| Autor: |
Chamon, Claudio, Mucciolo, Eduardo R., Ruckenstein, Andrei E., Yang, Zhi-Cheng |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
npj Quantum Information volume 10, Article number: 37 (2024) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1038/s41534-024-00831-y |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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