Learning properties of quantum states without the IID assumption
Abstract We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm designed for i.i.d. input states can be adapted to...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-024-53765-6 |
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| _version_ | 1850196545198096384 |
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| author | Omar Fawzi Richard Kueng Damian Markham Aadil Oufkir |
| author_facet | Omar Fawzi Richard Kueng Damian Markham Aadil Oufkir |
| author_sort | Omar Fawzi |
| collection | DOAJ |
| description | Abstract We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm designed for i.i.d. input states can be adapted to handle input states of any nature, albeit at the expense of a polynomial increase in training data size (aka sample complexity). Importantly, this polynomial increase in sample complexity can be substantially improved to polylogarithmic if the learning algorithm in question only requires non-adaptive, single-copy measurements. Among other applications, this allows us to generalize the classical shadow framework to the non-i.i.d. setting while only incurring a comparatively small loss in sample efficiency. We leverage permutation invariance and randomized single-copy measurements to derive a new quantum de Finetti theorem that mainly addresses measurement outcome statistics and, in turn, scales much more favorably in Hilbert space dimension. |
| format | Article |
| id | doaj-art-abcba239ae264c81898611291f3ac5e3 |
| institution | OA Journals |
| issn | 2041-1723 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-abcba239ae264c81898611291f3ac5e32025-08-20T02:13:26ZengNature PortfolioNature Communications2041-17232024-11-0115111910.1038/s41467-024-53765-6Learning properties of quantum states without the IID assumptionOmar Fawzi0Richard Kueng1Damian Markham2Aadil Oufkir3Inria, ENS Lyon, UCBL, LIPDepartment of Quantum Information and Computation at Kepler (QUICK), Johannes Kepler University LinzSorbonne Université, CNRSInria, ENS Lyon, UCBL, LIPAbstract We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm designed for i.i.d. input states can be adapted to handle input states of any nature, albeit at the expense of a polynomial increase in training data size (aka sample complexity). Importantly, this polynomial increase in sample complexity can be substantially improved to polylogarithmic if the learning algorithm in question only requires non-adaptive, single-copy measurements. Among other applications, this allows us to generalize the classical shadow framework to the non-i.i.d. setting while only incurring a comparatively small loss in sample efficiency. We leverage permutation invariance and randomized single-copy measurements to derive a new quantum de Finetti theorem that mainly addresses measurement outcome statistics and, in turn, scales much more favorably in Hilbert space dimension.https://doi.org/10.1038/s41467-024-53765-6 |
| spellingShingle | Omar Fawzi Richard Kueng Damian Markham Aadil Oufkir Learning properties of quantum states without the IID assumption Nature Communications |
| title | Learning properties of quantum states without the IID assumption |
| title_full | Learning properties of quantum states without the IID assumption |
| title_fullStr | Learning properties of quantum states without the IID assumption |
| title_full_unstemmed | Learning properties of quantum states without the IID assumption |
| title_short | Learning properties of quantum states without the IID assumption |
| title_sort | learning properties of quantum states without the iid assumption |
| url | https://doi.org/10.1038/s41467-024-53765-6 |
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