Efficient verification of anticoncentrated quantum states
Abstract I present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = τ τ , using simple quantum circuits and on-the-fly classical calculation (or lookup) of...
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Nature Portfolio
2021
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oai:doaj.org-article:767e2f03f98244aba338e0817676b0d42021-12-02T15:08:38ZEfficient verification of anticoncentrated quantum states10.1038/s41534-021-00455-62056-6387https://doaj.org/article/767e2f03f98244aba338e0817676b0d42021-08-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00455-6https://doaj.org/toc/2056-6387Abstract I present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = τ τ , using simple quantum circuits and on-the-fly classical calculation (or lookup) of selected amplitudes of $$\left|\tau \right\rangle$$ τ . The method is sample efficient for anticoncentrated states (including many states that are hard to simulate classically), with approximate cost 4ϵ −2(1 − F)d p coll where ϵ is the desired precision of the estimate, d is the dimension of the Hilbert space, and p coll is the collision probability of the target distribution. This scaling is exponentially better than that of any method based on classical sampling. I also present a more sophisticated version of the method that uses any efficiently preparable and well-characterized quantum state as an importance sampler to further reduce the number of copies of μ needed. Though some challenges remain, this work takes a significant step toward scalable verification of complex states produced by quantum processors.Ryan S. BenninkNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-10 (2021) |
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Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 |
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Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Ryan S. Bennink Efficient verification of anticoncentrated quantum states |
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Abstract I present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = τ τ , using simple quantum circuits and on-the-fly classical calculation (or lookup) of selected amplitudes of $$\left|\tau \right\rangle$$ τ . The method is sample efficient for anticoncentrated states (including many states that are hard to simulate classically), with approximate cost 4ϵ −2(1 − F)d p coll where ϵ is the desired precision of the estimate, d is the dimension of the Hilbert space, and p coll is the collision probability of the target distribution. This scaling is exponentially better than that of any method based on classical sampling. I also present a more sophisticated version of the method that uses any efficiently preparable and well-characterized quantum state as an importance sampler to further reduce the number of copies of μ needed. Though some challenges remain, this work takes a significant step toward scalable verification of complex states produced by quantum processors. |
| format |
article |
| author |
Ryan S. Bennink |
| author_facet |
Ryan S. Bennink |
| author_sort |
Ryan S. Bennink |
| title |
Efficient verification of anticoncentrated quantum states |
| title_short |
Efficient verification of anticoncentrated quantum states |
| title_full |
Efficient verification of anticoncentrated quantum states |
| title_fullStr |
Efficient verification of anticoncentrated quantum states |
| title_full_unstemmed |
Efficient verification of anticoncentrated quantum states |
| title_sort |
efficient verification of anticoncentrated quantum states |
| publisher |
Nature Portfolio |
| publishDate |
2021 |
| url |
https://doaj.org/article/767e2f03f98244aba338e0817676b0d4 |
| work_keys_str_mv |
AT ryansbennink efficientverificationofanticoncentratedquantumstates |
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