Fast pseudorandom quantum state generators via inflationary quantum gates

• URL: http://arxiv.org/abs/2304.09885v3
• Date: Sun, 21 Apr 2024 16:53:16 GMT
• Title: Fast pseudorandom quantum state generators via inflationary quantum gates
• Authors: Claudio Chamon, Eduardo R. Mucciolo, Andrei E. Ruckenstein, Zhi-Cheng Yang,
• Abstract summary: We propose a mechanism for reaching pseudorandom quantum states, computationally indistinguishable from Haar random, with shallow log-n depth quantum circuits. 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 $U(d2)$ with $dge 3$ and $d$ prime, or as special 3-qubit gates.
• Score: 3.5072186061740904
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\log n$ 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.

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