Fast pseudorandom quantum state generators via inflationary quantum gates
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910416079159296 |
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| author | Chamon, Claudio Mucciolo, Eduardo R. Ruckenstein, Andrei E. Yang, Zhi-Cheng |
| author_facet | Chamon, Claudio Mucciolo, Eduardo R. Ruckenstein, Andrei E. Yang, Zhi-Cheng |
| contents | We propose a mechanism for reaching pseudorandom quantum states, computationally indistinguishable from Haar random, with shallow log-n depth quantum circuits, where n is the number of qudits. We argue that $\log n$ depth 2-qubit-gate-based generic random quantum circuits that are claimed to provide a lower bound on the speed of information scrambling, cannot produce computationally pseudorandom quantum states. This conclusion is connected with the presence of polynomial (in $n$) tails in the stay probability of short Pauli strings that survive evolution through such shallow circuits. We show, however, that stay-probability-tails can be eliminated and pseudorandom quantum states can be accomplished with shallow $\log n$ depth circuits built from a special universal family of `inflationary' quantum (IQ) gates. We prove that IQ-gates cannot be implemented with 2-qubit gates, but can be realized either as a subset of 2-qudit-gates in $U(d^2)$ with $d\ge 3$ and $d$ prime, or as special 3-qubit gates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09885 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast pseudorandom quantum state generators via inflationary quantum gates Chamon, Claudio Mucciolo, Eduardo R. Ruckenstein, Andrei E. Yang, Zhi-Cheng Quantum Physics Statistical Mechanics High Energy Physics - Theory We propose a mechanism for reaching pseudorandom quantum states, computationally indistinguishable from Haar random, with shallow log-n depth quantum circuits, where n is the number of qudits. We argue that $\log n$ depth 2-qubit-gate-based generic random quantum circuits that are claimed to provide a lower bound on the speed of information scrambling, cannot produce computationally pseudorandom quantum states. This conclusion is connected with the presence of polynomial (in $n$) tails in the stay probability of short Pauli strings that survive evolution through such shallow circuits. We show, however, that stay-probability-tails can be eliminated and pseudorandom quantum states can be accomplished with shallow $\log n$ depth circuits built from a special universal family of `inflationary' quantum (IQ) gates. We prove that IQ-gates cannot be implemented with 2-qubit gates, but can be realized either as a subset of 2-qudit-gates in $U(d^2)$ with $d\ge 3$ and $d$ prime, or as special 3-qubit gates. |
| title | Fast pseudorandom quantum state generators via inflationary quantum gates |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2304.09885 |