the binary entropy function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_02654 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extending Matchgate Simulation Methods to Universal Quantum Circuits Mocherla, Avinash Lao, Lingling Browne, Dan E. Quantum Physics 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 $\boldsymbol{H}(λ)$ is the binary entropy function. |
| title | Extending Matchgate Simulation Methods to Universal Quantum Circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2302.02654 |