Multivariate trace estimation in constant quantum depth
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866911751947157504 |
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| author | Quek, Yihui Kaur, Eneet Wilde, Mark M. |
| author_facet | Quek, Yihui Kaur, Eneet Wilde, Mark M. |
| contents | There is a folkloric belief that a depth-$Θ(m)$ quantum circuit is needed to estimate the trace of the product of $m$ density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum information science. We prove that this belief is overly conservative by constructing a constant quantum-depth circuit for the task, inspired by the method of Shor error correction. Furthermore, our circuit demands only local gates in a two dimensional circuit -- we show how to implement it in a highly parallelized way on an architecture similar to that of Google's Sycamore processor. With these features, our algorithm brings the central task of multivariate trace estimation closer to the capabilities of near-term quantum processors. We instantiate the latter application with a theorem on estimating nonlinear functions of quantum states with "well-behaved" polynomial approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_15405 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multivariate trace estimation in constant quantum depth Quek, Yihui Kaur, Eneet Wilde, Mark M. Quantum Physics Data Structures and Algorithms High Energy Physics - Theory There is a folkloric belief that a depth-$Θ(m)$ quantum circuit is needed to estimate the trace of the product of $m$ density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum information science. We prove that this belief is overly conservative by constructing a constant quantum-depth circuit for the task, inspired by the method of Shor error correction. Furthermore, our circuit demands only local gates in a two dimensional circuit -- we show how to implement it in a highly parallelized way on an architecture similar to that of Google's Sycamore processor. With these features, our algorithm brings the central task of multivariate trace estimation closer to the capabilities of near-term quantum processors. We instantiate the latter application with a theorem on estimating nonlinear functions of quantum states with "well-behaved" polynomial approximations. |
| title | Multivariate trace estimation in constant quantum depth |
| topic | Quantum Physics Data Structures and Algorithms High Energy Physics - Theory |
| url | https://arxiv.org/abs/2206.15405 |