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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.23719 |
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| _version_ | 1866911307737858048 |
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| author | Heinrich, Markus Haferkamp, Jonas Roth, Ingo Helsen, Jonas |
| author_facet | Heinrich, Markus Haferkamp, Jonas Roth, Ingo Helsen, Jonas |
| contents | Until very recently, it was generally believed that the (approximate) 2-design property is strictly stronger than anti-concentration of random quantum circuits, mainly because it was shown that the latter anti-concentrate in logarithmic depth, while the former generally need linear depth circuits. This belief was disproven by recent results which show that so-called relative-error approximate unitary designs can in fact be generated in logarithmic depth, implying anti-concentration. Their result does however not apply to ordinary local random circuits, a gap which we close in this paper, at least for 2-designs. More precisely, we show that anti-concentration of local random quantum circuits already implies that they form relative-error approximate state 2-designs, making them equivalent properties for these ensembles. Our result holds more generally for any random circuit which is invariant under local (single-qubit) unitaries, independent of the architecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23719 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anti-concentration is (almost) all you need Heinrich, Markus Haferkamp, Jonas Roth, Ingo Helsen, Jonas Quantum Physics Until very recently, it was generally believed that the (approximate) 2-design property is strictly stronger than anti-concentration of random quantum circuits, mainly because it was shown that the latter anti-concentrate in logarithmic depth, while the former generally need linear depth circuits. This belief was disproven by recent results which show that so-called relative-error approximate unitary designs can in fact be generated in logarithmic depth, implying anti-concentration. Their result does however not apply to ordinary local random circuits, a gap which we close in this paper, at least for 2-designs. More precisely, we show that anti-concentration of local random quantum circuits already implies that they form relative-error approximate state 2-designs, making them equivalent properties for these ensembles. Our result holds more generally for any random circuit which is invariant under local (single-qubit) unitaries, independent of the architecture. |
| title | Anti-concentration is (almost) all you need |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.23719 |