Connecting quantum circuit amplitudes and matrix permanents through polynomials
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916359863009280 |
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| author | Thomas, Hugo Emeriau, Pierre-Emmanuel Mezher, Rawad |
| author_facet | Thomas, Hugo Emeriau, Pierre-Emmanuel Mezher, Rawad |
| contents | In this paper, we strengthen the connection between qubit-based quantum circuits and photonic quantum computation. Within the framework of circuit-based quantum computation, the sum-over-paths interpretation of quantum probability amplitudes leads to the emergence of sums of exponentiated polynomials. In contrast, the matrix permanent is a combinatorial object that plays a crucial role in photonic by describing the probability amplitudes of linear optical computations. To connect the two, we introduce a general method to encode an $\mathbb F_2$-valued polynomial with complex coefficients into a graph, such that the permanent of the resulting graph's adjacency matrix corresponds directly to the amplitude associated the polynomial in the sum-over-path framework. This connection allows one to express quantum amplitudes arising from qubit-based circuits as permanents, which can naturally be estimated on a photonic quantum device. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connecting quantum circuit amplitudes and matrix permanents through polynomials Thomas, Hugo Emeriau, Pierre-Emmanuel Mezher, Rawad Quantum Physics In this paper, we strengthen the connection between qubit-based quantum circuits and photonic quantum computation. Within the framework of circuit-based quantum computation, the sum-over-paths interpretation of quantum probability amplitudes leads to the emergence of sums of exponentiated polynomials. In contrast, the matrix permanent is a combinatorial object that plays a crucial role in photonic by describing the probability amplitudes of linear optical computations. To connect the two, we introduce a general method to encode an $\mathbb F_2$-valued polynomial with complex coefficients into a graph, such that the permanent of the resulting graph's adjacency matrix corresponds directly to the amplitude associated the polynomial in the sum-over-path framework. This connection allows one to express quantum amplitudes arising from qubit-based circuits as permanents, which can naturally be estimated on a photonic quantum device. |
| title | Connecting quantum circuit amplitudes and matrix permanents through polynomials |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.08857 |