Fast pseudorandom quantum state generators via inflationary quantum gates
Abstract 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 $$\log n$$ log n depth 2-qubit-gate-based generic random quantum circuits that are c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-04-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-024-00831-y |
| _version_ | 1797209241265635328 |
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| author | Claudio Chamon Eduardo R. Mucciolo Andrei E. Ruckenstein Zhi-Cheng Yang |
| author_facet | Claudio Chamon Eduardo R. Mucciolo Andrei E. Ruckenstein Zhi-Cheng Yang |
| author_sort | Claudio Chamon |
| collection | DOAJ |
| description | Abstract 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 $$\log n$$ 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 $$\log n$$ 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 ≥ 3 and d prime, or as special 3-qubit gates. |
| first_indexed | 2024-04-24T09:51:34Z |
| format | Article |
| id | doaj.art-e16d14d93cad4fa9b7b058914d5e5e71 |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-04-24T09:51:34Z |
| publishDate | 2024-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-e16d14d93cad4fa9b7b058914d5e5e712024-04-14T11:23:57ZengNature Portfolionpj Quantum Information2056-63872024-04-0110111110.1038/s41534-024-00831-yFast pseudorandom quantum state generators via inflationary quantum gatesClaudio Chamon0Eduardo R. Mucciolo1Andrei E. Ruckenstein2Zhi-Cheng Yang3Physics Department, Boston UniversityDepartment of Physics, University of Central FloridaPhysics Department, Boston UniversitySchool of Physics, Peking UniversityAbstract 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 $$\log n$$ 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 $$\log n$$ 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 ≥ 3 and d prime, or as special 3-qubit gates.https://doi.org/10.1038/s41534-024-00831-y |
| spellingShingle | Claudio Chamon Eduardo R. Mucciolo Andrei E. Ruckenstein Zhi-Cheng Yang Fast pseudorandom quantum state generators via inflationary quantum gates npj Quantum Information |
| title | Fast pseudorandom quantum state generators via inflationary quantum gates |
| title_full | Fast pseudorandom quantum state generators via inflationary quantum gates |
| title_fullStr | Fast pseudorandom quantum state generators via inflationary quantum gates |
| title_full_unstemmed | Fast pseudorandom quantum state generators via inflationary quantum gates |
| title_short | Fast pseudorandom quantum state generators via inflationary quantum gates |
| title_sort | fast pseudorandom quantum state generators via inflationary quantum gates |
| url | https://doi.org/10.1038/s41534-024-00831-y |
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