Unified framework for efficiently computable quantum circuits
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911883607408640 |
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| author | Ermakov, Igor Lychkovskiy, Oleg Byrnes, Tim |
| author_facet | Ermakov, Igor Lychkovskiy, Oleg Byrnes, Tim |
| contents | Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure that allows these circuits can be efficiently simulatable. The approach relies on analyzing the operator spread within a network of basis operators during the evolution of quantum circuit. Quantifying the complexity of a calculation by the number of operators with amplitude above a threshold value, we show that there is a generic form of the complexity curve involving an initial exponential growth, saturation, then exponential decay in the presence of decoherence. Our approach is naturally adaptable into a numerical procedure, where errors can be consistently controlled as a function of the complexity of the simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unified framework for efficiently computable quantum circuits Ermakov, Igor Lychkovskiy, Oleg Byrnes, Tim Quantum Physics Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure that allows these circuits can be efficiently simulatable. The approach relies on analyzing the operator spread within a network of basis operators during the evolution of quantum circuit. Quantifying the complexity of a calculation by the number of operators with amplitude above a threshold value, we show that there is a generic form of the complexity curve involving an initial exponential growth, saturation, then exponential decay in the presence of decoherence. Our approach is naturally adaptable into a numerical procedure, where errors can be consistently controlled as a function of the complexity of the simulation. |
| title | Unified framework for efficiently computable quantum circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.08187 |