The principle of majorization: application to random quantum circuits
- URL: http://arxiv.org/abs/2102.09999v1
- Date: Fri, 19 Feb 2021 16:07:09 GMT
- Title: The principle of majorization: application to random quantum circuits
- Authors: Raul O. Vallejos, Fernando de Melo and Gabriel G. Carlo
- Abstract summary: Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable.
We verified that all the families of circuits satisfy on average the principle of majorization.
Clear differences appear in the fluctuations of the Lorenz curves associated to states.
- Score: 68.8204255655161
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We test the principle of majorization [J. I. Latorre and M. A.
Martin-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three
classes of circuits were considered: (i) universal, (ii) classically
simulatable, and (iii) neither universal nor classically simulatable. The
studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford),
matchgates, and IQP (instantaneous quantum polynomial-time). We verified that
all the families of circuits satisfy on average the principle of decreasing
majorization. In most cases the asymptotic state (number of gates going to
infinity) behaves like a random vector. However, clear differences appear in
the fluctuations of the Lorenz curves associated to asymptotic states. The
fluctuations of the Lorenz curves discriminate between universal and
non-universal classes of random quantum circuits, and they also detect the
complexity of some non-universal but not classically efficiently simulatable
quantum random circuits. We conclude that majorization can be used as a
indicator of complexity of quantum dynamics, as an alternative to, e.g.,
entanglement spectrum and out-of-time-order correlators (OTOCs).
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